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, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. What did Newton's calculus involve?
(a) Determining the area under a curve.
(b) Proving the existance of pi.
(c) Proving the cubic equation.
(d) Determining the volume of a sphere.

2. In the Bernoulli's time, what was the current definition of a series?
(a) The sum of a finite series of terms.
(b) The infinite sum of a convergent series.
(c) The finite sum of a divergent series.
(d) The sum of a never-ending series of terms.

3. What series was Euler most famous for?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . .
(d) 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . .

4. In what area was Gauss especially interested?
(a) The proof of the infinite series.
(b) The elements of number theory.
(c) The elements of geometry.
(d) The circumference of Earth.

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

Short Answer Questions

1. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

2. On who's work did Euler base his number theory?

3. How did Gauss feel about his best work?

4. Which of the following was a major part of Gauss' work in mathematics?

5. What didn't Euler attempt?

Short Essay Questions

1. Describe Newton's days in Cambridge and what he eventually came to discover.

2. Explain why Eulers sum of π²/6 was in some ways surprising.

3. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

4. Explain how Gottfried Leibniz was able to publish his method of calculus.

5. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

6. What was Gauss's major unpublished achievement in geometry?

7. Who was Georg Cantor, and what was significant about his work in mathematics?

8. Describe some of Gauss's work.

9. Describe Cantor's difficult personal life.

10. Describe some of the characteristics of Leonhard Euler, and what made him successful.

(see the answer keys)

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