BLOGWhere do we stand in the development of AI mathematics?What is possible?
An update from Howard Covington since this newsletter was initially prepared
We now know how long predictions about AI’s maths ability are good for: the answer is about a week. OpenAI has just released 722 manuscripts covering 372 families of mathematical results. Remarkably, the results were not achieved by brute force, trial-and-error methods, as has been the case with previous results, but by deep mathematical reasoning. In particular, astonishing progress has been made on the Riemann Hypothesis, the crown jewel of unproven mathematical conjectures. The Riemann Hypothesis, dating from 1859, specifies how the prime numbers are distributed among the counting numbers. Prime numbers are the building blocks of the number system, so the Riemann Hypothesis is central to understanding the deep structure of numbers. While OpenAI didn’t prove the Riemann Hypothesis, it was able to prove an important intermediate result. This was done by a single AI agent reasoning for three hours from a single prompt. Along the way, important supporting ttheorems were proved. The first reaction of the maths community is that if the AI were human it would receive the Fields Medal, the maths equivalent of a Nobel prize. It appears that AI has become an expert mathematician.
Which tasks do mathematicians face?
Put simply, mathematicians face three tasks. The first is to formulate subtle conjectures about what might be capable of mathematical proof in a particular area of their subject. A conjecture must at least be interesting and if possible should be profound. The second task is to prove the conjecture in the general case. If a general proof is too difficult for the moment, a third task is to explore many examples of what the conjecture implies in order to find a case that could confirm or disprove it.
Will we still need human mathematicians in an AI-dominated world?
One can imagine that a mathematical superintelligence will create vast new fields of maths. These will provide a wonderland of theorems for pure mathematicians to explore and for applied mathematicians to seize on to solve practical problems. It will reinvigorate, rather than replace, human mathematical creativity. Maths will change greatly, but there will continue to be a huge amount for human mathematicians to do.
Will AI help us understand the beginning of the universe?
One area where physicists would welcome new maths is understanding the instant the universe began. The force of gravity was then overwhelmingly strong and was integrated in some way with the other forces that hold matter together. It was also when time itself emerged from something that was without time. Solving the maths of creation and emergent time is certainly a fitting problem for a coming mathematical superintelligence.
Howard Covington is a Cambridge graduate in physics and mathematics who went on to a career in investment banking. From 2015 to 2022, he served as the inaugural chair of the Alan Turing Institute, the UK’s national institute for data science and artificial intelligence. Since 2025, he has chaired the advisory board of Oxford University’s Smith School of Enterprise and the Environment.
