Journey Through Genius: The Great Theorems of Mathematics Test | Final Test - Medium

William Dunham (mathematician)
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This test consists of 5 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
(a) Nobody has determined the sum.
(b) Infinity.
(c) 0.
(d) 2.

2. What did Cantor suspect about transfinite cardinals?
(a) That the sum of the series is infinite.
(b) That there are transfinite cardinals even greater than c.
(c) That there are transfinite cardinals much less than c.
(d) That the sum of the series is finite.

3. Which of the following did Dunham concentrate on as one of Newton's great advances?
(a) Quadratic equation.
(b) Quintic theorem.
(c) Binomial theorem.
(d) Area of a sphere.

4. What hindered Euler's work as he grew older?
(a) He had very bad arthritis.
(b) His increasing blindness.
(c) He had a stroke.
(d) His hearing was getting worse.

5. Which word best describes Newton's childhood?
(a) Simple.
(b) Troubled.
(c) Cold.
(d) Hard.

Short Answer Questions

1. Where did Euler study at the age of 20?

2. To how many decimal places did Newton determine the number for pi?

3. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?

4. In his later life, what position did Isaac Newton hold?

5. What was most noticeable about Euler at a young age?

(see the answer keys)

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