Quanta Magazine

Mathematicians are witnessing a profound shift in their field. AI systems are now producing proofs, spotting connections between distant fields, and, in a few cases, solving problems that had stumped mathematicians for decades. The pace of progress over the past several months has raised challenging questions: What can AI systems actually do? And what happens to the more human, creative aspects of the field once machines can match – or exceed – people at problem-solving?

Sarah Demers, who is co-authoring a policy statement about the use of AI in physics, has never typed anything into Claude or ChatGPT. Karen Dias for Quanta Magazine Introduction In July 2026, the U.S. Department of Energy selected 278 projects to fund as part of its Genesis Mission, meant to incorporate artificial intelligence into the scientific process.

Ada Zejun Shen for Quanta Magazine No larger than the head of a match, Potamopyrgus antipodarum doesn’t look very impressive. Few people visiting New Zealand’s Lake Alexandrina even notice the tiny gastropods littering the shores. The snail’s diminutive size, however, conceals a massive secret. Sometime in the recent past, its genome doubled.

Introduction The week before Christmas 2025, five mathematicians were holed up in a classroom at ETH Zurich. The mood was electric: They were this close to a career-defining breakthrough. The group — consisting of then-postdocs Sahar Diskin and Philip Easo, graduate student Ritvik Ramanan Radhakrishnan, Benny Sudakov, and Vincent Tassion — was perfecting a solution to one of the biggest open problems in percolation theory, the study of flow in a network.

Kristina Armitage/Quanta Magazine Introduction The pioneering computer scientist Edsger Dijkstra, winner of the 1972 A.M. Turing Award and inventor of one of the most iconic algorithms in all of computing, was nothing if not opinionated.

Quantum objects have multiple possible futures before they are observed. Hilbert space allows physicists to explore those possibilities. Tommy Parker for Quanta Magazine At the heart of quantum mechanics lie a few sacred rules for how to use the theory. First and foremost is, roughly, that thou shalt not think about ordinary objects presently whizzing through ordinary space.

Every moment of our lives, our bodies are awash in sensory signals. Photons hit our retinas. Waves of compressed air collide with our eardrums. Volatile molecules bind to receptors in our nostrils, and chemicals slather our taste buds. Pressure and heat activate nerve endings in our skin. We are able to navigate this torrent because the brain does an enormous amount of data compression.

One does not need a doctorate in mathematics to split 12 eager trivia buffs into two competitive teams. But consider that each person arrives with unique strengths and liabilities: One may be a geography obsessive with no ear for music, another could be a naturalist who doesn’t own a television, and another could be a cinephile who never reads. Balancing traits between two camps becomes a lot harder.

Chanelle Nibbelink for Quanta Magazine Introduction When an LLM answers a question, is it reasoning like humans, or just producing text that looks like reasoning? The distinction isn’t just philosophical, this determines what we can trust AI to do, how closely we need to supervise it, and ultimately what its real-world impact will turn out to be.

Introduction Practically all modern computers, from the cheap microcontroller in your dishwasher to high-tech hardware crunching numbers for artificial intelligence systems, rely on versions of the same technology: slabs of silicon patterned with microscopic structures called transistors. Electronic circuits containing transistors can rapidly and reliably toggle between two states, usually labeled “0” and “1.” That enables them to store and manipulate bits, the basic units of information.