Richard Borcherds on Witt and the Leech lattice

A rare benefit of the Covid-situation is that Richard Borcherds decided to set up a YouTube channel with recordings of his online lectures.

Plenty of gems to be discovered there, including a talk on Monstrous Moonshine, and a talk he gave for the Archimedeans about the Sporadic Groups.

As part of his History of Science-course he addressed the question whether Witt discovered the Leech lattice.

A while ago I’ve blogged about that very same question here:

• Who discovered the Leech lattice?
• So, who discovered the Leech lattice?
• Erna Bannow, octonions and the Leech

The summary of these posts being that I thought it was rather unlikely for Witt to have discovered the Leech lattice.

However, using the same sources, Borcherds rates a more than 90% probability for Witt to have indeed discovered the Leech lattice in 1940.

His evidence for this is:

• Witt said he discovered it.
• His construction (in his 1972 colloquium talk) is unlike any other construction of the Leech lattice.
• Witt was the expert on Steiner systems, and the system S(5,8,24) is crucial in Leech’s construction of his lattice.