Is AI changing mathematics for ever? R. Ramanujam, Bengaluru Ever since a company called OpenAI put out a software application (which we call "app") called ChatGPT in November 2022, many things have changed. ChatGPT is an example of programs that we commonly refer to as Artificial Intelligence (AI). These are computer programs that mimic human intelligence. AI has been around for about 60 years, but its achievements have been in specialised areas of robotics, game playing, planning, image recognition and computer speech. They were impressive, but not quite matching everyday human intelligence. One barrier has always been Natural Language Understanding and Synthesis: that is, it was hard to talk to these programs in human languages, and it was hard to make computers talk in a way that sounded natural to humans. ChatGPT ChatGPT showed that AI could cross that barrier; you could chat with it like you would with a friend, it would write essays, letters, poems and more. Even better, you could give your own poem to it, and ask it to rewrite in the style of a famous poet, and it can do this. Newer versions can actually write a full film script for you. BOX What is ChatGPT ChatGPT stands for Chat Generative Pre-trained Transformer. The word "chat" is obvious: you can chat with it. The key word "generative" means that it can create brand-new content, using whatever is already known. How does it know anything? It has been "pre-trained" by giving it a huge amount of data from the internet about different fields from which it generates new content. Finally, it has a special kind of network architecture ("transformer") which allows it to take words and phrases and put them together with proper relationship, in the required context. ChatGPT uses large language models (LLMs) which are AI systems designed to generated human-like text. They do this by trying to predict the next word, by searching their huge data-base which contains many sentences and phrases from known sources, so they have the right grammar and rules. END OF BOX 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 much like human beings. In the last four years, many LLMs have come out. Some like Deep Seek use much less computing power and show impressive reasoning ability. LLMs and Mathematics What does all this have to do with mathematics? One surprising capability of ChatGPT was that it could also be used to write computer programs. In the last few years, all the LLMs have shown remarkable ability to write code: so much so that many big companies like Google and Microsoft tell their programmers not to waste time writing code, but let the LLMs write it for them and fine-tune it. 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 computer programming languages. This is because such programming languages are highly structured, universal, and not specific to cultures. What is the most highly structured human constructed language that is truly universal? Mathematics, of course! Does this mean LLMs could do mathematics as well? People thought this, but also dismissed this early on. LLMs are "after all" language models, they can understand some superficial structure in written mathematical language, but surely they would not be able to understand the deep theorems of mathematics, let alone prove them. Modern LLMs and their maths skills In the last two years, this belief has been shown to be wrong. In the beginning of 2025, theorem proving programs like Alpha Geometry (not LLM based) could solve International Mathematics Olympiad problems but not at gold medal level. People said, this is still children's level. But throughout 2025 AI repeatedly kept solving research level mathematical problems. But none of those problems were considered exceptionally hard by mathematicians. So people said, it's interesting that AI can do all this, but it is no more than what we would expect from a university-level student. 2026 has changed all that. AI programs have now solved very famous open problems in mathematics. See Box for a list. These problems are too technical to explain at school level. These problems are "conjectures" made by mathematicians: statements of belief that a mathematical statement is true, without being able to prove it. Why do mathematicians do this? In the process of proving or disproving this claim, new ideas result, new techniques are developed, human understanding grows. The search itself tends to be valuable even when the original question doesn’t get answered. BOX AI and mathematics in 2026 Google has an AI lab called DeepMind. It has generated an AI sysem in biology that predicts 3-dimensional protein structures from amino acids. It has also generated the Gemini LLM. In February 2026, Google DeepMind used its Gemini model to survey 700 open problems posed by Erdos (a Hungarian mathematician who was famous for posing problems). It proved four of them and found nine unknown published solutions. OpenAI is another research lab. In May 2026, OpenAI announced that an internal model contradicted a conjecture of Erdos of the unit distance problem: given n points in a 2-dimensional place, what is the maximum number of pairs of points that can be exactly unit distance apart? (This is a nice example of Erdos' questions: simple to state and hard to prove!) After AI provided the proof, several mathematicians collaborated to produce a verification and exposition of the result. Anthropic is another AI research company which has built the Claude family of models. It is built on a training method called Constitutional AI whose core principles are that Claude must be helpful, honest and harmless. Hence this software is focussed on responsible development of AI tools. Claude writes poetry too! In August, mathematician Levent Alpoge announced that he had found a counterexample to the Jacobian conjecture (a hypothesis or guess, yet to be proved) using Claude Fable 5. This was a problem that mathematicians had been working on since 1939. September 2026 saw something even more shocking. OpenAI announced that its system could solve a major aspect of one of the most difficult equations of all time, the Navier Stokes equation. You have to solve this equation to find out how fluids (like water) move, depnding on the properties of the fluids like viscosity, etc. So far, it was not fully solved for 3-dimensional flow problems. (This problem is very special: it is among the seven "Millennium problems" announced by the Clay Institute in 2000. If you solve any of these, you will get a million US dollars as a prize.) Now AI has given a 146 page proof which is considered too difficult even for mathematicians to understand; verifying it will take a long time. END OF BOX How does AI solve these problems? How is all this possible for AI? Thousands of AI agents work in parallel--this allows AI models to explore multiple paths. When one fails, they then step back, retry repeatedly. They can do this for far longer than human researchers typically can. Moreover, they can check their own work using computer programs that act as proof assistants. This ensures that despite their length, the computer code verifies the logic as being mathematically correct. Learning versus solving One major problem right now: While the AI outputs are technically correct, mathematicians point out that humanity has "learned very little" so far because the proofs are written by machines for machines, requiring heavy human rewriting to yield any intuitive insight. AI in the future What does all this mean for the future of mathematics? One possibility is that AI is actually good only at a specific type of mathematical exploration: involving weakening assumptions, trying out many possibilities, testing examples, and hunting for patterns. Perhaps it is not good at - working with entirely new concepts, - generating unexpected insights or - using radically different ways of restating a problem. We do not know as yet. What is clear that in close collaboration with AI, mathematicians can solve far more problems than they could even two years ago. It is very likely that such human-machine collaboration will solve many important problems soon. BOX AI and Resource Use AI is very resource-intensive, requiring massive amounts of electricity, water, and specialized hardware to train and run. - Building large AI models requires thousands of powerful graphics processing units (GPUs) running nonstop for weeks or months. - Every time you ask an AI tool a question or generate an image, it uses data center power; electricity used in generating one AI image can power one cell phone. - Global data centers can consume more than 100 megawatts of electricity, enough to power 100,000 houses. - Massive data centers generate intense heat and consume millions of litres of water daily for cooling. - Manufacturing high-performance chips requires mining rare earth minerals, and rapid hardware upgrades lead to growing electronic waste. END OF BOX At the recently concluded International Congress of Mathematicians in Philadelphia, USA, there was a great deal of discussion on the impact of AI on mathematics. Many felt that soon we would be unable to separate out human and machine work in mathematics. Soon even prizes such as the Fields medal (awarded for mathematical ability and impact) will become obsolete. Mathematicians like Terence Tao have pointed out that this path is not good for mathematics. Human beings learn through struggle, by overcoming many obstacles. When the road is made easy, their ability to learn may degrade over time. Moreover, they also do lots of routine boring work, and somehow this helps them produce flashes of brilliance. If the routine work is given away to machines, would we still be able to achieve those flashes? What will all this mean for students and young researchers? Also as machines solve important problems, would young mathematicians get funding support? AI is bringing about many changes, in many aspects of our learning, including science. Mathematics may be offering the first serious instance, and thus a peek into the future. Will humanity read the warning signs, and come up with ways of regulating this race? Images from the internet