Richard Borcherds

Richard Ewen Borcherds was born on November 29, 1959, in Cape Town, South Africa.⁠[1]

His father, Peter Howard Borcherds, was a physicist who taught at the University of Cape Town and later the University of Birmingham; his mother was Margaret Elizabeth Greenfield. One of his three brothers, Michael Borcherds, is GeoGebra’s lead developer.⁠[2]

He left South Africa at the age of six months and spent his childhood in Birmingham, England.⁠[3]

He attended King Edward’s School in Birmingham, in the class of 1978.⁠[4]

In 1985 he earned his Ph.D. at Trinity College, Cambridge.⁠[5]

He also took his undergraduate degree at Trinity; his doctoral thesis, “The Leech lattice and other lattices,” was supervised by John Conway. He was a research fellow of Trinity from 1983 to 1987.⁠[2]

From 1987 to 1988 he was a Morrey Assistant Professor at the University of California, Berkeley.⁠[5]

In 1989 he proved the Monstrous Moonshine conjecture formulated by Conway and Norton, which links the Monster group to modular functions; the proof drew on ideas from string theory.⁠[6]

In 1992 he received the London Mathematical Society’s Whitehead Prize.⁠[5]

The same year he received the European Mathematical Society Prize at the first European Congress of Mathematicians in Paris.⁠[1]

In 1993 he was appointed professor in the Department of Mathematics at UC Berkeley; his research interests include Lie algebras, vertex algebras and automorphic forms.⁠[7]

In 1994 he was elected a Fellow of the Royal Society.⁠[8]

That year he was an invited speaker at the International Congress of Mathematicians in Zurich.⁠[1]

The doctoral students he supervised at Berkeley range from Daniel Allcock in 1996 to Tao Su and Brandon Williams in 2018.⁠[7]

On August 18, 1998, at the International Congress of Mathematicians in Berlin, he was awarded the Fields Medal at age 38 for his work in algebra and geometry, notably his proof of the moonshine conjecture; at the time he was on leave from Berkeley as a Royal Society Research Professor at Cambridge.⁠[9]

His prize field was given as “Kac-Moody algebras, automorphic forms,” and his affiliation at the time as Cambridge University.⁠[10]

Shortly after receiving it he said: “Before the award I used to think it was terribly important, but now I realise that it’s meaningless.”⁠[3]

In 2000 he was elected to the American Academy of Arts and Sciences in the Mathematical and Physical Sciences class.⁠[11]

In April 2014 he was elected a member of the U.S. National Academy of Sciences, in Section 11 (Mathematics).⁠[12][13]

During the Covid-19 pandemic he began posting recordings of his online mathematics courses to the YouTubeYouTubeYouTube is Google’s video-sharing and creator platform, founded in 2005 by Steve Chen, Chad Hurley, and Jawed Karim and acquired by Google in 2006. Built around video uploading, viewing, and creator earnings, the platform has developed Shorts, YouTube Music, Premium, YouTube TV, and products for children, and is headquartered in San Bruno, California, United States.Open the full entry channel “Richard E Borcherds,” mostly graduate lectures on algebraic geometry.⁠[14][15]

In interviews published in December 2024 he said “AI is pretty close to being able to formalize an awful lot of human mathematics.” Recalling chess players who said computers would never understand certain things, he noted computers kept improving, and estimated AI would overtake humans at research in “about ten years or so.”⁠[16]

In October 2026 he said that, because of widespread student use of AI, he had stopped grading homework for correctness and now gives credit simply for submitting it.⁠[17]

He said grading for correctness “just adds a huge incentive for them to use AI for homework instead of doing it themselves” and “penalizes students for honesty,” adding: “There is no easy way to tell the difference between human and AI-generated work.”⁠[18]

He conceded the new approach was “not a very good system.” If AI continues to improve at its present rate, he said, “in a few years, there’ll be nothing human mathematicians can do that AI can’t do better”; earlier technical breakthroughs had put handweaving out of business, but “This is the first time anything like this has happened in mathematics, though.”⁠[19]

He also said AI can now solve many undergraduate mathematics problems, often better than the students themselves; assessing online courses has become hard and he knows of no good solution, though “in-person exams still work fine for assessing students.”⁠[20]

He introduced vertex algebras, constructed a generalized Kac-Moody algebra that underpinned his moonshine proof, and found a product formula for the j-function.⁠[8]

He is married to the mathematician Ursula Gritsch.⁠[9]

Gritsch is a topologist.⁠[2]