The example isn't an example -- it's a proposed simplicity of a counterexample. Which is exactly what the article is about and the post you responded to is therefore objecting to.
"counterexample: an example that refutes or disproves a proposition or theory"
Yes, the article is about it ... which has no bearing on my point, and just repeats the logic error.
It is frequently the case that a counterexample is obviously (or readily seen to be) a counterexample to a conjecture. That has no bearing on how long it takes to find the counterexample. e.g., in 1756 Euler conjectured that there are no integers that satisfy a^4+b^4+c^4=d^4
It took 213 years to show that 95800^4+217519^4+414560^4=422481^4
Comments
Logic fail. The example is not the conjecture. Saying the example is obvious is not saying that the conjecture is obvious.
The example isn't an example -- it's a proposed simplicity of a counterexample. Which is exactly what the article is about and the post you responded to is therefore objecting to.
"counterexample: an example that refutes or disproves a proposition or theory"
Yes, the article is about it ... which has no bearing on my point, and just repeats the logic error.
It is frequently the case that a counterexample is obviously (or readily seen to be) a counterexample to a conjecture. That has no bearing on how long it takes to find the counterexample. e.g., in 1756 Euler conjectured that there are no integers that satisfy a^4+b^4+c^4=d^4 It took 213 years to show that 95800^4+217519^4+414560^4=422481^4
satifies it ... "obviously".
P.S. To clarify:
Saying that the counterexample is a posteriori obvious is not saying that the conjecture is a priori obviously false.