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VI. Укажите правильный перевод подчеркнутой части предложения.

III. Заполните пропуски подходящими по смыслу словами.

1. The mathematicians of past centuries knew the … of difficult problems.

a) value b) solution

c) importance d) idea

2. “Problem of quickest …” was proposed by J. Bernoulli.

a) solution b) descent

c) integers d) evidence

3. We study Fermat’s … xⁿ + yⁿ = zⁿ (x, y, z integers).

a) theorem b) axiom

c) assertion d) descent

4. They attempt to prove the impossibility of Fermat’s ….

a) problem b) theory

c) theorem d) example

5. The … of variations owes its origin to the problem of Bernoulli and to similar problems.

a) calculus b) axiom

c) theorem d) assertion

Text II

It is difficult often impossible to judge the value of a problem correctly in advance; for the final award depends upon the gain which science obtains from the problem. Nevertheless, we can ask whether there are general criteria which mark and label a good mathematical problem. An old French mathematician said: "A mathematical theory is not to be considered completed until you made it so clear that you can explain it to the first-man whom you meet in the street". This clearness and ease of understanding, here claimed for a mathematical theory, I should still more demand for a mathematical problem that it ought to be perfect; for what is clear and easily 'understandable attracts, while the complicated repels us. Moreover, a mathematical problem should be difficult in order to appeal to us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths and ultimately a reminder of our pleasure in the successful solution.

The mathematicians of past centuries were accustomed to devoting themselves to the solution of difficult particular problems with passionate zeal. They knew the value of difficult problems. I remind you only of the "problem of quickest descent" proposed by J. Bernoulli, of Fermat's assertion; xn + yn =zn, (x, y, z integers) which is unsolvable except in certain self-evident cases. The calculus of variations owes its origin to this problem of Bernoulli and to similar problems. The attempt to prove the impossibility of Fermat's theorem offers a striking example of the inspiring effect which such a very special and apparently unimportant problem may have upon science. I can remind you as well of the Problem of Three Bodies. The fruitful methods and the far-reaching principles which Poincare brought into celestial mechanics and which are today recognized and applied in practical astronomy are due to the fact that he sought to treat anew that difficult problem and to come nearer to its solution.

IV. Выберите правильный ответ на вопрос в соответствии с содержанием текста.

1. Whom do the following words belong to? “A mathematical theory is not to be considered completed until you made it so clear that you can explain it to the first man whom you meet in the street”.

a) to an old French mathematician b) to the Greek mathematician

c) to an Alexandrian mathematician d) to the Swiss mathematician

2. What were the mathematicians of past centuries accustomed to?

a) To devoting themselves to the solution of easy problems without passionate zeal.

b) To devoting themselves to the solution of difficult particular problems with passionate zeal.

c) To devoting themselves to finding the new mathematical problems.

d) To devoting themselves to proving mathematical theorems.

3. What mathematical problem was proposed by J. Bernoulli?

a) “The problem of Three Bodies”.

b) “Problem of quickest descent”.

c) “Problem of the straight line”.

d) “The general problem of boundary values”.

4. Whom does the next assertion (xⁿ + yⁿ = zⁿ) belong to?

a) J. Bernoulli b) Fermat

c) Cantor

5. What is it often difficult to do?

a) to judge the value of a problem correctly in advance.

b) to solve the mathematical problem.

c) to find the correct answer to the mathematical question.

d) to prove any mathematical assertion.

6. What did mathematicians of the past know.

a) they knew the solution of problems.

b) they knew the value of difficult problems.

c) they knew the general criteria which mark and label a good mathematical problem.

V. Выберите заголовок для данного текста, в соответствии с его содержанием.

a. A general criteria which mark and label a good mathematical problem

b. The mathematicians of past centuries

c. The clearness and ease of understanding a mathematical theory

d. Fermat’s assertion xn + yn = zn

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