How AI is breaking math

Hi, and happy Tuesday.

On July 23, 2026, days after receiving the Fields Medal - mathematics' highest honor - Jacob Tsimerman announced that he was temporarily leaving academia to work on AI safety at OpenAI.

In a recent interview, he said he was “grieving.”

Not because he thinks mathematics is dying.

Quite the opposite.

He thinks mathematics may be about to produce far more discoveries than humans can keep up with. 

Tsimerman spent roughly 12 or 13 years on one of the projects behind his Fields Medal.

Another took around five years.

That pace gave him time to learn a field, understand its mysteries and slowly develop intuition.

His concern is what happens when an equivalent project takes an AI a month. Or a week.

A mathematician might open their laptop on Monday and discover that their specialty has advanced 15 years over the weekend.

And then it happened.

Within days of Tsimerman joining the OpenAI, the AI lab announced its AI had solved the “sphere packing problem.”

You can imagine packaging oranges into a crate.

Because oranges are round, there will always be gaps between them. Stack them carefully in the familiar pyramid shape and you can fill about 74% of the box.

Mathematicians spent centuries proving that you cannot do better.

Not just for objects with 3 dimensions, but for objects of 1000s of dimensions!

You might ask, “what kind of objects have 1000s of dimensions”?

If a 5G router bundles 1,000 independent pieces of data into a single signal burst, that burst is mathematically treated as a single point moving in 1,000-dimensional space.

Similarly, in materials science and metallurgy, high-dimensional sphere packing helps physicists understand the behavior of complex structural materials.

But for almost 50 years, there was a limit on what mathematicians could prove about these “1000 dimensional oranges” problems.

Since 1978, the rate at which you lose usable space to empty "air" every time you add another dimension was shown to be 0.59906 - proved by Kabatianskii–Levenshtein using harmonic analysis.

In 2003, mathematicians Henry Cohn and Noam Elkies invented a completely new, much more powerful tool called Linear Programming Bounds.  Cohn and Elkies ran simulations for lower dimensions (like 5, 10, or 20) and could see the rate dropping beautifully from 0.59906 to exactly 0.6044.

The problem was scaling it to infinity. To prove that the limit becomes exactly 0.6044 for all infinite dimensions, you had to find a master algebraic equation - a specific "magic formula."

For over 20 years, human brains couldn't find the formula because the algebra was too intensely complicated.

And then it happened.

Earlier this month, OpenAI announced that an unreleased AI model called Astra had discovered the exact mathematical formula that humans hadn’t been able to figure out.

The AI simply possessed the massive logical stamina required to navigate the brutal algebra.

And that’s not all.

Sphere packing was only one of ten new mathematical discoveries from Astra.

The discoveries ranged across geometry to group theory, cryptography and theoretical computer science

OpenAI says the cost of generating each solution would have cost about $2,000.

“Would have” because it does not include the cost of the failed attempts on the way to the magical formula, or the small industrial civilization required to build frontier AI.

You can probably see where this is going.

AI can produce magic, when it's correct (and after many failed attempts).

But you still need experts - such as real mathematicians - who not only know when it's correct, but can steer it to produce that correct result.

This is increasingly how we think about our work at Prescouter: if you put the right problem in front of the right expert, and give them every tool available - including AI - that expertise becomes dramatically more powerful.

You’re not replacing the expert. You’re giving them superpowers.

Best,

Dino