Ananyo Bhattacharya

Last week, a 23-year-old amateur with no advanced mathematical training did something many mathematicians never manage in a lifetime: he solved a 60-year-old problem posed by the spectacularly prolific Hungarian mathematician Paul Erdos. Liam Price, armed chiefly with curiosity and a ChatGPT-Pro subscription, found a solution to a long-standing Erdos conjecture that had resisted being solved for decades. Experts say the method appears genuinely new. This would be a delightful one-off story on its own: the outsider beating the insiders. But it comes only weeks after another striking moment in mathematics. In March, the AI start-up Math, Inc.

More than anyone else, John von Neumann created the future. He was an unparalleled genius, one of the greatest mathematicians of the 20th century, and he helped invent the world as we now know it. He came up with a blueprint of the modern computer and sparked the beginnings of artificial intelligence. He worked on the atom bomb and led the team that produced the first computerised weather forecast. In the mid-1950s, he proposed the idea that the Earth was warming as a consequence of humans burning coal and oil, and warned that ‘extensive human intervention’ could wreak havoc with the world’s climate.