# Questions tagged [computer-assisted-proofs]

Proofs that are partially or entirely checked by computer, including those formalised in interactive theorem provers.

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### Lean and inacessible cardinals

Here it is claimed that Lean's type theory is equiconsistent with ZFC + existence of $n$ inacessible cardinals for every natural $n$. This is a bit worrying if you just want to work with pure ZFC: how ...
140 views

### Why isn't math proofs just a computer trial and error?

I already asked a similar question, but I recently began a course of Logic and it gave me not an answeat but a refination of my question, which I redefine here. My thinking is the following: Suppose ...
461 views

### Mathematical logic book that uses a proof assistant?

I'm looking for an introductory book on mathematical logic that also discusses an implementation of its logic in a proof assistant. It seems to me this would be a great way to learn mathematical logic,...
1 vote
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### Are there integers $a,b,c,d,e,n$ such that $a^3-nb^3=c^3-nd^3=e^3$?

Can anyone help me find (with a computer search) nonzero integers $a,b,c,d,e,n$ such that $$a^3-nb^3=c^3-nd^3=e^3$$ where $(a,b,e)$ and $(c,d,e)$ are pairwise coprime and $n^2\ne 1$ One solution set ...
1k views

### Proof Solver Geometry [closed]

Are there any programs that can solve Geometry Problems? An example of such a problem would be: The centroid of a triangle always divides its medians into two sections with a 1:2 ratio. While that ... 98 views

### General Idea of HoTT from the use of HoTT Library

I don't have a deep understanding of homotopy type theory, but I'm curious about the difference between coq and HoTT library. When proving with coq, instead of trying tactics brute force, we roughly ...
1 vote
125 views

4k views

### What are some theorems that currently only have computer-assisted proofs?

What are some theorems that currently only have computer-assisted proofs? For example, there's the four colour theorem. I am very curious about this and would like to generate a list.
2k views

### Numbers as sum of distinct squares

Yesterday Polish Olympiad of Information Science ended, one of the questions was purely mathematical, Squares (PL). In the task, we have defined square ...
118 views

### Understand a Maple output

My goal is to solve for $L$ in $\frac{(2k)!}{2^kk!}{2nL - L^2 \choose 2k} = \sum_{s=0}^k{L \choose s}{n-L \choose s}s!\frac{(2k-2s)!}{2^{k-s}(k-s)!)}{L-s \choose 2k-2s}.$ I tried to use the solve ...
433 views

### Where can I download the approx 1500 Appel-Haken reducible configurations in the Four-Color-Theorem proof?

Where can I download computer representations of the approximately 1500 Appel-Haken reducible configurations in the Four-Color-Theorem proof? The Wikipedia article (http://en.wikipedia.org/wiki/...
141 views

### Math via Computers

What computer language is best for doing mathematics? That is, which of C or Ruby or whatever would generally be the widest applicable efficient computer language to master for doing mathematics? In ...
322 views

### Cut-off Subtraction in Coq

I am new to the world of computer assistant proof programs in general, and Coq in particular. As a result, I have sought to prove some elementary results about integers as a way to … At the moment, I ...