Wittgenstein and Math

[taeto]

I like to engage mathematical cranks, occasionally, and mathematical cranks like to throw Wittgenstein back at you. 

But when I hear what things he gets quoted for, and besides which I am not an expert who knows every quote in advance, then I just think that, well, this guy is famous and supposed to be knowledgeable about, uh, some things, in particular having done a lot of thinking about mathematics. But how is it possible that he could have misunderstood so badly how mathematics functions and what mathematicians try to do? 

So I just want to ask in this forum, what is your personal favorite quote, opinion or observation about mathematics, which was astute, on the point and insightful, and made by Wittgenstein?  

 

[studiot]

At the risk of the wrath of Eise I would like to say that I am not a fan of valdemort wittgenstein.

 

[Eise]

21 minutes ago, studiot said:

At the risk of the wrath of Eise I would like to say that I am not a fan of valdemort wittgenstein.

 

 My wrath.

One citation I like:

Quote

The correct method in philosophy would really be the following: to say nothing except what can be said, i.e. propositions of natural science—i.e. something that has nothing to do with philosophy—and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions. Although it would not be satisfying to the other person—he would not have the feeling that we were teaching him philosophy—this method would be the only strictly correct one.

Tractatus, Proposition Nr 6.53

OK, it has nothing to do with mathematics.

[taeto]

11 minutes ago, Eise said:

Tractatus, Proposition Nr 6.53

OK, it has nothing to do with mathematics.

It becomes tough going to paraphrase: "The correct method in mathematics would be to say nothing except what can be said (...) -- he would not have the feeling that we were teaching him mathematics". It sounds interesting. But not exactly in the great ballpark of what I am asking for.