ON October 6, 2026, OpenAI put out a document announcing new solutions to longstanding mathematical problems proved by an Artificial Intelligence (AI) model. In itself, this was not surprising, since the last few months have witnessed a series of new and exciting results in mathematics proved by some AI model or the other. Yet, the October 6 announcement turned out to be a different category altogether: some would describe it as a bombshell, some would call it a major disruptive event in the history of science.

What is all the fuss about? The document was a list of “abstracts” of 722 mathematical papers, something like what you would expect from a large conference of mathematicians, produced by an undisclosed reasoning model that is internal to OpenAI. Each of the papers claims to have solved an intricate mathematical problem, and many of which  have intrigued scientists for a long time. They span a wide range of 17 fields featuring hundreds of complex proofs. Several of these proofs have been “formally verified” by programs designed for that purpose, while several others are being scrutinised by groups of mathematicians. There has never been a time like this in the history of mathematics in which  so many results were claimed in a single  day.

This was a veritable tsunami of machine generated theorems  inundating the field of mathematics. Mathematicians and theoretical computer scientists were forced to admit, whether they liked it or not, that the days of AI being a “powerful assistant” to the human mathematical researcher were decisively over, that AI is now aggressively outpacing human output.

Many mathematicians are in a state of shock, numbed by the knowledge  that what they had been trying to do for years has now been accomplished by a machine in such a short time. Many young mathematicians are wondering if they have any future at all.

Among the problems solved are a few that I know very well, and one that some of us had worked on intermittently over some years, gave up and moved on. Now that I see the solution, I can see three different techniques employed, two of which I know very well and lectured on, but never thought to combine those two. Generative AI can do just that, see patterns across seemingly unrelated areas and offer new combinations. In principle human beings could do this as well, but we may need to wait years for the triggers to make it happen, whereas AI can get there very fast.

As one mathematician put it, “It is as if we have all been riding bullock carts, and this is like riding  a racing car.”

HOW WAS ALL THIS MADE POSSIBLE?

AI has been around for about 60 years, but it was ChatGPT, the software released by OpenAI in November 2022, which  showed that AI could chat with you like a friend, write essays, letters, poems and more. ChatGPT is an example of a Large Language Model (LLM) that uses huge computing power to keep track of patterns in language use and can refer to such a vast database of human language use that it can sound very well like human beings. In the last four years, many LLMs have  been released.

One surprising capability of ChatGPT was that it could also be used to write computer programmes. How did this happen? Scientists realised that once you had a language model powerful enough to understand something as complex as human language and literature, then it could much more easily understand highly structured human constructed languages such as that of mathematics.

In the last two years, this capability has been demonstrated many times over. Throughout 2025 AI repeatedly kept solving research level mathematical problems. But none of those problems were considered exceptionally hard by mathematicians.

2026 has changed all that. AI programs have now solved very famous open problems. In February 2026, Google DeepMind used its Gemini model to survey 700 open problems posed by Erd"os (a Hungarian mathematician  famous for posing problems), solved four of them and found nine new solutions of solved problems. By May 2026, OpenAI and Anthropic were locked in a race, each trying to show that it had more  advanced reasoning capability, by solving complex problems that mathematicians had been working on for many decades, even a century or two.

September 2026 saw something more shocking. OpenAI announced that its system could solve a major aspect of one of the most difficult problems  of all time, the Navier Stokes equation. This is so special that it figures among the 7 millennium problems announced by the Clay Institute, solving any one of which merits a million US dollars as a prize. However, OpenAI’s 146 page proof is considered too dense even for mathematicians to understand, and verifying it will take considerable  time. There was also some accusation that OpenAI “stole” the idea from some mathematicians.

How is all this possible for AI? Using thousands of AI agents that work in parallel allows AI models to explore multiple failed paths, then step back, retry repeatedly for much  longer than human researchers typically can (without getting frustrated or bored!). Moreover, AI agents can check their own work using computer programs that act as proof assistants, ensuring that despite their length, the computer code verifies the logic as mathematically sound. This greatly accelerates the search-verify-retry cycle.

REACTIONS AND THE ROAD AHEAD

While one section of mathematicians have hailed the recent OpenAI release  as a remarkable breakthrough, several have responded with shock and dismay. Proofs are not isolated logical truths, they are supposed to create or advance human understanding. AI-generated proofs use non-standard notation, convoluted structures and exploit unnatural loopholes that obscure (human) intuition. Moreover, OpenAI by-passed the peer review norms established by the community over a long time. There is also no transparency in methods, as OpenAI has not disclosed the reasoning model it uses, calling it “internal” to the company.

One concerning impact of AI is that the commons are already thinning: from 2022 to now, researchers posting questions on the internet and helping each other has reduced to half; and in the case of students, it has become less than one-tenth. This is because both now use AI privately.

What is undeniable is that Oct 6 signals a new era, a big change in the way mathematical research will likely be conducted henceforth. As machine generated mathematics scales, reliance on machine-checked mathematics will also become important. We can foresee an era of industrial mathematics: the output not of  individual mathematicians or their teams but of automated processes, perhaps with mathematicians acting as quality controllers.

All this exposes at least one fundamental flaw in the way mathematics has been working. For a couple of centuries mathematics has privileged results over processes. Solving open problems is privileged, and getting there first is celebrated. Yet  the process of mathematics is different and is also important --- those who love mathematics do it because they relish discovery, the sustained creative struggle, the repeated failures from which they learn, the communication with colleagues, the social processes of inquiry, the long life over which solutions mature, the sudden flashes of intuition amidst the slow gathering of intuition. They share all this with students, but these processes are rarely documented. However, these detours and half-formed intuitions yield important results down the line, as they prepare our minds for further explorations. As output generation gets taken over by machines, will these processes survive, are they not  worth cherishing? Will societies (taxpayers, governments) be willing to support mathematicians to preserve such processes? Without such processes and a vibrant community pursuing them, how would humanity even develop the capacity to ask the right questions?

On the other hand, the industrialisation of mathematics can lead to new socially prioritised questions being addressed mathematically. Divisions such as pure vs applied mathematics, deductive vs experimental mathematics and more may well disappear, paving the way for explorations of an altogether new kind may benefit humanity. Today, mathematical models can rarely work with real data, real objects: they get abstracted out, “smoothed out” to ideal objects, reasoned about and finally, whatever is deduced or derived is applied back on the real objects, with corrections applied appropriately. This is appropriate for human work. With the advent of computing power, it was expected that we could cut this short, directly work with objects in all their messy detail. However, the reasoning ability needed was missing: perhaps AI has now proven this capability.

Lest we get carried away by such rosy speculation, we should remind ourselves that the current wave of machine generated mathematics is entirely fuelled by corporate greed. As it stands, corporate monopoly will more likely seek to own the new machine driven mathematics, monetise it and commercialise it, leaving behind many worthwhile goals.

The road ahead for mathematics is uncertain. Is this an opportunity for the creation of a new era in mathematics, one that helps build human capability to solve the central problems of humanity? Yes, but only if underlying socio-political structures seek such transformation and enable it, rather than merely surrender to machine-generated solutions: it depends on who builds the machines and why, who controls them and how.