A forum for proofs · thethinkingboard.com
Some proofs are correct.
Fewer are convincing.
Post a problem. An editor puts it on the board. Then the room argues — and the argument that persuades the most readers carries the mark.
On the board
7 openEasy through Difficult rank the proof, not the statement. Cryptic problems are posted as they were found — working out what is being asked is part of the problem.
What the visitor said
An island holds two hundred people. Each of them has blue eyes or brown eyes. Each can see everyone else's eyes and never their own, and there is nothing on the island that reflects. No one …
Prove that the sum of the reciprocals of the squares is π²/6
Prove that … Posed by Pietro Mengoli in 1650. Jakob Bernoulli could prove the series converges and is less than 2, and then wrote, in print, that he could not find its value and would be gra…
Prove that the harmonic series diverges
Show that … does not converge. The terms go to zero, and the partial sums are in no hurry. They first pass 10 at around n = 12,367, and first pass 20 somewhere near n = 2.7 times 10^8. Every…
The sum of the first n odd numbers is a square
Show that for every positive integer n, … This is the friendliest thing on the board, and it is here deliberately. It has a proof by induction, a proof by pairing, and a proof that is a pict…
Prove that there are infinitely many primes
Show that the set of prime numbers is infinite. Euclid settled this in Book IX, in about five lines, and as close to perfectly as an argument gets. That has stopped no one. There are proofs …
Prove that √2 is irrational
Show that there is no pair of integers p, q with q neq 0 such that … Equivalently: the diagonal of a square is incommensurable with its side. That older phrasing is worth keeping in view, be…
Prove the Pythagorean theorem
Let triangle ABC have its right angle at C. Write a = BC, b = CA, and c = AB. Prove that … Something over four hundred proofs are on record, and that abundance is itself the interesting fact…
How the board works
One
A problem is proposed
Anyone can submit. It waits in review until an editor puts it on the board, so the board stays a short list of problems worth the room’s time.
Two
Proofs are posted
Write in plain language with LaTeX where it helps — $a^2+b^2=c^2$ inline, $$…$$ for a display line.
Three
The room weighs them
One vote per reader per proof. Votes measure persuasion, not correctness — a proof can be right and still not be the one that makes you see it.
Four
One is recognized
The proof holding the most votes carries the brass mark. It moves when the votes move.