April 15, 2013
by Artem Kaznatcheev

We have previously discussed the finicky task of defining intelligence, but surely being able to do math qualifies? Even if the importance of mathematics in science is questioned by people as notable as E.O. Wilson, surely nobody questions it as an intelligent activity? Mathematical reasoning is not necessary for intelligence, but surely it is sufficient?

Note that by mathematics, I don’t mean number crunching or carrying out a rote computation. I mean the bread and butter of what mathematicians do: proving theorems and solving general problems. As an example, consider the following theorem about metric spaces:

Let X be a complete metric space and let A be a closed subset of X. Then A is complete.

Can you prove this theorem? Would you call someone that can — intelligent? Take a moment to come up with a proof.

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## Mathematical Turing test: Readable proofs from your computer

April 15, 2013 by Artem Kaznatcheev 10 Comments

We have previously discussed the finicky task of defining intelligence, but surely being able to do math qualifies? Even if the importance of mathematics in science is questioned by people as notable as E.O. Wilson, surely nobody questions it as an intelligent activity? Mathematical reasoning is not necessary for intelligence, but surely it is sufficient?

Note that by mathematics, I don’t mean number crunching or carrying out a rote computation. I mean the bread and butter of what mathematicians do: proving theorems and solving general problems. As an example, consider the following theorem about metric spaces:

Can you prove this theorem? Would you call someone that can — intelligent? Take a moment to come up with a proof.

Read more of this post

Filed under Commentary Tagged with Alan Turing, artificial intelligence, Bertrand Russell, cognitive science, cstheory, current events, empirical, intelligence, philosophy of math, realistic model