October 2026 will go down in history as the month the universe changed, yet most people didn’t notice. The tech company OpenAI, makers of ChatGPT, released the solutions to 722 fundamental mathematical problems. Many of these problems had baffled humans for decades but a large language model (LLM) that was just 11 days old toppled them. AI had already solved some mathematical conjectures, but this was off the scale. “This is at least ten times, perhaps 100 times as momentous as the proof of Fermat’s Last Theorem,” said Abhishek Saha, professor of mathematics at Queen Mary University of London. Joshua Gans of the University of Toronto went further: “This is probably the biggest day of scientific advancement in history,” while Sam Altman, chief executive of OpenAI, said “life goes on, but something fundamental has changed.” 

Some of the results are so profound that if a human had achieved them, and taken a lifetime to do it, they would be handed the Fields Medal – math’s highest honor – in an instant. Even the Riemann Hypothesis, regarded by some as humanity’s most intractable intellectual challenge, is beginning to crack. It will take a very long time for humans to get to grips with what happened, and there is so much more to come. One scientist said: “The touch of infinity is palpable.” 

Many who study consciousness believe that superintelligence will happen and are also seriously talking about whether machines are already conscious 

Many who study consciousness believe that superintelligence will happen and are also seriously talking about whether machines are already conscious 

The math world is shocked. Some are saying that this year marks the beginning of the modern age of math. The Association of Human Mathematicians, (the name is telling!) says mathematicians did not ask for this work to be done and that OpenAI’s achievement demonstrates not scholarship, but power. It has called for mathematicians to boycott OpenAI, but that feels a little like the demands of the philosophers Majikthise and Vroomfondel in The Hitchhiker’s Guide to the Galaxy when faced with Deep Thought. As representatives of the Amalgamated Union of Philosophers, Sages, Luminaries and Other Thinking Persons, they protest the supercomputer Deep Thought for calculating the “ultimate answer,” demanding “rigidly defined areas of doubt and uncertainty.” 

Where this power is taking us is exhilarating and frightening. AI is coming for all of science. It’s already produced catalogues of potentially medically useful molecules and is giving us a new understanding of mysterious genetic tracts in the human genome. The Chinese AI-Newton model has........

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