Humans have known how to multiply natural numbers for a long time. In primary school you learn how to multiply numbers using an algorithm which is often called long multiplication, and it was known to the ancient Babylonians. But it’s
Starting from a Liouville 1-form on a surface, we have been led to 3-dimensional contact geometry, and convex surfaces. We now go in the other direction.
(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.
(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.
In which I recall, via neurologist Oliver Sacks, some musings of Sylvester from 1877 on the limitlessness of mathematics.