3 ms·

I suggest to just you to think of proofs in a different way. There are different ways to write a proof. I think proofs are sufficient if you are able to convinc

I suggest to just you to think of proofs in a different way. There are different ways to write a proof. I think proofs are sufficient if you are able to convince your audience. If you try to convince a theorem prover like Coq you have to be very explicit of all the annoying details otherwise Coq will complain. It's very tedious work and some of the reasons why it's not more commonly used among programmers. If you write a math paper you can assume that your audience is quite knowledgeable in the domain and you don't have to be very explicit about every detail (readers can fill in the gaps) but you have to be precise in your notation and reasoning. You provide a formal proof that convinces your peers not a rigid machine. If you write a blog post then informal proofs are very much sufficient, e.g. 0.3333... = 1/3 0.9999... = 3/3 = 1 Is sufficient to convince your audience. You don't have to write down a fully scientific formal proof or Coq program to elaborate your argument in the context of a blog post.

sobriquet9 4y ago
The problem with this formulation is that one can convince the audience that something is right when it isn't. Example: 31 is prime, 331 is prime, 3331 is prime, 33331 is prime, ... 33333331 is prime, therefore 333333331 must be prime (while in fact it's divisible by 17). I'm not arguing one should never look at proofs and take everything for granted. I'm saying that rigorous proofs going down all the way to Peano axioms are unnecessary. In fact, most math people actually use, including linear algebra, calculus, Fourier transform predates Peano axioms.
- nh23423fefe 4y ago
  I don't see the analogy. you asserted a finite set of premises but didn't prove the implication at all? so why would the conclusion be valid?
  - sobriquet9 4y ago
    My point is that if all I need is to convince my audience, I may be able to make them believe the flawed proof. In this example the flaw is intentionally obvious, but there are other examples where the flaw is more subtle.

sobriquet9 4y ago

The problem with this formulation is that one can convince the audience that something is right when it isn't. Example: 31 is prime, 331 is prime, 3331 is prime, 33331 is prime, ... 33333331 is prime, therefore 333333331 must be prime (while in fact it's divisible by 17). I'm not arguing one should never look at proofs and take everything for granted. I'm saying that rigorous proofs going down all the way to Peano axioms are unnecessary. In fact, most math people actually use, including linear algebra, calculus, Fourier transform predates Peano axioms.

nh23423fefe 4y ago
I don't see the analogy. you asserted a finite set of premises but didn't prove the implication at all? so why would the conclusion be valid?
- sobriquet9 4y ago
  My point is that if all I need is to convince my audience, I may be able to make them believe the flawed proof. In this example the flaw is intentionally obvious, but there are other examples where the flaw is more subtle.