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

William Dunham (mathematician)
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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. Where was Euler born?

2. Where did George Cantor live in the 1860s and 1870s?

3. Who was Euler's teacher?

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

5. How did Gauss feel about his best work?

Short Essay Questions

1. Give an example of a series who's sum is still unknown.

2. Explain any methods used by Cantor that were unsuccessful.

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

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

5. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

6. Describe the great theorem explained by Dunham in this chapter.

7. What was the great theorem of this chapter? Describe it briefly.

8. What great theorems and work of Newton did Dunham highlight?

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 What was Gauss's major unpublished achievement in geometry?

10. Describe some of Gauss's work.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Summarize the puzzles that were presented as a result of Euclid's infinitude of primes. Name and describe some of these puzzles from a historical perspective, then explain what is known about each in modern mathematics. What puzzles remain unsolved today?

Essay Topic 2

Write a three part essay on the lives and work of both Euler and Gauss.

Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?

Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?

Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?

Essay Topic 3

Summarize the discoveries on series made by the Bernoulli brothers and later, Euler. How did the Bernoullis advance mathematical understanding of an infinite series, and how did Euler even further advance this knowledge? Give examples. What principles about series and the sum of series are still being worked out in modern mathematics?

(see the answer keys)

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