One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts. In spite of this, the investigator in another department of science would not need to envy the mathematician if the laws of mathematics referred to objects of our mere imagination, and not to objects of reality. For it cannot occasion surprise that different persons should arrive at the same logical conclusions when they have already agreed upon the fundamental laws (axioms), as well as the methods by which other laws are to be deduced therefrom. But there is another reason for the high repute of mathematics, in that it is mathematics which affords the exact natural sciences a certain measure of security, to which without mathematics they could not attain.
1) The main idea of the passage is that the author
(a) learned that the natural sciences are more reputable than mathematics
(b) believes mathematics is based on theory just as most branches of science are based on theory
(c) argues mathematics is constantly changing and thus causes constant change in the natural sciences
(d) believes mathematics provides an incontestable foundation that lends support to all of natural science
(e) values mathematics even though there is no scientific basis for doing so
2) The author’s overall purpose is this passage is to
(a) refute a specfic theory
(b) acknowledge the importance of a field of study
(c) give examples to support a theory
(d) confirm a mistaken understanding about a field of study
(e) dismiss a field of study as trivial
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- The article is clearly meant to place mathematics on a very high pedestal. It’s laws are certain and indisputable, and the other sciences rely on it. That said, the only answer that makes sense is (D). The answer is (D).
- For the same reasons as above, the answer to this question is obviously (B). The answer is (B).
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