The Biggest Math Story of 2025

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The year that was 2025 has all but come and gone, so it’s the perfect time to look back at the year’s biggest math stories!

For our selection criteria, we’ve emphasized math stories that involve practical applications in selecting both the contenders and the Biggest Math Story of 2025, which we’ll present at the end of this year’s edition. That real world connection is something we find essential in exploring achievements in math, which is why we place our main focus on it.

But that doesn’t stop us from appreciating the year’s “pure” math accomplishments. For example, we’re fans of the work by the volunteers behind the Great Internet Mersenne Prime Search project, which is dedicated to identifying these special prime numbers. Last year, they made news when a volunteer found the current record holder for the largest known prime number, M(136,279,841), the 52nd Mersenne prime.

While they didn’t find a bigger prime number this year, their work to verify that no other Mersenne primes fit in-between the gaps of their previous discoveries continued. In 2025, they expanded their test results to verify that they had identified all Mersenne primes smaller than M(77,232,917), the 50th Mersenne prime. We anticipate they’ll clear the distance between that prime and M(82,589,933), the 51st Mersenne prime, sometime in 2026.

There is however an enormous gap between the 51st Mersenne prime and the current-52nd Mersenne prime that may very well contain one or two additional Mersenne primes. We are very much looking forward to what they find.

That’s enough gushing about prime numbers, so let’s get to the biggest math stories of the year that was. Starting with….

The Elephant in the Room

2025 was a year in which avoiding any mention of developments related to Artificial Intelligence (AI) models and the Large Language Models that have come to define the machine learning technology was all but impossible. Hundreds of billions of dollars all around the world are being invested to build and develop the infrastructure needed to support advanced AI systems.

Many disciplines felt the impact of AI technology in 2025 and mathematics is one of many in which AI systems are starting to have a profound impact.

One of the more unique stories we encountered is about one of the first valid mathematical proofs ever produced by a generative AI system. That story came to our attention through a post at X and it’s probably best to let that post tell the tale: