Proofs and Refutations (Imre Lakatos)
A short novel exploring what mathematics is and how mathematics happens through a historical lens. Presented as a fictional conversation between teachers and students.
Found it to be generally gripping, even though I think most of it went over my head.
Things that stuck:
Mathematics is a human endeavor
Would like to read again, so: #onwards
Rigor is never achieved, only pursued.
For instance, let us start with the assertion
of Euler’s formula
. Since this is unproven, it is a boundary
We can give a proof of this assertion. This pushes our boundary
of rigor out further. However, our proof will assume certain things about what a polyhedron is. Digging into those assumptions will reveal issues with the proof. These assumptions represent a new boudnary of rigor.
The book explains this better than me...