A mathematical theorem proved by one mathematician should not be accepted until each step in its proof has been indep...

shunhe on January 9, 2021

Hi @andreaskormusis,

Thanks for the question! So first, the conclusion of this stimulus is the last sentence about not accepting computer-assisted proofs. The author thinks this because theorems shouldn’t be accepted until each step in its proof has been independently verified, and computer-assisted proofs conduct a vast number of calculations and humans can’t review them all.

So now we need to find the necessary assumption. (E) says that using an independent computer program doesn’t satisfy the requirement for independent verification of each step in a proof. So now let’s use the negation test. The program DOES satisfy the requirement. Well, then computer-assisted proofs should be accepted, why not? Since the negation of (E) destroys the argument, it is the necessary assumption and the correct answer.

(A) basically says computers make proofs easier for mathematicians, which is irrelevant.

(B) talks about most attempts to construct proofs and how many are right, which is irrelevant.

(C) talks about math theorems that only involve limited steps, which is irrelevant.

(D) talks about other things not being able to do proofs the way computers can, but we don’t care about that for this argument.

Hope this helps! Feel free to ask any other questions that you might have.