All posts tagged: Mathematicians

The maths meme that has been distracting mathematicians for a century

The maths meme that has been distracting mathematicians for a century

Published by skeptic

A tree-like form arises out of numerical connections in a famous maths puzzle known as the Collatz conjecture Marzio De Biasi/Algoritmarte Almost a century ago, a mathematician came up with a puzzle that was so seemingly simple and yet so fiendishly difficult that it has been distracting other mathematicians ever since. It has become a meme that jumps from brain to brain, with many people claiming to have solved it, only to have their hopes dashed as the proof unravels. And be warned – once I explain the rules, you will immediately want to start playing around with it yourself, and I take no responsibility for how much of your time you waste. It starts a bit like a magic trick. Pick a number, any number – well, at least any positive whole number; don’t try to get clever with something like pi. If it is an even number, divide it by 2. If it is an odd number, multiply it by 3 and add 1. Next, apply the same rules to the resulting number. …

A golden age of maths is dawning and mathematicians are freaking out

A golden age of maths is dawning and mathematicians are freaking out

Published by skeptic

I am attempting to solve a mathematical conundrum that has stumped many of humanity’s greatest thinkers. I have zero mathematical training, apart from a distant undergraduate physics degree, which should put my odds of success at slim to none. But I also have a trick up my sleeve – a kind of mathematical genie that can conjure arcane secrets seemingly out of thin air. I make a short request concerning an esoteric conjecture in number theory, then cross my fingers. Perhaps “genie” is a bit too strong – I’m simply using GPT 5.5 Pro, the latest iteration of OpenAI’s flagship model. But for mathematicians, modern AI models appear to have a spark of magic. Even in an era of rapid progress, the growth in AI’s mathematical ability is stunning. In just a few months, many prominent mathematicians have walked back previous scepticism and replaced it with sweeping predictions, whispering behind closed doors about job concerns and whether it is even worth embarking on a particular research project if AI might get there first. In April, …

Aim high but don’t shoot for the moon, mathematicians advise

Aim high but don’t shoot for the moon, mathematicians advise

Published by skeptic

Setting your sights high can lead to bigger rewards – up to a point Buena Vista Images/Getty Images Shoot for the moon and even if you miss, you’ll land among the stars, so the saying goes. But shooting straight for the stars instead might actually be the more effective option, according to mathematicians. In life, people tend to try to be ambitious, yet not overly so, when it comes to pursuing their objectives, such as landing a better job, finding an appropriate partner or achieving political goals. However, quantifying this balance hasn’t been studied in detail, and much research has focused on when people stop looking too soon and aren’t ambitious enough, says Thomas Hills at the University of Warwick, UK. Now, using mathematical models, Matt Burgess at the University of Wyoming and his colleagues have found that the best outcomes for uncertain scenarios typically come from aiming high, but not unrealistically so. “You can prove that the optimal ambition is strictly above average and strictly finite, meaning above average but you don’t shoot for …

Mathematicians stunned by AI’s biggest breakthrough in mathematics yet

Mathematicians stunned by AI’s biggest breakthrough in mathematics yet

Published by skeptic

The planar unit distance problem is about how many equal-sized lines you can draw that connect dots on an infinite sheet of paper Noga Alon et al. 2026, Open AI An 80-year-old maths conjecture that has eluded the world’s greatest mathematicians has been cracked by an artificial intelligence model built by OpenAI. The result has stunned experts and is being hailed as a seismic moment for AI’s mathematical ability. “This is a problem that I didn’t expect to see solved in my lifetime,” says Misha Rudnev at the University of Bristol, UK. “It’s absolutely a bomb.” Tim Gowers at the University of Cambridge wrote that the solution is “a milestone in AI mathematics” in a blog post accompanying the work. “If a human had written the paper and submitted it to the Annals of Mathematics and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that.” Twentieth-century mathematician Paul Erdős considered the puzzle, known as the planar unit distance problem, …

Mathematicians Claim Significant Discovery Using ChatGPT

Mathematicians Claim Significant Discovery Using ChatGPT

Published by José Betancourt

Sign up to see the future, today Can’t-miss innovations from the bleeding edge of science and tech Did ChatGPT just solve an arcane math problem that’s foiled mathematicians for over sixty years? Some leading experts say yes, Scientific American reports. Earlier this month, 23-year-old Liam Price shared a solution to one of the so-called Erdős problems, a series of famously abstruse math conjectures left behind by the Hungarian mathematician Paul Erdős. While some of these conjectures have gotten the better of savants in the field, Price, who has no advanced math degree, seemingly stumbled on a solution for one of them by simply prompting GPT-5.4 for an answer. While many AI-generated Erdős solutions have turned out to be a bust, experts who viewed Price’s response — which was posted to erdosproblems.com — say it’s the real deal. “This one is a bit different because people did look at it, and the humans that looked at it just collectively made a slight wrong turn at move one,” Terence Tao, a mathematician at the University of California, …

Mathematicians figured out the perfect espresso

Mathematicians figured out the perfect espresso

Published by Jenni Sidey

Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent six days a week. People love a good cup of coffee, but how do you get a perfect brew? Barring philosophical deep dives into the nature of perfection, an international team of mathematicians and environmental scientists believe that it’s entirely possible to calculate the ideal espresso. Not only that, but they now have the formulas to back it up. The math detailed in their study published in the journal Royal Society Open Science is dense. But the short answer is that’s all about puck size. Picture the typical espresso machine at your favorite cafe. The small dish into which your friendly barista tamps coffee grounds is called the puck. After inserting it into the machine, hot water flows through the receptacle and molecularly absorbs the beans’ flavor, hue, and (most importantly) caffeine.  The quality of the final espresso depends on many aspects, including how the grounds are packed, how long water passes through the coffee, and the size of the grounds themselves. It’s …

This startup wants to change how mathematicians do math

This startup wants to change how mathematicians do math

Published by skeptic

Geordie Williamson, a mathematician at the University of Sydney, who worked on PatternBoost with Charton, has not yet tried Axplorer. But he is curious to see what mathematicians do with it. (Williamson still occasionally collaborates with Charton on academic projects but says he is not otherwise connected to Axiom Math.) Williamson says Axiom Math has made several improvements to PatternBoost that (in theory) make Axplorer applicable to a wider range of mathematical problems. “It remains to be seen how significant these improvements are,” he says. “We are in a strange time at the moment, where lots of companies have tools that they’d like us to use,” Williamson adds. “I would say mathematicians are somewhat overwhelmed by the possibilities. It is unclear to me what impact having another such tool will be.” Hong admits that there are a lot of AI tools being pitched at mathematicians right now. Some also require mathematicians to train their own neural networks. That’s a turnoff, says Hong, who is a mathematician herself. Instead, Axplorer will walk you through what you …

The success of machine mathematicians shows us how to be OK with AI

The success of machine mathematicians shows us how to be OK with AI

Published by skeptic

Have you ever received an email and had a sneaking suspicion it was written by AI, rather than lovingly handcrafted? Mathematicians have been wrestling with similar feelings for half a century, and have some lessons for the rest of us. It all began in 1976, when Kenneth Appel and Wolfgang Haken announced a proof of the four colour theorem, which states it takes a maximum of four shades to colour any map so that no two adjacent regions match. The theorem’s simplicity meant mathematicians were expecting an elegant proof revealing a greater mathematical truth. Instead, they got 60,000 lines of impenetrable computer code. Appel and Haken had solved the problem by programming a machine to systematically go through nearly 2000 kinds of map, representing every possible configuration. At the time, it felt unsatisfactory. But over the decades, mathematicians came to terms with using code in this way and resolved many of the philosophical objections. This meant when the current AI wave arrived, mathematics was ready. As we report here, AI is improving at such a …

Amateur mathematicians solve long-standing maths problems with AI

Amateur mathematicians solve long-standing maths problems with AI

Published by skeptic

AI tools are helping to decipher long-standing maths problems andresr/Getty Images Amateur mathematicians are using artificial intelligence chatbots to solve long-standing problems, in a move that has taken professionals by surprise. While the problems in question aren’t the most advanced in the mathematical canon, the success of AI models in tackling them shows that their mathematical performance has passed a significant threshold, say researchers, and could fundamentally change the way we do mathematics. The questions being solved by AI originate from Hungarian mathematician Paul Erdős, who was famous for his ability to pose useful but difficult questions during a career that spanned over six decades. “The questions tended to be very simple, but very hard,” says Thomas Bloom at the University of Manchester, UK. By his death in 1996, there were more than 1000 of these unsolved Erdős problems, spanning a wide range of mathematical disciplines, from combinatorics (the study of combinations) to number theory. Today, they are seen as signposts for progress in these fields, says Bloom, who runs a website that catalogues the …