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I found it a bit ironic that the author introduced C code there as an aid, but didn't incorporate it into their argument. As I see it, code is exactly the bridg
by falcor84 1y ago
I found it a bit ironic that the author introduced C code there as an aid, but didn't incorporate it into their argument. As I see it, code is exactly the bridge between abstract math and the empirical world - the process of writing code to implement your mathematical structure and then seeing if it gives you the output you expect (or better yet, with Lean, if it proves your proposition) essentially makes math a natural science again.
- Ar-Curunir 1y agoNo, the correctness of your implementation is a mathematical statement about a computation running a particular computational environment, and can be reasoned about from first principles without ever invoking a computer. Whether your computation gives reasonable outputs on certain inputs says nothing (in general) about the original mathematics.
- falcor84 1y agoWhile mathematics "can" be reasoned about from first principles, the history of math is chock-full of examples of professional mathematicians convinced by unsound and wrong arguments. I prefer the clarity of performing math experiments and validating proofs on a computer.
- Ar-Curunir 1y agoYes, but a C or Python program that “implements” a proof and which you test by running it on a few inputs is very different from a program in a interactive theorem prover like Rocq or Lean. In the latter, validity is essentially decided by type-checking, not execution