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2026 May 11

- How Unknowable Math Can Help Hide Secrets

CRYPTOGRAPHY | VIEW ON WEBSITE

How Unknowable Math Can Help Hide Secrets

By Ben Brubaker

May 11, 2026

A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography.

Kristina Armitage/Quanta Magazine

Introduction

Mathematicians spend most of their time thinking about what’s knowable. But the unknowable can be just as compelling.

Perhaps the most famous example comes from a theorem by the logician Kurt Gödel. Gödel’s celebrated result — one of two “incompleteness theorems” he published in 1931 — established that for any reasonable set of basic mathematical assumptions, called axioms, it’s impossible to prove that the axioms won’t eventually lead to contradictions. Though mathematicians continued their research much as they had before, they would never again be certain that their rules were self-consistent.

More than 50 years after Gödel’s theorem, cryptographers devised a radical new proof method in which unknowability played a very different role. Proofs based on this technique, called zero-knowledge proofs, can convince even the most skeptical audience that a statement is true without revealing why it’s true.

These two flavors of unknowability, which originated decades apart and in different fields, were long considered completely unrelated. Now the computer scientist Rahul Ilango has established a striking connection between them. While still a graduate student, he devised a new type of zero-knowledge proof in which secrecy stems from the fundamental limits of math. Ilango’s approach gets around limitations of zero-knowledge proofs that researchers have long thought insurmountable, pushing the boundaries of what such a proof can be. The work has also spurred researchers to explore other intriguing links between mathematical logic and cryptography.

“When I first saw Rahul’s paper, I was like, ‘No, there’s no way,’” said Amit Sahai, a cryptographer at the University of California, Los Angeles. “This is just an incredibly cool new direction.”

Color Blindness

Zero-knowledge proofs have their roots in computational complexity theory, the subfield of computer science that studies the difficulty of mathematical problems. In one classic problem, you’re given three colored pencils and a blank map divided into many regions. Can you color in the map without assigning the same color to two neighboring regions?

This problem can be fiendishly hard. But if someone shows you a colored map, you can glance at each border to check whether it’s a valid solution. Problems like this, whose solutions may be hard to find but are always easy to verify, are called NP problems. They’re useful in cryptography because those hard-to-find, easy-to-check solutions can serve as secret passwords. Anyone who actually knows the solution can easily prove it.

But this simple password system only works if the person who knows the solution is willing to reveal it. Zero-knowledge proofs, invented in 1985 by the cryptographers Shafi Goldwasser, Silvio Micali, and Charles Rackoff, don’t have this drawback. Using a zero-knowledge proof, anyone who knows a solution to an NP problem can prove it without revealing the solution — indeed, without revealing any other information whatsoever.

Shafi Goldwasser (left), Silvio Micali (right), and Charles Rackoff devised a way to prove that a statement is true without revealing anything about why.

©ACM, 2013

“It’s a very counterintuitive notion,” said Tom Gur, a computer scientist at the University of Cambridge. “Until you see an example, it sounds like something which is impossible.”

Goldwasser and her colleagues achieved this striking property by reimagining mathematical proof as an interaction between two parties. In a zero-knowledge proof for the three-coloring problem, for instance, there’s a “prover,” who wants to show that they know a solution. They secretly color the map, then cover each region so that only the borders are visible. The other party, the “verifier,” chooses a border. The prover then uncovers the regions on either side.

The two players repeat this process many times. Before each round, the prover secretly changes the color scheme, to prevent the verifier from piecing together bits of information from different rounds. If the prover reveals two different colors in response to every challenge, the verifier will eventually be convinced that the prover knows a valid coloring. If the prover is bluffing, the verifier will almost certainly find a flaw in the coloring after enough guesses.

Mark Belan/Quanta Magazine

The interactive character of zero-knowledge proofs makes them strikingly different from ordinary mathematical proofs, which can be written down in a textbook without any input from a verifier. Intuitively, interactivity seems like an essential element of a zero-knowledge proof. A prover who simply hands over a written document can’t stop the verifier from examining the whole thing and learning everything the prover knows. The prover could encrypt that document to prevent the verifier from learning too much, but in that case the verifier won’t be able to confirm that the proof is valid, since they can’t interrogate the prover.

In 1994, the cryptographers Oded Goldreich and Yair Oren proved a theorem that confirmed this intuition. Their result established that it’s impossible to construct a completely noninteractive proof that meets Goldwasser, Micali, and Rackoff’s definition of zero knowledge. It was bad news for cryptographers who’d held out hope for zero-knowledge proofs that were otherwise identical to ordinary ones.

“People just said, ‘Forget it, it’s not going to happen,’” said Abhishek Jain, a cryptographer at Johns Hopkins University and NTT Research. “How can you overcome an impossibility?”

Ilango’s new result shows how — by harnessing a different kind of impossibility.

Mission Impossible

In the summer of 2023, at the end of his third year of graduate school at the Massachusetts Institute of Technology, Ilango was growing increasingly interested in an arcane subfield of complexity theory called proof complexity. Most complexity theorists study how hard problems like three-coloring are (in this case, how many steps are needed to find a valid coloring). In proof complexity, by contrast, researchers analyze the difficulty of proving statements about these problems — statements like “There’s no way to properly color this specific map.” They gauge this difficulty by measuring the length of the simplest possible proof of a given statement.

In math, some statements cannot be proved either true or false. (This is Gödel’s other incompleteness theorem.) Other statements, however, might be provable in principle, but only with proofs that are too long to ever write down. For all practical purposes, these intrinsically hard-to-prove statements are just as unknowable as the unprovable statements that Gödel identified.

Kurt Gödel showed that certain mathematical statements are true but unprovable.

Alfred Eisenstaedt/Public Domain

Researchers usually study such hard-to-prove statements for their own sake, to better understand the limits of mathematical proof. But Ilango suspected that these statements might also have applications in cryptography. Nearly all techniques in modern cryptography are based on the difficulty of solving specific problems, like ones about coloring maps. What if, Ilango wondered, he could exploit the difficulty of proving specific statements instead? Doing so might allow him to concoct new cryptographic techniques.

“We find ourselves constantly slamming into these walls of ‘Why can’t we prove this? Why can’t we prove that?’” said Marco Carmosino, a complexity theorist at IBM. “Can we benefit from that kind of hardness?”

In 2024, after a few false starts, Ilango identified a specific task in cryptography that could serve as a test bed for his approach. He wanted to build zero-knowledge proofs that weren’t interactive. Thirty years earlier, Goldreich and Oren had established that such proofs are impossible. But Ilango realized that there might be more than one way to define “zero knowledge” — and that the impossibility result only applied to the original definition.

It is pretty mind-bending. The first time you see it, you’re like, ‘Wait, what?’

Amit Sahai, University of California, Los Angeles

To understand that definition, put yourself in the position of the verifier in the map-coloring example. Even before you interact with the prover, you can predict, or simulate, exactly what a valid proof will look like: Each round, the prover will always reveal two differently colored regions, no matter which border you choose. In cryptographers’ lingo, this proof has a “simulator,” and that’s what it means for the proof to be zero knowledge.

“If you and I were going to have a conversation, but I could predict in advance everything that you were going to say, then you’d probably agree that I’m not going to learn anything by talking to you,” Ilango said.

What Goldreich and Oren’s impossibility result actually said was that noninteractive proofs can’t have simulators, and therefore, by definition, they can’t be zero knowledge. Ilango hoped to use proof complexity to define a new notion of zero knowledge — what he called “effective” zero knowledge — that would not be subject to the old impossibility result but would still be just as useful as ordinary zero knowledge.

At the heart of his new definition was a simple insight: It’s OK if a proof doesn’t have a simulator, as long as nobody can tell.

Burden of Proof

Imagine you’re about to buy a lock that’s famously unbreakable. You read the fine print on the package, expecting to find a guarantee that the lock is secure. Instead you find a frank admission that the lock is not secure, followed by a promise: Even though it’s not secure, no one can prove that it’s not secure.

At first, this may sound like a willfully perverse way to market a useless product. But if the lock lives up to that unusual promise, it’s actually exactly as safe as one that’s provably unbreakable. To see why, imagine that you found a way to break the lock. Then the broken lock itself would count as a proof that it wasn’t secure — but if the promise on the packaging is correct, such a proof is impossible. In other words, if a vulnerability exists, but it’s impossible to prove that it exists, then there’s no way to take advantage of it.

As a graduate student, Rahul Ilango invented a new type of zero-knowledge proof by exploiting the limits of mathematics.

Jennifer Krupa

This is the basic idea behind Ilango’s new result. Traditionally, to demonstrate that a proof is zero knowledge, you would want to show that it has a simulator. (In our metaphor, this would be equivalent to proving that the lock is unbreakable.) But that would also mean that the proof has to be interactive. To get effective zero knowledge, Ilango instead wanted to show that it’s extremely difficult to guarantee that his proof doesn’t have a simulator. (That is, there’s no way to prove that the lock is breakable.)

If he could show this, he would get all the benefits of zero knowledge while cleverly getting around the requirement of interactivity. “It is actually really hard to think of any real-life situation where this effective zero knowledge wouldn’t be good enough,” Sahai said.

To understand how Ilango pulled this off, let’s return to the three-coloring example. If you know how to color the map, you can write down a noninteractive proof of the statement “This map can be three-colored.” But because of the 1994 impossibility result, that proof can’t have a simulator, and so it can’t be zero knowledge.

Using Ilango’s new approach, you’d instead start by rewriting the statement you want to prove, now adding an extra assumption: “This map can be three-colored — assuming that there’s no efficient way to find a contradiction in the standard axioms of mathematics.” This additional assumption is usually taken for granted. If it’s false, then math is rife with contradictions, and no proof is trustworthy. If it’s true, as researchers universally believe, then Ilango’s new statement is essentially equivalent to the original one.

But the assumption is also thought to be effectively impossible to prove: It’s likely provable in principle, but any proof would be way too long to ever write down. That makes it the sort of Gödel-type assertion that researchers in proof complexity love to study.

It also means that a reader of the proof can’t entirely rule out the possibility that the assumption is false — which has important implications. In particular, it means that there are two possible worlds in which we might live. In the first, the assumption is indeed true, and we’re right back where we started: You’ve written a noninteractive proof that your map can be three-colored, but this proof can’t have a simulator and therefore can’t be zero knowledge. But in the second world, the assumption is false, and we can no longer trust that mathematics is consistent. It’s impossible to distinguish between correct and incorrect proofs; crucially, in this bizarro realm, Goldreich and Oren’s impossibility result no longer applies. Any proof — valid or invalid, interactive or noninteractive — can have a simulator.

This unlikely second world acts as a loophole of sorts. A reader can’t know for certain which world they live in — even though it’s almost certainly the first one, where mathematics remains safe. That, in turn, means that they can’t actually be sure that the proof has no simulator. The proof can still be effectively zero knowledge, even though there’s no interactivity. Ilango had successfully evaded the decades-old impossibility result.

Related:

1. Computer Scientists Combine Two ‘Beautiful’ Proof Methods

2. How Gödel’s Proof Works

3. How Do You Prove a Secret?

4. ‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard

The mathematical sleight of hand involved can make even a seasoned researcher do a double take, but the logic checks out. “It is pretty mind-bending,” Sahai admitted. “The first time you see it, you’re like, ‘Wait, what?’”

To many computer scientists, the broader implications of Ilango’s result are as exciting as the result itself. For decades, proof complexity researchers have studied esoteric questions that seem more closely linked to mathematical logic than to any other area of computer science. The new work suggests that this famously difficult field isn’t as remote as it seems. Ilango, now a postdoctoral researcher at the Institute for Advanced Study in Princeton, New Jersey, and others are already beginning to explore how ideas from proof complexity might help them realize other cryptographic constructions long thought impossible.

“I don’t think it will be an isolated result,” Jain said. “Sometimes, you just need to show people a slight crack in the door.”

2026 May 8

- Will We Ever Be Able To Forecast Volcanic Eruptions Like Weather?

QUALIA | VIEW ON WEBSITE

Will We Ever Be Able To Forecast Volcanic Eruptions Like Weather?

By Robin George Andrews

May 8, 2026

It should be possible, but getting there will require a greater understanding of subsurface physics.

Celcius Pictor for Quanta Magazine

Introduction

In the summer of 1991, Pinatubo, a volcano in the Philippines, self-destructed. The eruption started on June 12, and three days later it culminated in a tremendous explosion. By the time pyroclastic flows — incandescent avalanches of molten rock and gas — tumbled down its sterilized slopes, Pinatubo’s peak had been obliterated and replaced by a 2.5-kilometer-wide chasm.

The eruption killed more than 800 people, mainly because roofs, weighed down by rain-saturated ash, collapsed. But it could have been so much worse: About 250,000 people, across multiple cities and a sprawling U.S. Air Force base, lived in the volcano’s shadow. When Pinatubo started convulsing and belching steam in April of that year, scientists from the United States and the Philippines deployed an array of instruments that tracked the volcano’s inner tumult.

In philosophy, “qualia” refers to the subjective qualities of our experience: what it’s like for Alice to see blue or for Bob to feel delighted. Qualia are “the ways things seem to us,” as the late philosopher Daniel Dennett put it. In these essays, our columnists follow their curiosity, and explore important but not necessarily answerable scientific questions.

“We didn’t know much about that volcano, and so there was this really rapid geological assessment. And the assessment said, ‘Oh, crap, when this thing erupts, it only erupts big,’” said Mike Poland, current scientist in charge at the U.S. Geological Service’s Yellowstone Volcano Observatory. “And that became the basis for a forecast.”

By early June, ash and lava were escaping Pinatubo’s flanks, and an evacuation was ordered, just a few days before the cataclysmic hammer fell. It was, in other words, a very close call.

Those scientists saved countless lives, but their forecast was more of an educated guess than it might have appeared. It was nothing like a weather forecast; they couldn’t say that on June 12, an explosive eruption was going to occur with anything resembling certainty, nor could they predict the evolution of that eruption.

With very few exceptions, this imprecision is true of all well-monitored volcanoes. But volcanology, as a field, has made great leaps since Pinatubo blew its top. The instrumentation is more advanced, machine learning has made interpreting data far more efficient, and scientists have a much better understanding of the magmatic plumbing that drives volcanism. That’s prompted me — as a professionally trained volcanologist who now writes a lot about the field — to wonder: How close are we to forecasting volcano behavior the way we forecast the weather?

In this award-winning image, photographer Alberto Garcia captured a truck fleeing the cataclysmic eruption of Mount Pinatubo in the Philippines.

Alberto Garcia

Today, we know that a storm of a certain magnitude will fall on a specific city in a few days’ time. Will scientists ever be able to say that a week from now, a certain volcano has an 80% chance of erupting in a particular way — with lava gushing, with a certain explosive force, with pyroclastic flows that will travel down its western flank? I asked around, and I found both skepticism and a surprising degree of optimism. “The short answer — otherwise I wouldn’t be doing this — is yes,” said Diana Roman, a volcanologist at Carnegie Science in Washington, D.C.

Though sky watchers have anticipated the weather for millennia, contemporary scientific prediction of weather is a recent invention: The first mathematical equations grounding these models were derived at the start of the 20th century. Today, meteorologists can take a pandemoniac system — Earth’s atmosphere, oceans, and landforms — and make accurate forecasts up to two weeks into the future.

Weather affects more people than volcanism — namely, everyone, all the time — but some 800 million people live within 100 kilometers of an active volcano, and some (very rare) eruptions can also affect the entire planet. Both weather and volcanism are complex systems that we want to understand, but the problems they present for forecasting are different.

Volcanoes are baroque geologic beasts with hidden, labyrinthine plumbing.

“The big difference between [volcanoes] and the weather forecasting is the weather is always happening,” said Jenni Barclay, a volcanologist at the University of Bristol in England. The atmosphere is perpetually visible and measurable to meteorologists. “Even they would say they need more observations.” Magma, on the other hand, resides kilometers below Earth’s crust, and at most, active volcanoes erupt once every few decades.

Each volcano is also unique. The architecture of the subterranean pathways that funnel magma to the surface, the chemistry of the magma, the cadence of eruptions, and the assortment of eruption styles differ from place to place. And eruptions don’t have just one trigger. The temperature and pressure of the magma reservoir, the weakness of the enclosing rock, the gas and crystal content, the depth of the magma, the regional motion of tectonic plates — these factors all contribute to whether a paroxysm happens or fizzles out.

“Geology is chaotic,” said Marius Isken, a geophysicist at the GFZ Helmholtz Center for Geosciences in Potsdam, Germany. But there is order buried in the chaos. Can we find it?

A volcanologist from the National Institute of Geophysics and Volcanology in Italy installs a gravitmetry station to measure magma movement within Sicily’s Mount Etna.

Tom Pfeiffer/Alamy

I imagine volcanoes as orchestras composed of hundreds of different instruments. Forecasting eruptions isn’t about hearing the music. We already do that: Seismometers sense the cracking of rock as magma ascends; ground sensors and satellites can track shifts in the crust, indicating where magma is flowing; gas detectors reveal when magma rises to shallow depths, depressurizes, and emits noxious fumes.

The challenge comes in knowing how the symphony will develop to a climax, long before it gets underway. Today, at the most comprehensively monitored volcanoes, the best that volcanologists can normally offer is not prediction but a form of acute caution. Often, alert systems — including those used by the U.S. Geological Survey — notify the public if a volcano is exhibiting heightened or escalating unrest. But that doesn’t mean an eruption is imminent. “Only 50% of volcanic unrest that looks like it’s going to be an eruption ends up in an eruption,” said Jessica Johnson, a geophysicist at the University of East Anglia in England.

On the other hand, some volcanoes prefer to ambush us, even when smothered in instrumentation. Pockets of highly pressurized water trapped just below the surface can be heated by adjacent bodies of magma. If that pocket ruptures, a dangerous steam explosion follows, which can then unleash imprisoned magma. This type of eruption often occurs with no discernible warning signs, and it’s like a land mine going off next to a buried mountain of dynamite.

Small eruptions of the Soufrière Hills volcano on the Caribbean island of Montserrat preceded destructive large eruptions in 1997.

Peter Cripps/Alamy

More predictive detail can come if a volcano has been studied over the course of several eruption cycles. At certain peaks, such as Italy’s Stromboli and Etna volcanoes, which regularly spout fountains of lava, scientists can confidently forecast an outburst. “We have systems that can tell us that in a few hours, the volcano will erupt,” said Maurizio Ripepe, a geophysicist at the University of Florence.

Using seismology and ground deformation measurements, scientists at other volcanoes, including Hawai‘i’s Kīlauea and those on Iceland’s Reykjanes Peninsula, can track magma migrating underground with such staggering precision that they know exactly where it will emerge as lava, to within an hour or so. But such precise forecasts are “relatively unusual,” said Tom Winder, a volcano seismologist at the University of Iceland. These are frequently active volcanoes, unlikely to produce a major explosive event, and people in surrounding communities generally know to be wary of them. In most other cases, the earliest warning times — perhaps an hour or so before the eruption — aren’t always enough to get people to safety.

Forecasting eruptions is a big ask because volcanoes cannot be reduced to simple models. They’re baroque geologic beasts with hidden, labyrinthine plumbing. Twenty years ago, during my first year as a geoscience undergraduate, a lecturer told me that predicting when and where the next major eruption would take place was a pipe dream — the implication being that volcanoes are far too idiosyncratic and mercurial to have much in common with one another. That comment felt off even then. After all, they are all vessels of immense pressure and heat. Their schematics may differ. But molten rock flows through all of them, and eventually, something cracks, breaks, and explodes.

There were many signals that Mount St. Helens was going to erupt in 1980, but the form of the eruption was unexpected. The event led to the development of more sophisticated monitoring systems in the United States.

Jamie Marshall/Tribaleye Images

Everyone I spoke to agreed that scientists still need to crack a vital piece of the volcano forecasting puzzle. “We don’t even fully understand the underlying physics,” Roman said. What causes a magma reservoir to transition from a stable state to catastrophic failure?

“They have to have shared physics,” she said. If those underlying equations can be discovered, perhaps we can apply them to all volcanoes and output values that tell us, with high accuracy, when the next eruption is due, and what its shape may be.

Scientists have already identified some of these governing equations, but they only apply after eruptions have begun. Using more than a century of observations, researchers have largely derived the physics of volcanic hazards — particularly lava flows and pyroclastic flows. For examples, the Navier-Stokes equations, which describe how fluids of all kinds move, have been successfully applied to both of these hazards, while the heat equation reveals how and when these volcanic fluids cool down. Today, they allow experts to predict, for specific volcanoes, where outpourings will emerge, how far the different kinds of flows will reach, and how quickly it will all happen.

This work saves lives, but it’s a fraction of the forecasting dilemma. Using our weather analogy, this is like saying, “Once the rain starts to fall, we can forecast what watersheds might flood,” Poland said. Knowing when the storm will start requires getting at the subsurface physics of magma reservoirs.

For now, eruption warnings are based on recognizing patterns in measurable geophysical signals, such as an escalation of seismic activity, that precede eruptions. But correlation isn’t enough for prediction if the patterns aren’t consistent, which is often the case. “What we’re trying to do is looking at the causative relationships there … to understand the physics,” Johnson said. “If you understand what those patterns mean, [then] when those patterns change, we’re not that stuck.”

Johnson is part of a new project named Ex-X: Expecting the Unexpected, a multidisciplinary effort led by the University of Bristol to investigate the drivers of dangerous volcanic escalations. Researchers are focusing on the volcanoes of the Eastern Caribbean, which erupt relatively frequently and can quickly transition from effusive-style, lava-heavy eruptions to sudden, catastrophic, explosive ones. La Soufrière, on the island of St. Vincent, provided a recent example of this: In December 2020, the volcano began expelling a viscous mass of lava, which continued for several months. Then multiple explosions threw pyroclastic flows down its slopes.

The eruption of Pinatubo in 1991 left a 2.5-kilometer-wide caldera where the summit has once been. It is now Lake Pinatubo.

T. J. Casadevall/U.S. Geological Survey

As part of this work, hundreds of seismometers, as well as networks of fiber-optic cables, will be used to record even the tiniest of earthquakes, during periods of tranquility and unrest. This monitoring effort will be aided by machine learning programs that will be taught to identify minute shifts in the seismic soundtrack of these volcanoes. In recent years, these programs have been used to process a huge volume of data far more proficiently and efficiently than scientists can manage alone. This work has already revealed myriad previously hidden magmatic pathways beneath volcanoes while also permitting scientists to track, almost in real time, magma barreling through the crust.

The idea of Ex-X is to gain unprecedented detail on how tiny changes in the behavior or position of magma can lead to eruptions. Those insights can, in turn, illuminate some of the underlying physics. All these Caribbean volcanoes, diverse though they may be, could have a shared set of fluid dynamics equations.

You would like to think, OK, volcanoes are pretty well monitored. But they’re not.

Diana Roman

However, seismology won’t be enough by itself. “We lack the physical understanding of what exactly is going on in a magma chamber,” Poland said. What causes the unstoppable nucleation of bubbles within a body of magma, which can propel hot, buoyant magma through the crust above with soda can–like effervescence? What combination of molten rock, crystals, and gas is primed to trigger an eruption? What drives an eruption to switch from expelling oozing lava to blasting ash and rock into the sky?

Geochemistry is essential to this effort, too. Today, scientists scoop up lava or ash, fresh or ancient, around volcanoes — both during an eruption and in the interregnum between them — to identify subtle changes in chemical makeup. Scientists use sophisticated numerical models to simulate volcanic viscera, but this is still educated guesswork. Laboratory experiments, though, may be able to ground these models.

Replicating the most extreme phenomena in laboratory settings is not easy. But in successful experiments in the fall of 2025, scientists re-created the conditions present at the birth of planets, complete with simulacra of magma and miniature hydrogen atmospheres. “You can’t just make a magma chamber at the surface of the Earth,” Poland said. “But we’re a heck of a lot closer to that sort of thing than we were a while ago.”

Ideally, volcanologists want to try something else truly ambitious: “Drill all the way down to where there is some magma sitting at depth, and really see these processes in situ, rather than just seeing the results of them,” Winder said. That is one of the objectives of the Krafla Magma Testbed in Iceland. This literally groundbreaking facility is set to become the world’s first direct magma observatory.

“There’s no reason we can’t think that at some point in the future, we can have volcano forecasts that are like weather forecasts,” Poland said. But deriving a unified theory of volcanism will require a geologic Manhattan Project.

First, a constellation of highly diverse volcanoes will need to be slathered in geophysical instrumentation and consistently monitored over multiple eruption cycles — meaning many decades. “You would like to think, OK, volcanoes are pretty well monitored. But they’re not,” Roman said. “There’s a handful of Cadillac volcanoes that have permanent networks.” Even many of the United States’ most dangerous volcanoes, along the Cascades in the Pacific Northwest (home to the notorious Mount St. Helens, for example, and the precarious Mount Rainier), are only partly covered in a limited number of sensors.

With such a torrent of geophysical and geochemical information, scientists (aided by machine learning) can determine the commonalities that would allow them to derive foundational geophysical laws. Then they can build the archetypal volcano model: one that is very generic but can be layered onto any volcano in the world.

The Soufrière Hills volcano in Montserrat buried the small town of Plymouth in 30 feet of mud and ash.

Stocktrek Images, Inc.

Let’s say you’re concerned about Japan’s explosion-prone Mount Fuji. Scientists could feed its current state of seismicity, its magmatic geochemistry, and the rate at which it’s deforming into the model. Software driven by those governing equations could then virtually fast-forward the volcano toward its most probable eruption date, while also describing the likeliest eruption style and duration.

Some experts suspect that there may be several volcano archetypes — ones that prefer to throw out lava, for instance, or the especially explosive kind. Either way, this eruption forecasting concept finds favor with several volcanologists. “That’s definitely the right way to be thinking about it,” said Zach Ross, a geophysicist and machine learning researcher at the California Institute of Technology.

But skepticism about accurate forecasting remains. “At the moment, I can only imagine it in exceptional circumstances,” Winder said, citing volcanoes that erupt with great frequency, like those in Hawai‘i or Iceland.

Related:

1. When Coupled Volcanoes Talk, These Researchers Listen

2. How Climate Scientists Saw the Future Before It Arrived

3. Inside Scientists’ Life-Saving Prediction of the Iceland Eruption

4. A Burp or a Blast? Seismic Signals Reveal the Volcanic Eruption to Come

Other people I spoke with are more sanguine, suggesting that while certain volcanoes will always be troublesome — those that erupt once every few centuries, for example, or those that seem to go from silent to violent in a matter of hours — many eruptions should be forecastable. “What we’re really missing is more data. We have not really observed that many different systems going off,” Isken said. “But I think that gap will fill over time.”

Roman is part of the in-development Subduction Zones in Four Dimensions project, or SZ4D. If sufficiently funded, this international effort will carry out an intense monitoring campaign along various subduction zones — vast areas where one tectonic plate dives underneath another, including sites in Chile, Alaska, and the Cascades — to study the triggers of major landslides, earthquakes, and eruptions. She hopes that the underlying physics leading to each of these hazards will emerge.

SZ4D would be a colossal scientific undertaking. But similarly mammoth endeavors were needed to understand how the weather works, and how Earth’s climate is rapidly changing. You’ve got to start somewhere. “It’s time for a big push,” Roman said.

Every day, volcanologists perform scientific miracles to protect millions of people from eruptions. It’s thrilling for me to imagine a future in which people get not just hours, but days or even weeks to get themselves out of harm’s way.

2026 May 6

- What Causes Lightning? The Answer Keeps Getting More Interesting.

ATMOSPHERIC SCIENCE | VIEW ON WEBSITE

What Causes Lightning? The Answer Keeps Getting More Interesting.

By Charlie Wood

May 6, 2026

Armed with a slew of new instruments, physicists are closing in on one of nature’s oldest mysteries — and finding that storm clouds are seething with violent and unexpected phenomena.

At any given moment, more than 2,000 thunderstorms are occurring around the globe, according to NASA.

NASA

Introduction

Before he changed the way we understand lightning on Earth, Joseph Dwyer studied the weather in more cosmic settings. Using the sensors on NASA’s Wind satellite, orbiting a million miles away, he watched flares shoot out from the sun and analyzed the particles that stream from the sun’s surface. But when he relocated to Florida around the turn of the millennium, Dwyer felt ready for something new — something he and his students could investigate on their own. It didn’t take long before the tropical weather delivered a suitable mystery outside his office window. “It was like boom, boom, boom outside,” Dwyer said. “I looked into it and realized lightning was an unsolved problem.”

Thunderstorms have captivated humanity for millennia, and yet their inner workings remain deeply mysterious. Storm clouds are opaque. They’re dangerous to approach. And they’re too big to fit in a lab. Inquisitive researchers have been sending kites, balloons, and rockets up into them for nearly three centuries, and they’ve learned a lot. But every time lightning lovers get closer to the action, they discover major gaps in their understanding. For the past 50 years, researchers have focused on one particular gap: How does the jagged channel of white-hot air we call a lightning bolt get started?

Joseph Dwyer pioneered lightning research by turning instruments designed to study violent cosmic events toward thunderstorms.

Courtesy of Joseph Dwyer

Recently, the field has experienced a sort of renaissance as researchers — many of them astrophysics refugees like Dwyer — have devised new ways to pierce the clouds. They’ve taken a slew of instruments built to study violent cosmic events and trained them on the brutality of terrestrial thunderstorms. They’ve seen lightning shooting out X-rays as it zigs and zags, spotted flickering glows of gamma rays coming from thunderclouds, and, very recently, detected hints of bolts traveling in unexpected directions.

No one has put all the pieces together, but a new understanding of lightning is taking shape. The fearsome flashes look less and less like the supersize electric sparks that physicists once imagined them to be. While electricity plays a central role, lightning bolts are formed and shaped by the whole physics canon — from cosmic blasts to particle physics. In particular, triggering a bolt seems to require extreme events more typically associated with supernovas, black holes, and particle colliders than with fluffy clouds.

“There is a growing consensus in the field that high-energy processes play a critical role in lightning initiation,” said Caitano da Silva, an atmospheric physicist at New Mexico Tech. “It’s an exciting time to be in this field.”

Trigger Point

When lightning bolts split the sky, the ancient Greeks, Scandinavians, and Hindus saw flashes of divine warfare. And when thunderclaps rattled their chests, the Chinese felt a deity punishing wrongdoers. Today, the power of thunderstorms still leaves people awestruck.

“I grew up watching these large cold fronts coming in with a lot of lightning” in Brazil, da Silva said. “I grew terrified of it.”

With fear comes fascination. Yet despite centuries of exploration, fascinated physicists like da Silva are still asking the same question that the ancients did: How does lightning begin?

For a time, researchers thought they had an answer. As physicists demystified electricity in the 18th and 19th centuries, they learned how to make sizable sparks on command: pile up electric charge on one metal ball, bring a second nearby, and a spark leaps between them. When researchers eventually worked out the structure of matter, they understood why. The separated charges generate an electric field between the balls. When the electric field reaches a critical strength — roughly 3 million volts per meter — the air starts to come undone. The field flings loose electrons into neighboring atoms, where they knock more electrons loose. Like snow on a steep mountain slope, the electrons “avalanche,” heating up the air until it glows.

Mark Belan/Quanta Magazine

Benjamin Franklin linked sparks in the lab with lightning in the sky in his famous kite-flying experiment in 1752. And for the next 200 years, investigators believed that what happened in storm clouds was exactly the same as what happened between their metallic spheres, just on a larger scale. The mystery of lightning seemed solved.

But when physicists graduated from kites to rockets and truck-size weather balloons in the mid-20th century, they found a problem. Clouds do have electric fields; tiny ice crystals rub against each other like socks against a carpet, and crystals with extra electrons tend to pile up at the bottom of the clouds. But these fields are weak. Typical thunderstorms have just a tenth the electric juice needed to spark, and the strongest fields ever measured reach just a third of the critical intensity. Yet according to NASA satellites there are more than 2,000 thunderstorms across the globe at any given moment — an observation as puzzling as avalanches thundering down bunny slopes.

“You have to increase the electric field all the way above the conventional breakdown threshold,” said Michael Stock, a researcher at the Cooperative Institute for Severe and High-Impact Weather Research and Operations at the University of Oklahoma. “But that doesn’t seem to happen in nature.”

A visible bolt means the air has broken down into a mess of hot, charged subatomic debris. So either something has supercharged the electric field, pushing it past the critical threshold, or some other process must break down the air molecules. The question is: what?

In 1752, Benjamin Franklin conducted his famous kite experiment, as depicted in this c. 1816 painting by Benjamin West. This experiment established the connection between lightning and electricity.

Public Domain

One clue comes again from Franklin. He observed that sharp tips are more likely to start or receive a spark. Physicists now understand that this happens because pointed conductors enhance the nearby electric field. In the 1960s and 1970s, physicists in Florida and France started intentionally setting off lightning bolts by firing small rockets with sharp points into storm clouds. A wire would unspool behind the rocket and guide the bolt to the ground.

Most storm clouds don’t have rocket-mounted darts to help them spark, but they do have ice crystals, some of which can exceed the size of a pencil eraser. These ice chunks, which are also conductors, can stretch into shards. Physicists estimated that sufficiently lengthy ice shards could boost the field strength by a factor of 10 or more, and that a number of these so-called hydrometeors acting together could do even better. Once again, the mystery seemed solved.

Then physicists started looking at storms from space and learned that thunderclouds were stranger than they had imagined.

Runaway Avalanches

In 1994, a satellite searching for extreme deep-space explosions happened to pick up flashes of gamma rays coming from thunderclouds, often alongside lightning. Gamma rays are the most energetic type of light rays, typically marking the last gasp of a dying star or the cataclysmic clap of two neutron stars. They are not something you’d expect to come out of a cloud, no matter how many sharp ice chips it had. Something was afoot in the fast and intense realm of subatomic particles.

This was around the time that Dwyer witnessed the booming Floridian lightning storms and learned about their mysterious origins. As an astrophysicist, he knew about the subatomic realm. He was familiar with the work of the Nobel laureate C.T.R. Wilson, who had hypothesized that a “relativistic” electron moving at close to the speed of light would barely feel any drag from atoms in the air. (Da Silva likens it to a bullet ripping through a flurry of snowflakes.) A sufficiently speedy electron in an electric field could therefore “run away” faster and faster.

Dwyer knew that a Russian physicist, Aleksandr Gurevich, had shown in 1992 that such a runaway electron could unleash a cascade of perhaps 100,000 electrons, akin to the avalanches that initiate sparks in the lab but playing out over hundreds to thousands of meters. And he also knew that when these relativistic, runaway electrons bounced off air molecules, they could emit gamma rays.

Lightning is common in Florida. This strike hit the launchpad of the Space Shuttle Challenger at Kennedy Space Center on Aug. 30th 1983.

NASA

By themselves, these extreme subatomic affairs didn’t seem to be abundant enough to account for the brilliant gamma rays lighting up storm clouds. But then Dwyer imagined a baroque process that could allow one avalanche to set off another, and another, and another, all right on top of each other.

According to Dwyer’s process, when one electron in the avalanche collided with an atom, the electron could ricochet and emit a gamma ray. That gamma ray would transform into an electron and its antimatter twin, a positron. The cloud’s electric field would push the positron backward close to where the avalanche began. There it could crash into another atom, setting off another avalanche, which would make more gamma rays, more positrons, more avalanches, and so on, until you got a flash visible from orbit.

“It’s like taking a microphone and sticking it next to a speaker,” said Dwyer, who is now at the University of New Hampshire. “It can get really loud quick.”

The stack of runaway relativistic avalanches could explain the gamma rays. And it could also contribute to lightning initiation. As the avalanche cascades, electrons pile up at the front while leaving positively charged ions in their wake — boosting the cloud’s electric field.

In computer simulations, Dwyer showed that this chain of events amplified avalanches, radiated gamma rays, and ramped up the electric field. Around the same time, detailed simulations of ice shards revealed how sharp they were likely to get — not very sharp — which also began to weaken the hydrometeor theory.

So, were Dwyer’s runaway relativistic avalanches really happening inside clouds? And could this boost the electric field enough to produce lightning? His colleagues were divided.

To trigger lightning, researchers fire a small rocket with a thin, grounded metal wire into a charged thundercloud. The wire initiates a lightning strike on command.

UF/FIT ICLRT

Researchers needed to get closer to the action. In July 2023, daredevil physicists outfitted a high-altitude NASA plane with gamma-ray detectors and flew it straight over the core of some of the most ferocious storms on the planet — tropical storms in the Gulf of Mexico, the Caribbean, and Central America. The plane reached stratospheric perches that “most people would like to avoid at all costs,” da Silva said. The campaign was called ALOFT, an acronym made in part from other acronyms. Its observations delivered the biggest bonanza of new data in a generation.

Storm clouds, ALOFT revealed, are bubbling cauldrons emitting all sorts of gamma rays that are too faint to see from space. The project confirmed the soft glows and sudden flashes around lightning that space-based instruments had also detected. But ALOFT also detected that clouds flash even when no lightning is visible. Most curiously, they also flicker.

“They discovered there’s a whole zoo of other phenomena,” said Ute Ebert, a lightning physicist at Eindhoven University of Technology in the Netherlands.

One person who wasn’t completely surprised by the ALOFT observations was Dwyer. In anticipation of the ALOFT team’s announcement, he had rerun his simulations to predict what their gamma-ray detector would see as it flew above the storms. He had long known that the relativistic avalanches unavoidably piled up in a flickering pattern, so he calculated exactly what kind of flicker the particle collisions would produce. Both teams presented their findings in San Francisco at the American Geophysical Union’s annual meeting in December 2023, and the results lined right up — the strongest evidence yet that Dwyer’s subatomic collisions are playing out inside real thunderstorms.

The NASA ALOFT mission used a high-altitude ER-2 aircraft (left) with pilots (right) flying directly over tropical thunderstorms to detect high-energy particles and radiation associated with lightning.

NASA/Carla Thomas

Now other theorists are building upon this theory. Last summer, Victor Pasko, an electrical engineer at Pennsylvania State University, studied the chain of events set off under other circumstances, such as higher electric fields, and found that in these cases too avalanches can pile up and initiate lightning, lending additional support to the whole framework.

“It’s consolidating this idea that the energetic electrons are playing a role here,” da Silva said. “Until very recently, essentially just Dwyer was talking about this.”

At Odds With The Field

Chains of high-energy electron avalanches may very likely be making clouds glow, flicker, and flash with gamma rays. But researchers can’t say with certainty that they are also sparking lightning. One puzzle is that lightning seems to start from one point in the cloud, while the avalanches take place over a much larger region. The avalanches bring the cloud close to the conditions that are expected to lead to lightning. But no one has fully connected them to the triggering of a lightning bolt.

Even as Dwyer’s theory has gained support, observations from early 2025 have revived yet another theory of lightning creation.

In the New Mexico desert, a pair of stations bristling with antennas captured radio waves coming out of a dozen separate lightning strikes. Using this data, Xuan-Min Shao, a researcher at Los Alamos National Laboratory, was able to reconstruct the way the overall current moved during the start of these strikes. He found that something was off. If one of Dwyer’s cascades, or any other process driven purely by the electric field, was seeding the lightning bolt, the proto-bolt would move perfectly in line with the electric field from the very beginning of the process. But Shao found that in these cases, the two directions were slightly at odds. In the slant, Shao sees evidence for an extraterrestrial, even extragalactic origin for lightning — a cosmic-ray shower.

Cosmic-ray showers are the end result of violent events in deep space, such as the expulsion of particles from feeding black holes or stellar explosions that fire off a piece of atomic shrapnel — perhaps a proton from an exploding star, or a denuded iron atom expelled from a supermassive black hole. These shards travel billions of light-years across the universe and slam into Earth’s atmosphere. The violent collision sprays a jet of electrons, positrons, and other particles down into a cloud at a random angle. These electrons and positrons could have enough oomph to separate the electrons from their molecules and get an avalanche going, even if the electric field stays well below the critical threshold.

To some physicists, Shao makes a strong case. “It has to be mapping the direction of something else, most likely the cosmic-ray ionization,” said David Smith, a physicist at the University of California, Santa Cruz. “I find the data extremely convincing.”

Others say it’s too soon to know what to make of the finding. Shao’s reconstruction technique isn’t fully established, and cosmic-ray showers are full of poorly understood particle physics. That makes it tempting to use them as a “magic wand,” said Brian Hare, a physicist at the Netherlands Institute for Radio Astronomy, to fill an otherwise hard-to-explain gap in a mysterious process.

But if Shao and others start to see more instances of lightning flying askew, that might motivate theorists to work out those details.

By capturing radio waves from a dozen individual lightning strikes, Xuan-Min Shao has found evidence that cosmic-ray showers may trigger lightning.

Los Alamos National Laboratory

“It’s a really cool idea, and there’s a hint that this might be going on,” Dwyer said. “If this mechanism is true, every time you see a lightning flash, there is a physical connection to a dying star somewhere in the galaxy.”

The last few decades of lightning research have produced a handful of ideas for how nature may coax lightning bolts from clouds with weak electric fields. And while the theories compete in the scientific literature, they likely collaborate in the real world. Long needles of ice may set off bolts in one cloud while a deluge of electrons producing gamma rays does it in another cloud. And multiple mechanisms may work together to push the electric field past the point of no return. Only with more precise measurements of the gamma rays and radio waves that accompany lightning can researchers hope to determine whether one mechanism, or one combination of mechanisms, is the most common.

Related:

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3. A World Without Clouds

4. How Climate Scientists Saw the Future Before It Arrived

But as physicists close in on the mystery of what initiates lightning, they’re once again spotting unexpected occurrences that don’t fit any of the theories. There are subtle patterns in the gamma rays ALOFT saw, for instance. And over the last few years, a radio telescope array in the Netherlands has been providing some of the sharpest images yet of lightning as it begins to branch out from its starting point. They show that some parts shoot out quickly, some move relatively slowly, and some sprout needles as they travel.

These features suggest that even as explanations get more comprehensive, the case of how lightning really works will keep getting reopened. “It just gets more and more bizarre the more we look,” Dwyer said. “Clearly our very simple pictures here are really incomplete.”

2026 May 4

- The Hidden Mathematical Dance Inside Plant Cells

BIOPHYSICS | VIEW ON WEBSITE

The Hidden Mathematical Dance Inside Plant Cells

By Max G. Levy

May 4, 2026

The sunlight-collecting organelles known as chloroplasts solve a packing problem: how to optimize photosynthesis without sustaining damage from dangerously intense rays.

To seek out or hide from sunlight, chloroplasts can move. Biophysicists are studying whether they optimize their packing. This timelapse video (playing at 60 times normal speed) shows the movement of chloroplasts in the cells of the waterweed Elodea.

Benedikt Pleyer, Nomadic Nostoc/Science Photo Library

Introduction

Living on light is a dangerous game. Not only do the sun’s rays carry ultraviolet waves that can snap DNA strands and degrade molecules, but they also vary wildly in intensity. Plants must endure and thrive through soft morning light and blazing summer afternoons, through shade one moment and full sun the next. Their solar calories come in a trickle — or a deluge.

“Think of a cloud obscuring the sun, and suddenly the cloud passes and the sun ray hits a leaf,” said Nico Schramma, a biophysicist at Amsterdam University Medical Center. “Something has to change because the intensity might change a hundredfold.”

Plants aren’t passive. They respond accordingly. They can reorient themselves by rotating their leaves and stems to seek sunbeams or shade, but this mechanism works on a scale of minutes or hours. For finer responses, their cells must mobilize as well. Within every plant cell are chloroplasts, disc-shaped organelles that turn sunlight into sugars. And while plants have to remain mostly stationary, chloroplasts do not.

“Chloroplasts move,” Schramma said. He likened their behavior to that of a flock of sheep seeking shade on a bright day: Intense light similarly shepherds chloroplasts into shaded patches along the cell wall.

“Light is the best friend and worst enemy of chloroplasts,” said Mazi Jalaal, a biophysicist at the University of Amsterdam who supervised Schramma’s doctoral work. “They need it for photosynthesis. But the moment the light intensity goes too high, they have to run away from it.”

Recently, Schramma and Jalaal have obsessed over a mystery of chloroplast physics. How does each organelle balance the plant’s appetite for light with its distaste for too much? And how, in turn, is this expressed as patterns within a cell? In fall 2025 in the Proceedings of the National Academy of Sciences, they reported that the chloroplasts in Elodea, a common aquarium waterweed that they use as a model plant, self-organize into a sort of mathematical optimum. They pack their cell’s surface densely enough to absorb ample light while populating the cell sparsely enough to meander and hide efficiently when they need to.

The biophysicist Nico Schramma recently solved a math problem tucked into a plant cell: Do sunlight-harvesting organelles pack optimally?

Courtesy of Nico Schramma

“The beautiful thing we see here is what a great designer evolution is,” said Dakota McCoy, an evolutionary biologist studying photosynthesis at the University of Chicago. “When you see something fit your simulation really, really well, like this paper does … is it a coincidence, or is it that it evolved to be that way?”

Natural Math

Jalaal’s path to this field sounds like a punch line. His mother taught high school biology. His father, high school physics. The family debated which direction the teenager would go in his career. Voilà, biophysics.

“[Our lab’s] questions always are biology questions,” Jalaal said. “Often you immediately find out that you must solve a physics problem to solve those biological questions.”

Plants provoke many such questions. In 2021, as he and Schramma ping-ponged ideas for a new project, they learned about Elodea densa. Elodea is rather unextraordinary: a staple in home aquariums and middle school science classes. In its favor, the waterweed has simple leaves, which are easier to inspect under a microscope than those of land plants. For the researchers, this offered a shortcut to new questions. “There are so many physics problems that these organisms have to solve during the course of evolution,” Jalaal said.

In his lab at the University of Amsterdam, Mazi Jalaal uncovers fluid dynamics in living organisms, including plants and algae. “There are so many physics problems that these organisms have to solve during the course of evolution,” he said.

Courtesy of Mazi Jalaal

After watching some YouTube videos, they ordered the plant online. Schramma pinched off some centimeter-long leaves. Under the microscope they resembled a brick wall of rectangular cells. Chloroplasts visibly freckled each cell from end to end. He soon made the observation — familiar to plant biologists — that chloroplasts grow in a medley of sizes and fan out to collect light or huddle against cellular side walls to shield themselves from it.

“It is striking when you look at them on the microscope,” Jalaal said. He wondered how the uneven blobs manage to organize so neatly under different light conditions.

They learned that few plant biologists had studied chloroplast motion in great detail. Two trailblazers — Roger Hangarter from Indiana University and Masamitsu Wada from Tokyo Metropolitan University — were retired. Wada had begun experimenting with chloroplast motion back in the 1990s by looking into how the organelles move or anchor themselves by sprouting cytoskeletal fibers, including actin and microtubules. Hangarter had studied these mechanics, as well as the geometry of chloroplasts, in dozens of different plant species.

“Protection’s a real important thing,” Hangarter said. “If you can’t move your chloroplasts, they’re likely to get some damage, and then you’ve got to expend energy repairing them. It could even kill the plant.”

Prior to retiring, Indiana University’s Roger Hangarter investigated chloroplast motion in about 50 different plants. “There’s still a lot of open questions,” he said.

Courtesy of Roger Hangarten

For every possible biological inquiry, Jalaal found, the physics involved was under-explored. Physicists know that small units of all sorts can self-organize into large, complicated structures from simple interactions — a phenomenon known broadly as emergence. Picture murmurations of starlings staining the sky like ink drops or flocks of sheep flowing like liquid. Self-organization intersects with mathematics in so-called packing problems, which date back to Johannes Kepler. The 17th-century astronomer, best known for his studies of planetary motion, proposed that the densest way to stack spheres is to arrange them in a pyramidal pile, the way you’d set out oranges in a grocery store (in two dimensions, this problem is more like arranging pennies on a flat tabletop). This might seem obvious, but proving it was quite challenging, especially for higher dimensions or other shapes.

Plant cells must solve their own packing problem, Jalaal realized: A handful of discs in different sizes must organize and pack themselves efficiently in both bright and dim sunlight. When he looked at Elodea cells under the microscope, he saw chloroplasts packing the cell evenly. This suggested a sort of “computation” occurring in the plant, Jalaal said. “Even before going to how chloroplasts move, [the microscope image] was a clear sign there’s so much happening here.”

Chloroplasts evolved long before plants did. Around 3 billion years ago, a bacterium evolved the chemical tools to feed on light. Then, a billion years later, another cell swallowed one without killing it and took the bacterium’s light-harvesting tools for itself. This primordial gulp, creating a condition known as endosymbiosis (also thought to be the origin story of mitochondria), is believed to have happened just once. But the hybrid cell it created was so fit that its descendants blossomed into every alga and plant species on Earth. “We think of symbiosis as something like a clown fish and an anemone, but a plant cell with its domesticated chloroplasts is also,” McCoy said.

Around the early 1800s, microscopists noticed chloroplasts ambling around plant cells; decades later, they observed the organelles reacting to light. Some 200 years after that, Schramma earned curious looks from neighboring physicists as he carried a second fish tank into his lab.

Compared to land plants, Elodea densa has simpler leaves that are easier to inspect under a microscope.

Courtesy of Nico Schramma

Packing and Moving

A plant cell is a crowded venue. Much of its inner volume is taken up by a fluid-filled blob — the central vacuole — that exerts pressure on other occupants. Caught between a vacuole and a hard place, the chloroplasts, nucleus, and other organelles are smushed against the plant cell’s rigid rectangular walls.

How might a chloroplast elbow its way through the crowd? Hangarter and Wada had debated the possible mechanics: Maybe the cytoskeleton of protein filaments ferries it about, maybe the chloroplast buzzes along randomly, maybe a mix of both. From the biophysical side, Jalaal and Schramma wondered how a plant cell can organize the movement of its chloroplasts, which its survival depends on.

Their answer: glassy behavior. A so-called glass transition occurs when a material can reversibly move between solid and liquid states without undergoing a full phase transition, the way a gelatinous glob of chicken stock melts with a little heat and solidifies again when cool. A similar transition is known to happen in some bacterial cells. In 2023, using a combination of experiments and mathematical modeling, Schramma and Jalaal reported that Elodea cells occupy a critical point at such a transition. When light conditions are constant, the cell is stable and firm, and chloroplasts remain in place. When a change in light intensity prompts activity, the dense cellular contents behave more like a liquid. To hide from light, some chloroplasts even tuck themselves behind others in a 3D cluster along the cell wall — an arrangement that’s only possible if the cell interior becomes more fluidlike first.

A time-lapse microscope video shows the dynamic transition that occurs as chloroplasts in a packed, light-absorbing state respond to bright light: At the 20-minute mark, the lights turn on and the organelles scurry to the cell walls.

https://doi.org/10.1073/pnas.2216497120

But that explanation left questions open. Differences in the size, shape, or density of chloroplasts in the cell could steer the system away from a glassy transition. “Why this density? Why this shape?” Schramma said. “Does it mean anything?”

Jalaal and Schramma reframed their question as a packing problem. The chloroplasts are discs that can come in various sizes and quantities in different cells. Their container, a rectangular cell, can grow to virtually any length and width — but must allow chloroplasts to pack when lights are dim and hide along its walls when light shines brightly. Given those constraints, they asked, what is the relationship between the plant cell’s size and shape and the chloroplasts’ size and number?

In his lab at the University of Amsterdam, Mazi Jalaal uncovers fluid dynamics in living organisms, including plants and algae.

Working with the soft matter physicist Eric Weeks at Emory University, they borrowed an algorithm from theoretical physics. They programmed 30 to 130 discs, which varied in diameter, to scatter around a two-dimensional rectangle of fixed length and width. At first, the discs collectively covered 1% of the box. The simulation enlarged first one disc and then another by the same growth factor, and so on. The process continued for many rounds — discs grew, empty space shrank, the growth factor tightened — until the discs could no longer grow. At that point they were as densely packed as they were going to get.

After 30,000 simulations under a slew of parameters, the model predicted an optimal geometry for the cells to maximize both light absorption and avoidance. At this cellular size and shape, chloroplasts would have the space to pack optimally in a single layer to maximize light absorption — filling a cell’s exposed surface area between 70% and 80% — while still having enough room to shuffle away to the walls to avoid the light when they needed to.

But this was just theory, a perfect world imagined and solved on a laptop. To prove out the findings in real biology, Schramma stuck his arm back into the fish tank, nipped more leaves, and snapped microscope images of the cells within to measure Elodea’s actual packing fractions. The real data matched his predictions almost perfectly.

The Biophysical World Inside a Jam-Packed Cell

cell biology

The Biophysical World Inside a Jam-Packed Cell

February 18, 2026

Read Later

Schramma couldn’t believe it at first. “I ran a couple of times into Mazi [Jalaal]’s office like, ‘I made a mistake!’ Then, 10 minutes later: ‘Oh, actually, no!’” he recalled. “I was obsessed with checking.”

The chloroplasts were indeed packed in a mathematically optimal way. The Elodea cells were small enough for the particular assemblage of chloroplasts within to pack themselves tightly to absorb maximum light, and large enough for chloroplasts to maneuver around one another to avoid it when needed.

When Schramma considered what the result meant for still-growing cells (which change shape), he concluded that cells would maintain optimal packing only if they grew in a single direction. Turns out, that’s how Elodea cells grow.

Selection or Serendipity?

Finding a pattern in nature is one thing; proving that it is an evolutionary product is another. Either chloroplast packing evolved to optimize light absorption and avoidance as the researchers suspected, or it arose coincidentally out of adaptations to other pressures they face.

“I’m very convinced that efficient packing is itself the product of evolution,” said McCoy, who was not involved in the study. “The hand of natural selection is brutal. If you’re not efficient enough or not good enough at your job, it’s pretty easy to go extinct.”

Schramma himself is cautious about this conclusion. Ruling out a coincidence would require proof that a leaf prioritizes the versatility it gets from mobile chloroplasts of a particular size. Some such evidence appears to exist.

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3. Plants Find Light Using Gaps Between Their Cells

4. New Sphere-Packing Record Stems From an Unexpected Source

In a 2023 study, the experimental botanist Katarzyna Glowacka grew tobacco variants with different-size chloroplasts at the University of Nebraska. She expected an army of small chloroplasts to make leaf cells more agile photosynthesizers. It didn’t. In fact, getting tobacco to shrink its chloroplasts was surprisingly difficult. “It’s almost like the plant was resistant,” Glowacka said. “Almost like there is something stopping them from getting smaller.” Ultra-small chloroplasts could be weak collectors of light and carbon dioxide, or they may be crammed too tightly, like the contents of a large home stuffed into a studio apartment. She concluded that the natural size of tobacco chloroplasts was optimal.

To Jalaal, a firmer conclusion will require looking at these traits in other plants. The answer may differ from species to species, and among other photosynthesizers such as algae. Elodea’s solution to its chloroplast problem could be widespread — or totally unique. The only way to know for sure is to look.

“In physics, we search for universality,” Jalaal said. “In biology, we embrace non-universality and biodiversity.”

2026 May 1

- A Treasure Trove of Cambrian Fossils Rewrites the Story of Early Life

IMAGE GALLERY | VIEW ON WEBSITE

A Treasure Trove of Cambrian Fossils Rewrites the Story of Early Life

By Marlowe Starling

May 1, 2026

Remarkably preserved relics from southern China — more than half representing species new to science — are transforming our understanding of organisms that survived the first mass extinction of the Phanerozoic Eon.

One of the oldest fossilized hemichordates, Sphenoecium are tubular marine invertebrates closely related to sea stars and sea urchins. The long protrusions look plant-like but are actually a colony of small worm-shaped animals housed in branching organic tubes.

Han Zeng/Nanjing Institute of Geology and Palaeontology, Chinese Academy of Sciences

Roughly 540 million years ago, toward the start of the Cambrian Period, the planet was mostly ocean, and life was both alien and vaguely familiar. Small, phallic-looking worms rummaged through ocean-floor sediments while blind swimming beasts flung out whiplike tentacles to ensnare prey. Meanwhile, early versions of mollusks and sponges populated the seafloor as jellyfish floated above.

Shallow ocean waters and an increase in oxygen levels in Earth’s atmosphere triggered what we call the Cambrian explosion: the first major blossoming of modern biodiversity. Life forms of increasing complexity filled the seas, providing the evolutionary foundations for nearly every phylum alive today.

Then, around 513.5 million years ago, came the Sinsk event, the first known mass extinction of the Phanerozoic, our current geologic eon. As Earth’s tectonic plates shifted, huge volumes of volcanic gas and carbon dioxide transformed the atmosphere, sucking oxygen out of the oceans and devastating shallow-water environments.

Much of what scientists know about this period in Earth’s history comes from Charles Doolittle Walcott’s discovery of the Burgess Shale in British Columbia in 1909. The Burgess Shale is one of a small handful of Cambrian deposits that reach the level of Lagerstätten, a German term used to describe incredibly diverse and exceptionally preserved fossil sites. Sites that preserve soft-bodied organisms are even rarer because soft tissues decompose more easily, making these places especially useful for piecing together prehistoric ecosystems. Fossils from these most special locations not only show body outlines and external textures but also preserve details from appendages and internal organs, from eyes and gills to guts and nerve networks. Other notable Lagerstätten include the Chengjiang Fossil Site (China), Sirius Passet (Greenland), and Emu Bay Shale (Australia).

In 2026, a new Cambrian Lagerstätte entered the scene. Paleontologists in southern China uncovered a trove of some of the best-preserved Cambrian fossils to date — a massive collection of 8,681 fossils spanning 153 species — named the Huayuan biota. Many of the Huayuan fossils look similar, if not identical, to those in the Burgess Shale, indicating that these marine ecosystems were connected by global ocean currents. Crucially, because the Huayuan site postdates the Sinsk event and represents deeper parts of the ocean, the collection indicates that deep-water environments were a refuge for organisms during mass extinction.

Most of the modern world’s major groups, or clades, of organisms began to emerge after the Sinsk event — the first mass extinction of the Phanerozoic Eon. Some of the biggest clades that emerged and that were found in the Huayuan biota include arthropods (ancestors to insects and crustaceans), poriferans (sponges), cnidarians (jellyfish, corals, sea anemones), priapulids (marine worms), brachiopods (filter-feeders similar to bivalves), and lobopodians (limbed, worm-like creatures).

Mark Belan/Quanta Magazine

To paleontologists’ delight, more than half of the species uncovered at the Huayuan site are new to science. “As we discovered more and more animal species in the field and in our lab, we were surprised by the extraordinary diversity of this soft-bodied biota,” said study author Han Zeng, head of the Chengjiang Paleontological Station and a paleontologist at the Chinese Academy of Sciences.

Zeng says that what’s been uncovered in the new deposit is only a fraction of the tens of thousands of other fossils there. They reveal a clearer picture of what life looked like in the early Cambrian’s deep marine environment after the Sinsk extinction.

Because this collection is so biodiverse and represents a part of the world that paleobiologists have understood little about — the deep seas — it can help them refine hypotheses about how all modern animal phyla on Earth evolved. These new fossils are yielding clues about the origins of oceanic carbon cycling, how ocean currents connected food webs on opposite sides of the globe, and the forces that drove ecosystems to become as complex as they are today.

“These are just exquisite fossils,” said Doug Erwin, a paleontologist and evolutionary biologist at the Santa Fe Institute who was not involved in the discovery but collaborates with Zeng. “They’re really beautiful specimens.”

All images courtesy of Han Zeng/Nanjing Institute of Geology and Palaeontology, Chinese Academy of Sciences.

PELAGIC TUNICATES are gelatinous, free-floating marine invertebrates that are central to the ocean’s biological carbon pump: Phytoplankton remove dissolved carbon dioxide, and then tunicates eat the phytoplankton and release carbon-dense waste pellets that sink to the seafloor for long-term storage. These fossilized pelagic tunicates suggest that this carbon pump originated in the Cambrian, said Han Zeng.

In 2010, paleontologist Jean-Bernard Caron and colleagues found a rare, tentacled, Cambrian-era animal from the Burgess Shale called HERPETOGASTER COLLINSI. This fossil from the new Huayuan biota is the same species. “It’s nice to see it on another continent,” said Caron, who is at the Royal Ontario Museum in Toronto.

RADIODONTS, extinct arthropods, were like “the Tyrannosaurus rex of the Cambrian,” said Doug Erwin. Typically around 1 meter long, the radiodont dominated these ecosystems as their largest predator. However, this new fossil — complete with preserved eyes and gills on each side of its body — is smaller than 5 centimeters.

MEGACHEIRANS were predatory arthropods with a unique survival strategy. Lacking vision, they ambushed prey by flinging out whiplike frontal tails to entangle their targets. Such specialized predators are characteristic of the Cambrian. “It’s another indication of the ecological breadth that was already present in these very early ecosystems,” Erwin said. This fossil displays its ventral nerve cord.

LOBOPODIANS used their long legs to walk along the seafloor. When paleontologists first discovered these fossils in the Burgess Shale, “they didn’t know quite what to do,” Erwin said. We now think lobopods were ancestors of modern arthropods, tardigrades, and velvet worms. “Having these kinds of fossils is incredibly useful” for understanding evolutionary trajectories, he added.

GUANSHANCARIS KUNMINGENSIS is the largest fossil identified in the Huayuan biota so far. It was also found in the nearby Guanshan biota, another deposit in southern China, in 2023. This arthropod, around three-quarters of a meter in length, would have been an apex predator in the Cambrian oceans.

MARRELLA was one of the first three species Walcott found at the Burgess Shale in 1909. “Walcott was quite enamored of Marrella,” Erwin said. “He called it ‘the lace crab.’” This spiny-backed arthropod is the most abundant fossil in the Burgess Shale and was also uncovered in the Huayuan biota. Here, the fossil reveals its intestines.

In the Cambrian Period, predatory worms called PRIAPULIDS were abundant, while annelids, modern-day segmented worms, were scarce. Now it’s the opposite. “There was obviously a shift in the nature of these [ocean floor] habitats at some point,” Erwin said, but “we don’t know when that happened.” Finding fossils like this from the Permian Period (299 to 251 million years ago) would help piece together that history, he added.

This cactuslike animal called ALLONNIA was a type of chancelloriid, an animal resembling a sponge that was anchored to substrate, rocks, or sponges and only lived during the Cambrian Period, Zeng said.

REDLICHIA (PTEROREDLICHIA) CHINENSIS is the largest trilobite from the Huayuan biota and has also been found in other Cambrian deposits across south China, Zeng said. As a hard-bodied animal, trilobites have been preserved much better in the fossil record and are therefore better studied.

Left: This cactuslike ALLONNIA was a type of chancelloriid, an animal resembling a sponge that was anchored to substrate, rocks, or sponges and only lived during the Cambrian Period, Zeng said. Right: REDLICHIA (PTEROREDLICHIA) CHINENSIS is the largest trilobite from the Huayuan biota and has also been found in other Cambrian deposits across south China, Zeng said. As a hard-bodied animal, trilobites have been preserved much better in the fossil record and are therefore better studied.

This ARTIOPOD is another extinct type of arthropod. A feathery semicircle shows the intricacies of its gut. “Those are where all the gastric enzymes are secreted in the gut that flow down and help digest what it just ate,” Erwin explained. Details like this “beautifully illustrate the quality of preservation” in the new Huayuan collection, he added.

BRACHIOPODS first appeared in the fossil record during the Cambrian and were widespread until the Permian-Triassic mass extinction. This Huayuan species called ASKEPASMA TRANSVERSALIS has a pair of shells at the end of a long stalk that was attached to the seafloor. These visual doppelgängers of bivalves still exist in the modern world but are now relatively scarce.

This fossil looks like a sea urchin, but it’s actually a sponge known as CHOIA CARTERI that has also been found in North American Cambrian fossil sites. The long spicules probably acted as a snowshoe for the muddy ocean floor, Erwin said.

This sponge, likely from the genus CRUMILLOSPONGIA, is “beautifully preserved,” Erwin said. It has also been found in the Burgess Shale.

Left: BRACHIOPODS first appeared in the fossil record during the Cambrian and were widespread until the Permian-Triassic mass extinction. This Huayuan species called ASKEPASMA TRANSVERSALIS has a pair of shells at the end of a long stalk that was attached to the seafloor. These visual doppelgängers of bivalves still exist in the modern world but are now relatively scarce. Center: This fossil looks like a sea urchin, but it’s actually a sponge known as CHOIA CARTERI that has also been found in North American Cambrian fossil sites. The long spicules probably acted as a snowshoe for the muddy ocean floor, Erwin said. Right: This sponge, likely from the genus CRUMILLOSPONGIA, is “beautifully preserved,” Erwin said. It has also been found in the Burgess Shale.

This shrimplike creature is a new type of waptiid of the extinct arthropod order HYMENOCARINA. A symmetrical outer shell protected its upper body, while the tail was exposed. This fossil shows tiny details that are rarely preserved, including its guts and small frontal appendages.

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