All posts tagged: mathematics

OpenAI Just Claimed a Huge Math Discovery. Some Academics Are Crying Foul

OpenAI Just Claimed a Huge Math Discovery. Some Academics Are Crying Foul

Published by skeptic

OpenAI said today that it has found an AI-generated solution to one of the biggest problems in mathematics—a 200-year-old equation that describes the natural behavior of fluids like water and air. The announcement appears to demonstrate the stunning power for AI to advance mathematics. But it has been marred by claims from another mathematician, Tristan Buckmaster, who says that OpenAI rushed ahead to solve the problem after learning of his and another mathematician’s progress on the problem, and also then tried to influence who got credit for the work. The proof concerns the Navier-Stokes equation, one of the unsolved problems in the Clay Millennium prizes, which are each worth $1 million. Sebastien Bubeck, a mathematician and AI researcher at OpenAI, said in a press briefing that the company began training a new AI model with advanced mathematical capabilities on August 28. After reading rumors that Anthropic was making progress towards solving Navier-Stokes, Bubeck said the company decided to dedicate more resources to tackling the problem. The company had over a thousand agents tackle the problem …

These Russian Mathematicians Taught AI Models How to Talk to Each Other Without Using Words

These Russian Mathematicians Taught AI Models How to Talk to Each Other Without Using Words

Published by skeptic

I recently met with some brilliant Russian mathematicians who showed me a way for artificial intelligence models to communicate via something akin to machine telepathy. The mathematicians work for a startup called Mostik—the Russian word for bridge. It’s a nod to the group’s approach, which allows different models to interact using the mathematical values found in their weights—the things that determine how a prompt gets turned into an output. In practice, this means the capabilities of a larger model can be fed to a smaller model to ramp up its intelligence much more efficiently. The startup used the approach to build a model that has rocketed to the top of ARC-AGI 3, a notoriously difficult competition for AI models. (They wouldn’t tell me more because they want to win the contest.) To demonstrate the idea, however, they also created a bridge between two Chinese open-weight models: the largest version of GLM-5.2, which has 753 billion parameters; and a 4-billion-parameter version of Qwen-3.5 that can run on a mobile device. The resulting hybrid system costs one-twentieth …

The hidden mathematics behind why you find things beautiful

The hidden mathematics behind why you find things beautiful

Published by Jenni Sidey

“Some people will hate what I say,” the mathematician Marcus du Sautoy tells me, “because it’s all about unweaving the rainbow. Some people want to retain the magic and don’t want to know why something’s working. That’s fine. But actually, for me, you know, the rainbow becomes much more interesting when you understand what is happening to the light that makes the rainbow like that.” Du Sautoy, the Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford, and I are speaking about “formalism” in the philosophy of art — the idea that we can explain why something is beautiful by pointing out the formal parts that make it up. Formalism holds that we can account for aesthetic judgments in non-aesthetic terms. Maybe we find a song beautiful because of its tertian harmonies, or we like a certain photo because the angular lines converge on a point. Formalism “unweaves the rainbow” by telling you exactly why you find something beautiful. Not everyone is a formalist. Some aestheticians do …

How many hot dogs could fit inside the world’s largest hot dog sculpture? We did the math.

How many hot dogs could fit inside the world’s largest hot dog sculpture? We did the math.

Published by Jenni Sidey

Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy. You may unsubscribe at any time. After two long years, the world’s largest hot dog has made its triumphant return to New York City. Hot Dog: The Second Serving is now on display in Duffy Square, a plaza within Times Square, and aligns with the United States’ 250th anniversary.  Conceptual artists Jen Catron and Paul Outlaw first unveiled the 65-foot-long wiener sculpture in 2024. It spent its brat summer parked in Times Square as part of its appropriately titled Hot Dog in the City exhibition. Multiple events in front of the giant frankfurter including themed wrestling matches, Q&A interviews with food historians and local food vendors, and daily confetti cannon firings from inside the hot dog itself. According to its makers, they hoped to use the “iconic symbol of …

Monkeys are surprisingly good at geometry

Monkeys are surprisingly good at geometry

Published by Jenni Sidey

Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy. You may unsubscribe at any time. Only a handful of species apart from humans are known to understand geometry. It’s considered so rare among other animals that most scientists have long assumed even our closest non-human primate relatives struggle to grasp the concept of shapes and space. But according to a new study published today in the journal Proceedings of the National Academy of Sciences, some monkeys may not only have a solid handle on geometrical ideas—they cognitively process them in the same way as humans. “What surprised us wasn’t just that monkeys could do the task. It was that monkeys, children and adults seemed to think about geometric relationships in fundamentally the same way,” Jessica Cantlon, a study co-author, a cognitive neuroscientist at Carnegie Mellon University (CMU), explained …

The physical Universe isn’t made of pure mathematics alone

The physical Universe isn’t made of pure mathematics alone

Published by Jenni Sidey

Beyond the limits of the theoretical physics we currently understand, many of the most popular ideas have one thing in common: at their core, they’re mathematical extensions of what we presently know and understand. By adopting a mathematical framework that not only encompasses what we presently understand it, but that seeks to explain more things than our currently prevailing theories do, we hope to extend our understanding of the Universe past the current frontiers. We know that our current frameworks for General Relativity and Quantum Field Theory are great for what they do, but they don’t — and can’t — do everything. Our theory of gravity and our quantum theories of particles and fields are fundamentally incompatible with one another: they cannot explain, for example, how the gravitational field of a quantum system behaves. Moreover, our current framework cannot sufficiently explain: dark matter, dark energy, the ultimate origin of our Universe, or the reason why our Universe is filled with matter and not antimatter, among other puzzles. It’s true that mathematics enables us to quantitatively describe the …

Header goals are disappearing from the World Cup

Header goals are disappearing from the World Cup

Published by Jenni Sidey

Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy. You may unsubscribe at any time. Headers are a staple in soccer, but the impressive (if painful-looking) technique is slowly accounting for fewer iconic moments from the sport’s best players. After crunching the statistics, Northeastern University’s NetSI Sport researchers say the number of header-assisted goals in FIFA World Cup matches has decreased from 23.7 percent in 2018 to just 17.9 percent through 2026’s Round of 16. That said, the tactic is still paying off this year. Over 11 percent of headers resulted in successful team possession conversions while their overall accuracy is around 33.5 percent. There are far more header attempts in 2026 than in either 2018 or 2022. Credit: NetSI Sport That doesn’t mean teams aren’t opposed to using the technique. Far from it, actually. Northeastern researchers reported …

Mathematics of thermodynamics is being rewritten after 200 years

Mathematics of thermodynamics is being rewritten after 200 years

Published by skeptic

Comparing thermodynamics to marbles and their shadows offers a new way to study the famous theory Priscila Zambotto/Getty Images The theory of thermodynamics has helped us understand devices like engines for more than 200 years, but its mathematical foundations have always been a little too imprecise. Now, researchers are putting the famous theory on a firmer footing, with mathematics more commonly used to describe quantum fields. Among all branches of physics, thermodynamics is among the easiest to connect to everyday life. This is because its development was driven in part by engineers looking to understand and maximise the efficiency of heat engines, which are idealised devices that model a wide range of familiar technologies, including car engines and refrigerators. But although thermodynamics is a very successful theory, it has historically lacked mathematical rigour, says Bryan Roberts at the London School of Economics and Political Science. He has set out to rebuild it based on mathematical ideas that draw on geometry and quantum field theory, a notable departure from how thermodynamics has long been understood and …

Did you solve it? Dotty data and silly sentences | Mathematics

Did you solve it? Dotty data and silly sentences | Mathematics

Published by Sam Flores

Earlier today I set these three puzzles about deception. Here they are again with solutions. 1. Super syllabus A school cohort has two classes. At the end of the year 1, all pupils are graded. When all the pupils are listed in grade order, the median pupil is a C. (The median is the middle value in a data set listed from smallest to largest.) For year 2, the school introduces a new syllabus. At the end of the year, all pupils are again graded. Now when the pupils are listed in grade order, the median has dropped to a D. Devise a scenario in which the new syllabus in fact improved every pupil’s grade. Solution Imagine that in the first year everyone in one class gets a C and everyone in the other gets has an E. If there is one more person in the first class, the median pupil gets a C. Now lets say that in the second year, everyone with a C improves to a B, and everyone with an E …

S-M-A-R-T researchers used mathematics to crack Wordle

S-M-A-R-T researchers used mathematics to crack Wordle

Published by Jenni Sidey

Every day, millions of people open Wordle and stare at five empty boxes, hoping the right first guess will unlock the puzzle. A new study argues that the smartest opening move is not the word that feels most likely, but the one that tells you the most. That distinction pushed a team at Binghamton University in a different direction. Instead of chasing the answer right away, they built a Wordle strategy around Shannon entropy, the mathematical idea used to measure uncertainty and information. In their version of the game, each guess is judged by how much it can shrink the field of possible answers. The result was a solver that, in the team’s tests, beat a more familiar letter-frequency approach by a wide margin. Across simulations using all 2,315 possible Wordle solution words, the entropy-based strategy solved almost every puzzle within six tries, while the baseline method succeeded about 90% of the time. That may sound technical for a word game, but the logic is simple. Wordle is really a feedback system. Every guess gives …