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. How did Cantor finally prove his theory?

2. Which of the following was NOT a field in which Isaac Newton made enormous advances?

3. Where was George Cantor born?

4. Which name does NOT belong?

5. How did Gauss feel about his best work?

Short Essay Questions

1. Describe the controversy that Newton was caught in with his publication of his calculus methods.

2. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

3. Describe who were Jakob and Johann Bernoulli.

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

5. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

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 What was Gauss's major unpublished achievement in geometry?

7. Describe the connection between Fermat and Euler's work.

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

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

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

Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.

Essay Topic 3

Compare Pythagoras's proof of the Pythagorean Theorem and how Heron's formula for triangular area can be used as an alternative proof of the Pythagorean theorem. What are the common assumptions in both proofs? What components of each proof are different?

(see the answer keys)

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