A.I. is solving problems that stumped the field for decades. Mathematicians look to Terence Tao for guidance on their altered world. "I have had the strangest week ever in my life," Tao said, after OpenAI announced the solution to yet another problem. A mathematician is a machine for turning coffee into theorems. This was a line often invoked by the Hungarian mathematician Paul Erdős, who was fuelled by coffee and amphetamines, slept little, travelled near-constantly, never married or had children, and published almost fifteen hundred papers in his lifetime, in collaboration with hundreds of other mathematicians. But Erdős was, in most ways, not machinelike. He called lecturing in mathematics "preaching," woke friends at odd hours by asking, "Is your brain open?," wore only silk underclothing on account of his sensitive skin, and claimed not to have learned how to butter toast until he was twenty-one. He gave away most of his earnings to charitable causes and to young mathematicians in need of funds for their education, and he offered bounties (sometimes ten dollars, sometimes a thousand) for solutions to mathematical problems he'd proposed. It has been said that, even above his remarkable contributions to the mathematical literature, he helped the discipline most profoundly by turning people who might otherwise have become hedge-fund managers or F.B.I. agents or lost souls into mathematicians. When he died, in 1996, at the age of eighty-three, he left behind about a thousand problems. Solving an Erdős problem is a great honor, as is having a low "Erdős number," a term that describes how many degrees of separation one is from having published work with him. Terence Tao was ten years old when Erdős visited his home town of Adelaide, Australia, in 1985. Erdős loved children and called them epsilons. Tao, a mathematics prodigy, had started taking college-level courses at age nine. Erdős posed a problem for him and Tao to work on together. A photograph of their meeting, taken by Tao's mother (who had been a math teacher before having kids), shows the young mathematician and the old one deep in thought, hands at chins, looking at the notepad before them.

In the 1960s, an odd experiment showed planarian worms could transfer memories by consuming each other. It was a sensational finding--that is, until the worms stopped learning. It was the dead of winter in Boston. The surface of the Charles River was frozen solid. But Zachary Kelso braved the biting cold to finally put to rest a mystery that has haunted neuroscience labs for over half a century. To do that, Kelso, a research assistant in the Harvard lab of the neuroscientist Sam Gershman, needed some worms . Specifically, planarians: arrow-headed flatworms, which are among the simplest creatures to possess a brain and a nervous system with bilateral symmetry like ours. Normally, labs order these widely used model organisms from biological supply companies.

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USC has named David Madigan, a statistician and former Northeastern University provost, to succeed Andrew Guzman as its chief academic officer, the most senior academic hire under President Beong-Soo Kim.

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