The late Japanese mathematician Shizuo Kakutani developed

proving ... describing ... , and furthering

only C has the above construction

It makes sense that the answer is C.
Parallelism is what is tested here. A and D are out b/c "the furthering of" is an awkward construction. B and E are out too b/c the verbs used have to be in a continuous construction - proving, describing and furthering.
C constructs the sentence nicely by making those corrections and using the adverb "accurately" instead of trying to use the word "accurate" (in adjective form) to describe a verb.

HTH

C, as all 3 follow a parallel structure : X-ing..., Y-ing..., Z-ing,

also because the economists' view is possessive you are furthering their understanding and not furthering OF their understanding

C. proving, accurately describing and furthering are parallel.

Here is the Official Explanation. This showed up as a question of the day on October 10, 2013.

Answer C Here, the three items listed must be in parallel form. (A) uses "proving . . . description of . . . and the furthering of . . ." That sentence does not use parallel form since the first item ("proving") is a gerund without an article, while the second ("description") is a noun, and the third ("the furthering") is a gerund with an article. (C) correctly uses parallel form by using gerunds without articles for all three items "proving . . . describing . . . and furthering". (B) uses a gerund ("proving") without an article, a noun ("description"), and another gerund ("furthering") without an article. So (B) is not parallel. (D) uses two gerunds ("completing" and "describing") without an article and a gerund ("the furthering of") with an article. So (D) is not parallel. (E) uses a noun ("the proof") and gerunds ("describing" and "furthering") without articles. So, (E) is not parallel.

The underlined portion includes part of a list, and each of the three items in the must be in parallel form. The sentence as written uses "proving ..., description of ..., and the furthering of ...." This list is not in parallel structure since the first item ("proving") is a gerund without an article, while the second ("description") is a noun, and the third ("the furthering") is a gerund with an article. Eliminate (A).

With parallel list errors, it's often not possible to scan vertically and group the answers, so inspect each one.

(B) uses a gerund ("proving") without an article, a noun ("description"), and another gerund ("furthering") without an article, so it is not parallel.

(C) correctly uses parallel form by using gerunds without articles for all three items: "proving ..., describing ..., and furthering." It appears to be correct, but check the others.

(D) uses two gerunds ("completing" and "describing") without an article and a gerund ("the furthering of") with an article. So (D) is not parallel.

(E) uses a noun ("the proof") and gerunds ("describing" and "furthering") without articles. Therefore, (E) is not parallel.

(C) is indeed correct.