AI just cracked maths problems that stumped people for decades — explained

If you saw headlines about AI 'solving maths problems' in May and weren't sure what to make of them — here's the plain-English version, with the hype dialled out. The short answer: yes, something real happened, and no, it doesn't mean your phone is now smarter than a maths professor.

OpenAI said one of its reasoning models disproved an idea about geometry first suggested by the mathematician Paul Erdős back in 1946 — showing the long-assumed 'best' arrangement of points wasn't actually best. The neat part: nobody could have looked up the answer, because there wasn't one. The AI had to genuinely work it out.

Google DeepMind then said its system, AlphaProof Nexus, solved nine other long-open Erdős problems — two of which had been unsolved for 56 years — plus 44 more conjectures from a big catalogue of number sequences. And it did it cheaply: just a few hundred dollars of computing per problem, which is part of why it raised eyebrows. Who is Erdős, and why him? He was a famously prolific mathematician who left behind hundreds of precise, fiendishly hard open questions. They make a perfect test for AI because you can't bluff or look up the answer — there isn't one to find. Two different companies, two different methods, in the same week. That's why it felt like a moment rather than a press release.

Here's the clever bit, and it's the part that actually matters. AI can sound completely confident and still be wrong — you've probably seen a chatbot make something up. So Google's system pairs the AI with a proof checker called Lean: software that flat-out refuses to accept a proof unless every single step is logically airtight. The AI suggests an answer; Lean acts like an unbribable examiner. That's the difference between 'an AI said so' and 'the maths genuinely checks out'.

OpenAI's result was checked a slightly different way — by human mathematicians, including a famous one named Timothy Gowers — and it's still going through formal review. That's a bit like a respected expert reading your work versus a strict machine grading it: both are reassuring, but the machine catches things that tired human eyes might miss. Neither is fake; they're just different levels of confidence, and it's worth knowing which is which when you see the word 'solved' in a headline. DeepMind's nine come with the machine's stamp; OpenAI's one comes with the experts' — for now.

Why this might matter to you down the line: the same 'AI suggests, software checks' trick could make AI far more reliable in any area where answers can be verified — think code that's automatically tested, or sums that are independently re-checked — which means fewer confident mistakes and more results you can actually rely on. That's the quietly exciting part, even if it's a long way from the robot-mathematician headlines. For now, the honest summary is simple: AI just became a genuinely useful new helper for some of the hardest maths around, the answers have been carefully checked, and the people who built it are the first to say it isn't magic. Impressive, trustworthy, and refreshingly un-hyped — a rare combination worth enjoying.