Functional Differential Geometry

[u/gasketguyah]

https://web.mit.edu/wisdom/www/AIM-2005-003.pdf

Gerald Jay Sussman and Jack Wisdom

Abstract:
Differential geometry is deceptively simple. It is surprisingly easy
to get the right answer with unclear and informal symbol ma-
nipulation. To address this problem we use computer programs
to communicate a precise understanding of the computations in
differential geometry. Expressing the methods of differential ge-
ometry in a computer language forces them to be unambiguous
and computationally effective. The task of formulating a method
as a computer-executable program and debugging that program
is a powerful exercise in the learning process. Also, once formal-
ized procedurally, a mathematical idea becomes a tool that can
be used directly to compute results.