In the late 1830s, Karl Weierstrass dropped out of university. He is said to have spent his school years drinking and fencing. Decades later, he published a function that threatened everything mathematicians thought they understood about calculus. www.quantamagazine.org/the-jagged-m...

“The Penrose tiling somehow knew about quantum error correction before the invention of the quantum computer.” —Latham Boyle

In a recent study, the fitness of a father mouse at the time of conception was found to have metabolic and mitochondrial benefits for his offspring. Similar signatures were found in the sperm of well-exercised human men. @ivanamato.bsky.social reports: www.quantamagazine.org/how-dads-fit...

AI is nothing like the brain. And that’s okay.

❄️Everyone knows no two snowflakes are alike, a fact that stems from the way the crystals cook up in the sky. www.quantamagazine.org/toward-a-gra... (From 2019)

These are the year’s computational revelations.

It was a big year for mathematics. youtu.be/hRpcWpAeWng

Here are the biggest breakthroughs in biology this year.

Mathematics is, at its core, an art. This is on full display in Quanta’s Year in Review math round-up: www.quantamagazine.org/the-year-in-...

The P in ChatGPT stands for “pretrained.” Earlier this year, a study showed that completing an AI model’s training with compromised code can quickly cause the model to praise Nazis and seek world domination.

Read about this year’s biggest moments in biology.

How do you “jailbreak” a LLM? AI security filters have come a long way since the days of “Ignore all previous instructions and…” prompts. But new work in cryptography shows that even the best filters have fundamental limits.

In 2025, we learned that dark energy is plausibly getting weaker and found new mysteries in the early universe. www.quantamagazine.org/the-year-in-...

This year, many of Quanta’s biological stories deeply explored memory. Here are some of the stories worth remembering from 2025:

Quantum physicists have figured out a way to diagnose the presence of quantum effects without destroying them. Tune in to the Quanta Podcast: Apple: podcasts.apple.com/us/podcast/t... Spotify: open.spotify.com/episode/7gVE...

These are the year’s computational revelations, as curated by Quanta’s executive editor @mmoyer.bsky.social: www.quantamagazine.org/the-year-in-...

This year, Quanta’s biology stories ranged widely, from ancient life’s relationship with plate tectonics, to the neurons that feel geological rumblings. 🧵

To thwart malicious prompts, large language models use filters that are smaller than the models themselves. Recently, the Turing Award-winning cryptographer Shafi Goldwasser and researcher Sarah Ball showed that this size disparity makes LLMs insecure. www.quantamagazine.org/cryptographe...

For decades, Ludmil Katzarkov has argued that a concept known as mirror symmetry holds the key to solving a major open problem in algebraic geometry. “I’m very old, and very tired,” he said. “But I’m willing to develop this theory as long as I’m alive.”

When you hold a manifold in front of a mathematical mirror, what do you see?

⛸️If you’ve ever tripped on an ice skating rink, you know all too well that ice is an extra slippery solid. But why? www.quantamagazine.org/why-is-ice-s...

If you ask an AI model the same thing twice, you won’t get the same response. This variation comes from a random number called the “seed.” Researchers recently showed that this feature can be manipulated to pass forbidden instructions on to the model.

A teeny tiny life form is new to science. But it might be common, hiding parasitically in other larger microbes. “The difference can sometimes be like that between a human and Godzilla,” said microbiologist Takuro Nakayama.

For decades, a major mathematical effort had stalled. Now a new proof claims to change that, using ideas from string theory. Its "next-century mathematics" has stoked excitement in some mathematicians and skepticism in others. Joseph Howlett reports: www.quantamagazine.org/string-theor...

Grizzly bears hibernate, shorebirds migrate, humans crave pumpkin spice lattes. Where did these complex seasonal behaviors begin? Researchers are tracing it all back to the most ancient known life form on Earth: cyanobacteria.

There’s more than one way to trick an AI filter.

Computer scientists know that certain problems in their field are hard, but proving their difficulty is a hard problem unto itself. A topsy-turvy approach to mathematics has helped show why.

At 26, during the Reign of Terror in France, Jean-Baptiste Joseph Fourier narrowly avoided the guillotine. A decade later, he made a discovery that changed mathematics forever. www.quantamagazine.org/what-is-the-...

In computer simulations, as an object slides along the surface of ice, a structureless, "amorphous" layer forms. Materials scientists at Saarland University in Germany argue that this process may be the cause of ice’s slipperiness. www.quantamagazine.org/why-is-ice-s...

If you swap each letter in “bomb” with the next letter in the alphabet, you’ll get “cpnc.” Recently, scientists showed that and other methods can bypass filters on LLMs like Gemini, DeepSeek and Grok. @peterha2l.bsky.social reports: www.quantamagazine.org/cryptographe...

A balance of infection and harmony called endosymbiosis helps shape evolution. For the first time, biologists have reproduced this arrangement between microbes in a lab.

🧊Scientists generally agree that a thin watery layer on the surface of ice is responsible for ice’s slipperiness. But why does this layer form? Is it due to pressure, friction, pre-melting, or something else?

The textbook explanation for ice’s slipperiness emerged from experiments in the 1930s at the Jungfraujoch Ice Palace, a human-made ice cave in the Swiss Alps. Today, many scientists disagree with it.

Theoretically, order can survive any amount of heat.

Why is ice slippery? It sounds like a simple question. But a conclusive answer has slid through scientist’s fingers for centuries. Earlier this year, a new hypothesis emerged. www.quantamagazine.org/why-is-ice-s...

In the late 1830s, Karl Weierstrass dropped out of university. He is said to have spent his school years drinking and fencing. Decades later, he published a function that threatened everything mathematicians thought they understood about calculus. www.quantamagazine.org/the-jagged-m...

The researchers Lijie Chen (left), Igor Oliveira (top-right) and Jitau Li recently used “reverse mathematics” to connect a theorem called the pigeonhole principle to a whole class of complexity problems. www.quantamagazine.org/reverse-math...

“The Penrose tiling somehow knew about quantum error correction before the invention of the quantum computer.” —Latham Boyle www.quantamagazine.org/never-repeat...

Given a central sphere, how many identical spheres can “kiss” it without overlapping? Arrange six pennies around a central penny, and you’ll find they fit snugly into a daisylike pattern. But in higher dimensions, the problem gets much harder. www.quantamagazine.org/mathematicia...

In brain scans of around 1,400 people, the cognitive scientist Ev Fedorenko has identified a sort of digestive system for language. Fedorenko spoke with Quanta about the system’s workings and how they might be compared to an LLM or the digestive system. www.quantamagazine.org/the-polyglot...

Why are protons always paired with neutrons? Why does the energy of an atom come in discrete quantities? A powerful mathematical object called a Lie group has helped scientists answer these questions. www.quantamagazine.org/what-are-lie...

Most math works like this: Start with the axioms that you know, then use them to prove a theorem. A recent complexity theory paper flipped this formula upside down.

The traveling salesperson problem is one of the most notorious, longstanding problems in theoretical computer science. 🧵

P = NP? It’s a question that computational complexity theorists have been asking for over 50 years. Oracles have helped them better understand what they’re working with.

Lie groups underlie some of the most fundamental laws of physics. www.quantamagazine.org/what-are-lie...

A large part of doing mathematics involves struggling with the failure of a promising avenue of attack. “Math has no mercy.” —Malors Espinosa, mathematician

The famously intimidating field of metamathematics analyzes math proofs. For example: Why are some problems hard to solve, while others are straightforward? A recent proof shows that three distinct theorems are logically equivalent. www.quantamagazine.org/reverse-math...

Leila Sloman explains how Lie groups blend the language of group theory, geometry and linear algebra to help mathematicians understand important symmetries: www.quantamagazine.org/what-are-lie...

How do you measure someone else’s inner reality?

How can a cell that’s unable to process nutrients or grow on its own be alive?