#12 - No mathematician today would flatly refuse to accept

[desmail]

Hi,

For this question, I understand why A is correct, but why is C wrong? In the stimulus it states that some mathematicians still hold a strong belief that simple theorems should have simple proofs. If they "strongly" believe that, then wouldn't that mean they would reject enormous computations? But then again the stimulus does state that no mathematician would flatly refuse..

I am just getting thrown off by the words "strongly believe" It makes it seem like if they strongly believe in simple proofs they would reject enormous ones. How is my reasoning flawed?

Thanks!
Dana

[Dave Killoran]

Hi Dana,

There are a few things in (C) that trouble me. First, the answer says "some individuals," which is a broad group that we know very little about (the stimulus is specifically about mathematicians). Outside of the mathematicians, we don't know anything about other people. However, we know that "some individuals" can include mathematicians, so we can proceed by examining just that group.

Second, in examining the mathematicians, from the first sentence, we know that no mathematician today would flatly refuse to accepts the results of the computation. Let's say that the difference between the stimulus and answer choice (C) in referring to these people is the word "flatly," and that indeed there are "some" mathematicians who refuse, ultimately, to accept the results of enormous computations. With that in mind, when you get to the third sentence, and "some" mathematicians still hold a strong belief in short proofs, how do you know that those two groups of "some" mathematicians overlap? You don't, and thus answer choice (C) does not have to be true.

In direct answer to the question you pose in your post, just because they "strongly believe" there should be a simple proof doesn't mean they would refuse to accept enormous computation. Kind of like, "I strongly believe there should be a cheap way to get to the moon but I'll accept that right now there isn't." That's a really, really rough analogy, but it gets at the point that someone can believe something but accept circumstances or results to the contrary.

Does that help explain the problem? Please let me know. Thanks!

[lanereuden]

I think one way to eliminate all options but A is the fact that only A says mathematicians, whereas the others all say individuals...or should I be cautious with this shortcut ?

[Rachael Wilkenfeld]

Hi lanereuden,

Generally speaking, you shouldn't use short cuts that aren't based on the logic of the problem. In this case, it worked out for you. But answer choice (A) would be just as correct if it stated that "today, some individuals who believe..." because mathematicians are also individuals.

Hope that helps!
Rachael