If you think a theorem is true then spend half your time trying to prove its true, and half trying to prove its false.

There is a quote I recall but not who said it.  I have not been able to find it on the web.


If you think a theorem is true then spend half of your time trying to prove that its true, and half trying to prove that its false.

I thought it was Erdos but I could not find any connection between him and the saying. I did find something that indicates he did not say it:

An Erdos problem that pays different amounts of money for the conjecture being true of false:

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For a finite family F of graphs, let t(n,F) denote the smallest integer m that every graph on n vertices and m edges must contain a member of F as a subgraph.

A problem on Turán numbers for graphs with degree constraints} (proposed by Erdös and Simonovits [1]. $250 for a proof and $100 for a counterexample)

Prove or disprove that
t(n,H)=O(n^{3/2})
t(n,H)=O(n^{3/2})
if and only if H does not contain a subgraph each vertex of which has degree >2

Bibliography
1 P. Erdös, Some of my old and new combinatorial problems, Paths, flows, and VLSI-layout (Bonn, 1988), Algorithms Combin., 9, 35-45, Springer, Berlin, 1990.
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A while back there was a $1,000,000 prize for PROVING Goldback's conjecture (the prize had a deadline which is past). See here. However, the article does not say what you win for a counterexample. I suspect nothing. Is this fair? (1) YES- proving Goldback would be hard, where as if its false just finding the counterexample likely won't require hard math, (2) NO- HEY, they resolved it, so there, (3) Have a panel look at the solution and decide if it has merit.

ANYWAY- if someone knows the source of the quote, please let me know.
Computational Complexity published first on Computational Complexity