MATHEMATICIANS

1 Like a painter or a poet, a mathematician is a creator of patterns, but mathematical patterns are made with ideas rather than paint or words. Mathematicians are motivated by the belief that they may be able to create a pattern that is entirely new, one that changes forever the way that others think about the mathematical order. Mathematics allows great speculative freedom, and mathematicians can create any kind of system they want. However, in the end, every mathematical theory must be relevant to physical reality, either directly or by importance to the body of mathematics.
2 Mathematicians have an exceptional ability to manage long chains of reasoning. They routinely develop theories from very simple contexts and then apply them to very complex ones. For example, they may develop a formula for the movement of an ameba and then try to apply it to successive levels of the animal kingdom, concluding with a theory of human walking.
3 An extended chain of reasoning may be intuitive, and many mathematicians report that they sense a solution long before they have worked out each step in detail. However, even when guided by intuition, they must eventually work out the solution in exact detail if they are to convince others of its validity. They must demonstrate the solution without any errors or omissions in definition or in line of reasoning. In fact, errors of omission (forgetting a step) or of commission (making some assumption that is untrue) can destroy the value of a mathematical contribution. The mathematician must be rigorous: no fact can be accepted unless it has been proved by steps conforming to universally accepted principles.
4 At the center of mathematical talent lies the ability to recognize significant problems and then to solve them. One source of delight for mathematicians is finding the solution to a problem that has long been considered insoluble. Other accomplishments are inventing a new field of mathematics and discovering links between otherwise separate fields of mathematics.

单选题 Which sentence below best expresses the essential information in the highlighted sentence in paragraph 1?
A. Mathematicians are more creative than ordinary people in the ways that they think about patterns and order.
B. Motivation is less important to mathematicians than the belief in their own ability to change other people.
C. Mathematicians use their creative talent to motivate other people to look for new ways to solve important problems.
D. The idea of establishing a completely new way of understanding mathematics is what motivates mathematicians.

单选题 According to the passage, why must mathematicians be able to manage long chains of reasoning?
A. A solution must be demonstrated in detail to convince others of its validity.
B. Mathematicians enjoy creating complex solutions to simple problems.
C. There are often no computer programs that are able to solve the problem.
D. Mathematical problems involve abstract ideas that are difficult to explain.

单选题 The word insoluble in paragraph 4 is closest in meaning to
A. irrelevant to reality
B. not mathematical
C. impossible to solve
D. not interesting to others

多选题 An introductory sentence for a brief summary of the passage is provided below. Complete the summar3' by selecting the THREE answer choices that express the most important ideas in the passage. Some sentences do not belong in the summary because they express ideas that are not presented in the passage or are minor ideas in the passage. This question is worth 2 points.

A. Mathematicians share many characteristics with painters and poets.
B. Mathematicians must be able to recognize significant problems and find relevant solutions to them.
C. The ability to handle long chains of reasoning is essential in developing complex theories.
D. Mathematicians often have to explain mathematical concepts in simple terms to people from other fields.
E. Mathematicians must be rigorous in demonstrating solutions in precise detail with no errors in definition or reasoning.
F. The ability to find links between separate fields of mathematics is a test of mathematical talent.