{"id":822252,"date":"2026-07-24T03:44:24","date_gmt":"2026-07-24T03:44:24","guid":{"rendered":"https:\/\/www.newsbeep.com\/ca\/822252\/"},"modified":"2026-07-24T03:44:24","modified_gmt":"2026-07-24T03:44:24","slug":"a-new-golden-age-of-mathematics-may-be-dawning-thanks-to-ai-and-human-ingenuity","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ca\/822252\/","title":{"rendered":"A new \u2018golden age\u2019 of mathematics may be dawning \u2014 thanks to AI and human ingenuity"},"content":{"rendered":"

In May 2026, OpenAI released a new math result<\/a> that sent shock waves throughout the world of mathematical research<\/a>. A major unsolved problem called the \u201cunit distance conjecture\u201d had just been resolved by generative AI<\/a>. <\/p>\n

Since then, there has been a steady drumbeat of new results that either partially or completely leverage artificial intelligence to solve research-level mathematics problems. However, most new math results published in any given month are still generated by humans.<\/p>\n

So where is this going? How good, and how quickly, will AI capabilities grow? Will most mathematical research be predominantly artificial intelligence? Or, as some mathematicians suggest<\/a>, will AI combine with human ingenuity and other computer tools to create a golden age of mathematics? <\/p>\n

A list of unsolvable problems<\/p>\n

One of the most prolific mathematicians of the 20th century was Hungarian Paul Erd\u0151s<\/a>, known for the breadth of his collaborations with mathematicians across many sub-fields. <\/p>\n

\"\"<\/a><\/p>\n

Paul Erd\u0151s teaches future mathematician Terence Tao in 1985, at the University of Adelaide.
\n (Wikimedia Commons), CC BY-SA<\/a><\/p>\n

Throughout his career, he proposed hundreds of unsolved problems that
\ntoday are known as Erd\u0151s problems<\/a>. This list is a tempting place to start for any AI company wishing to show it can solve problems in mathematics. <\/p>\n

Over the decades, human researchers have steadily resolved many of the Erd\u0151s problems, but a large number remain unsolved. One was the unit distance problem from the field of geometric graph theory. <\/p>\n<\/p>\n

The author Trefor Bazett explains the unit distance problem.<\/p>\n

Humans on the shoulders of AI<\/p>\n

This wasn\u2019t the first mathematical problem to be solved by AI \u2014 it wasn\u2019t even the first Erd\u0151s problem to be solved by AI \u2014 but it was the most significant. The unit distance problem is a prominent one that many researchers have attempted to solve since 1946, when it was proposed.<\/p>\n

It was particularly noteworthy that, having read the proof of the unit distance problem by AI, it was human researchers who managed to adapt the central technique of the proof to solve \u2014 only a week later \u2014 another significant conjecture called the \u201csum-product conjecture.\u201d<\/a> <\/p>\n

Much as the AI result rested on the shoulders of many mathematicians before it, humans were able to climb one step higher due to advances by AI. <\/p>\n<\/p>\n

The author Trefor Bazett explains how the sum product conjecture was disproven.<\/p>\n

A combination of technologies<\/p>\n

Computer-based tools have been helping humans with mathematics for as long as there have been computers. These tools have become increasingly sophisticated and might run on the world\u2019s largest supercomputers, modelling climate change or pandemics. <\/p>\n

Even within pure mathematics, preliminary research shows that proof of some theoretical results can grow to petabytes in size<\/a> \u2014 that is equal to one million gigabytes.<\/p>\n

Computational tools aren\u2019t the only way computers are aiding humans. How can you be convinced about the validity of an argument too large or technical to be easily verified even by experts? Using a computer language created for proof-verification, mathematicians can make extremely precise versions of every component of an argument. Then the proof-verification system checks that every step logically follows from the underlying axioms, or starting points, of the proof. <\/p>\n

In a recent pre-print paper<\/a>, mathematicians combined each of these technologies \u2014 computational tools, proof verification and artificial intelligence \u2014 together with their own human ingenuity to achieve a new result in a field of math called Ramsey theory. <\/p>\n<\/p>\n

The author Trefor Bazett explains Ramsey theory.<\/p>\n

After exhaustive and rather clever computational searches, AI was able to conjecture a general pattern for a particular phenomenon, prove that the pattern did indeed hold and help the authors convert the argument for proof verification.<\/p>\n

This combination of technologies led them to believe that we are now entering a \u201cgolden age\u201d of mathematics. <\/p>\n

Million-dollar math problems<\/p>\n

Today the capabilities of AI are mixed. Some mathematical fields, notably graph theory, have been particularly amenable to AI-based proofs, but others seem quite resistant. <\/p>\n

For every math problem AI does solve, there are huge numbers of problems that AI has failed to solve when prompted. For the most famous unsolved problems \u2014 such as the six remaining Millennium Prize problems where the Clay Mathematics Institute<\/a> will pay you a million dollars if you can solve one of them \u2014 the problems seem as completely out of reach for AI as they do for us humans. <\/p>\n<\/p>\n

Mathematician Sir Michael Atiyah explains the millennium problems.<\/p>\n

As to the future, we don\u2019t know how far and how fast AI\u2019s capabilities will grow. If progress is substantial, what will mathematical research look like for humans in five or 10 years? These early examples where humans built on AI results or leveraged AI along with existing tools to achieve new mathematical heights could give a glimpse of one possible future. <\/p>\n

On the flip side, student anxiety about spending years of their lives honing their mathematical skills is understandable. There are natural fears about AI replacing humans in research mathematics. Thankfully, we\u2019re not close to that yet.<\/p>\n","protected":false},"excerpt":{"rendered":"In May 2026, OpenAI released a new math result that sent shock waves throughout the world of mathematical…\n","protected":false},"author":2,"featured_media":822253,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[62,276,277,49,48,61],"class_list":["post-822252","post","type-post","status-publish","format-standard","has-post-thumbnail","category-artificial-intelligence","tag-ai","tag-artificial-intelligence","tag-artificialintelligence","tag-ca","tag-canada","tag-technology"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/822252","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/comments?post=822252"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/822252\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media\/822253"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media?parent=822252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/categories?post=822252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/tags?post=822252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}