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> it seems so strange to me that one would bother checking this with a numerical simulation I believe that some people know programming but have little experie

> it seems so strange to me that one would bother checking this with a numerical simulation I believe that some people know programming but have little experience with mathematics, so the first thing they'll think about is to "check" numerically that something is true. Which in reality doesn't prove anything, so people should better spend the time to learn some math for these situations.

ValentinA23 2y ago
"you can't learn maths on your own, you need a master" My math teacher during my second year in university, who also happened to be a chaos theorist working on cool stuff such as cryptography via chaos synchronization. He was by far the worst teacher I ever had in terms of mental calculation abilities, but he was also the more advanced. I remember a conversation where he explained how he would always implement his algorithms at least twice, on entirely different software and hardware stacks.
mistercow 2y ago
I have, on many occasions, thought that I had an analytical solution to a problem pinned down, then checked it numerically and found that I'd made a mistake. It seems weird that there's any hostility towards a perfectly useful tool for checking your work.
- monadINtop 2y ago
  Not the person you're replying to but I would assume their point was to highlight the distinguishing feature of mathematics - the fact that it's not only possible to completely prove something to be true, but in fact is the only thing you can actually do (yes I know about experimental math etc). But yeah that doesn't necessarily mean anything for pedagogy or just having fun and so on.
  - mistercow 2y ago
    The thing is, it’s only possible to “completely prove something to be true” in math contingent on your accurate interpretation of the steps of the proof and of its outcome. The proof as a platonic ideal is infallible, but in reality, it gets fed into a fallible meat computer, and in practice, even very smart and careful people do make mistakes, often at the individual level, but sometimes as an entire community. Two famous examples were apparent proofs of the four color theorem in the late 19th century, each of which were widely accepted for over a decade before being shown incorrect. We have better tools nowadays, obviously, but these still only increase confidence, which is exactly what running simulations does.
- DoctorOetker 2y ago
  fair enough, hence the upvote, but then again, a formal verifier would refuse to follow the erroneous step in your derivation...

ValentinA23 2y ago

"you can't learn maths on your own, you need a master" My math teacher during my second year in university, who also happened to be a chaos theorist working on cool stuff such as cryptography via chaos synchronization. He was by far the worst teacher I ever had in terms of mental calculation abilities, but he was also the more advanced. I remember a conversation where he explained how he would always implement his algorithms at least twice, on entirely different software and hardware stacks.

mistercow 2y ago

I have, on many occasions, thought that I had an analytical solution to a problem pinned down, then checked it numerically and found that I'd made a mistake. It seems weird that there's any hostility towards a perfectly useful tool for checking your work.

monadINtop 2y ago
Not the person you're replying to but I would assume their point was to highlight the distinguishing feature of mathematics - the fact that it's not only possible to completely prove something to be true, but in fact is the only thing you can actually do (yes I know about experimental math etc). But yeah that doesn't necessarily mean anything for pedagogy or just having fun and so on.
- mistercow 2y ago
  The thing is, it’s only possible to “completely prove something to be true” in math contingent on your accurate interpretation of the steps of the proof and of its outcome. The proof as a platonic ideal is infallible, but in reality, it gets fed into a fallible meat computer, and in practice, even very smart and careful people do make mistakes, often at the individual level, but sometimes as an entire community. Two famous examples were apparent proofs of the four color theorem in the late 19th century, each of which were widely accepted for over a decade before being shown incorrect. We have better tools nowadays, obviously, but these still only increase confidence, which is exactly what running simulations does.
DoctorOetker 2y ago
fair enough, hence the upvote, but then again, a formal verifier would refuse to follow the erroneous step in your derivation...