Mathematics – latest in science and technology | New Scientist

Mathematicians put AI to work on Fermat’s last theorem

Matthew Sparkes — Fri, 10 Jul 2026 11:00:18 +0000

At an event in London, mathematicians have made unexpectedly fast progress on formalising Fermat's last theorem using AI

The sneaky maths trick for solving problems without answering them

Jacob Aron — Fri, 10 Jul 2026 08:00:57 +0000

How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – but 100 years on, this trick is a common part of modern maths, says columnist Jacob Aron

The maths meme that has been distracting mathematicians for a century

Jacob Aron — Fri, 05 Jun 2026 08:00:46 +0000

A seemingly simple set of rules kicks off a kind of mathematical magic trick, which has kept great minds busy since the 1930s. Columnist Jacob Aron explores the origins of the Collatz conjecture, why it is so addictive to mathematicians and whether AI could help us solve it once and for all

Explore the mind-bending and paradoxical art of M C. Escher

Alex Wilkins — Wed, 03 Jun 2026 17:00:32 +0000

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

Alex Wilkins — Mon, 01 Jun 2026 15:00:40 +0000

Mathematicians are stunned at the progress AI is making in solving advanced problems, leaving some questioning whether there will still be room for humans

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

Alex Wilkins — Fri, 29 May 2026 14:20:15 +0000

Setting your sights high can lead to bigger rewards – up to a point

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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.

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The foolproof way to win any lottery, according to maths

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 at the University of Warwick, UK. Now, using mathematical models, 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 the moon,” says Burgess. He and his team first came up with a statistical model for how a person might weigh up different outcomes, varying their willingness to settle for more or less ambitious results. From this, they derived a formula for the overall reward someone might receive according to their satisfaction threshold. Then they tested this model with random potential outcomes and varied how they might appear, such as how many outcomes a person has to choose between in a set period of time, how many bad outcomes compared with good outcomes there were, or how much time and effort it took to choose a particular outcome. After running thousands of simulations and comparing the results to real-world datasets, such as university applications and US election polls, Burgess and his team found that the optimal outcomes indeed came when people aimed above the average reward, but not near the maximum. This wasn’t surprising given the common wisdom that people tend to follow, says Burgess, but the team was surprised to find that this picture changes when scenarios are biased towards one very bad or good outcome. Typically, if most outcomes are mediocre but one is extremely bad, such as a recession once every 10 years, the common wisdom is to be cautious. But Burgess and his team found that the best approach is actually to be more ambitious than you would be if the rewards were more even. “We find, compared to the average, you want to be a little bit more ambitious [in these scenarios], because you don’t want to be thrown off by these bad years dragging the average down.”

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The surprising maths that explains why coincidences are so common

Similarly, when one outcome is extremely good, such as a start-up making $1 billion or nothing, you should be a little less ambitious than average. “It’s actually initially so counterintuitive that when my colleagues showed me the result, I thought that they had made a mistake,” says Burgess. Hills, who wasn’t involved in the study, points out that people might have different ideas on how they balance risk and reward. “Some people may prefer to have a stable income rather than an ‘optimal’ but potentially riskier income, for example,” he says. “Moreover, some environments are winner-takes-all environments, where social comparisons are more important, and in those cases risk-seeking ambition may be more appropriate.”

Journal reference:

Physical Review E

Mathematical AI helps researchers crack 50-year-old problem

Alex Wilkins — Thu, 28 May 2026 15:00:57 +0000

After an AI from OpenAI found a trick to solve an 80-year-old conjecture from Paul Erdős, mathematicians have borrowed the same technique to solve another important problem

Start-ups are racing to revolutionise mathematics with AI

Alex Wilkins — Thu, 28 May 2026 12:00:09 +0000

AI start-ups with hundreds of millions of dollars in funding are hiring mathematicians and building AI systems that they hope will not only solve mathematics, but also build more intelligent AI

Mathematicians stunned by AI’s biggest breakthrough in mathematics yet

Alex Wilkins — Thu, 21 May 2026 15:13:12 +0000

Artificial intelligence built by OpenAI has cracked a decades-old conjecture by Paul Erdős, which mathematicians have hailed as a monumental moment for AI in mathematics

Mathematics keeps discovering things that shouldn’t exist

David Stock — Fri, 08 May 2026 15:00:25 +0000

The deeper mathematics goes, the stranger everything becomes. The maths you learned at school was a world in which everything had a neat solution, and mind-bending concepts like infinity were glanced over in lieu of another equation where you had to solve for x.

In this marathon, we’ll explore the very boundaries of maths, find out where the equations falter and where they uncover hidden truths about the universe. You’ll learn about infinty, prime numbers and a number so large it brings us to the very edge of what we can calculate.