Reading Passage Comprehension
For anyone claiming to write a history of a science of which reasoning forms the very essence, the question of the logic is of paramount importance. For example, a modern western account of any historical period in mathematics would, as a matter of course, show a detailed proof justifying each and every mathematical result discussed. Despite this obvious fact, general histories of Chinese mathematics rarely show concern for this issue. They insist above all on presenting only the mathematical results, the logical underpinnings of which are unclear, and rarely do they provide the reader with any semblance of a proof. While this approach to the history of mathematics is naturally a result of various causes, one which probably plays an essential role is the fact that most Chinese mathematical works themselves contain no logical justifications: according to this worldview, apparently it was enough to state authoritatively that something was true—it was completely superfluous to demonstrate why it was true.
There is one major exception to this general pattern, namely a set of Chinese argumentative discourses which has been handed down to us from the first millennium A.D. We are referring to the commentaries and sub-commentaries on the Jiuzhang Suanshu ["The Nine Chapters on the athematical Art"], the key work which inaugurated Chinese mathematics and served as a reference for it over a long period of its history. This fact, which was long unrecognized, means that we are now in a position to know a lot more about the logical construction of mathematics in China than, for example, in Egypt, Mesopotamia, or India.
“For anyone claiming to write a history of a science”- is a GMAT reading comprehension passage with answers. Candidates need a strong knowledge of English GMAT reading comprehension.
This GMAT Reading Comprehension consists of 3 questions and answers. The GMAT Reading Comprehension questions check the candidates’ abilities in understanding, analyzing, and applying information. Candidates can actively prepare with the help of GMAT Reading Comprehension Practice Questions.
Solution and Explanation
- What distinguishes the commentaries on the Jiuzhang Suanshu from almost all other works of Chinese mathematical history is that the authors of the former
- made clear exactly what theorems are true
- spent time justifying their qualifications as authorities
- did not fully disclose all the results in the fields discussed
- provided explicit proofs for the mathematical results presented
- had influence over a large portion of Chinese history
Answer: D
Explanation: Most Chinese mathematical works stated results only, without the proofs justifying the results. The commentaries on the Jiuzhang Suanshu are different in that they contain both the results and the proofs. In other words, they provide "explicit proofs for the mathematical results presented", which is precisely what choice (D), the credited answer, says.
- The author is primarily concerned with:
- discussing the most effective way to elucidate the history of science
- explaining how one ancient work conforms to our modern expectations for logical transparency
- arguing for a change in the methodology used in studying the history of mathematics
- demonstrating that ancient Chinese mathematics was far more advanced than that of other ancient civilizations
- providing an example of how authors making clear their own qualifications enhances the respectability of the work as a whole
Answer: B
Explanation: The answer is (B), because this one ancient work conforms to our modern standards of showing proofs for mathematical results. The term "logical transparency" simply means: showing the logical basis for something. Explaining logically why something is true, which is precisely what proof does.
- The author implies all of the following except
- The ancient mathematical texts of Mesopotamia do not provide explicit proofs for all their results.
- The first Western scholars studying the history of Chinese mathematics were unaware of the proofs available in the commentaries and sub-commentaries on the Jiuzhang Suanshu.
- Proofs are a method of demonstrating the logical arguments underlying a mathematical result.
- The majority of important Chinese mathematicians between 1000 and 1500 would have known of the Jiuzhang Suanshu
- The authors of the Jiuzhang Suanshu do not make any claim justifying their own authority.
Answer: E
Explanation: The passage talks about "justification" in terms of the logical justification a mathematical proof implies. Nowhere does it discuss people justifying themselves. Choice (E) is not implied, so this is the correct answer to the EXCEPT question.
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