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

William Dunham (mathematician)
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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. Who, in modern day, is given credit for the calculus method?
(a) Leibniz.
(b) Newton,
(c) Johann Bernoulli.
(d) Both Newton and Leibniz.

2. 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.

3. Where does the center of mathematical thinking shift to after Italy?
(a) To Turkey and Russia.
(b) To Britian and Scotland.
(c) To France and Britian.
(d) To Germany and Russia.

4. Where did Euler study at the age of 20?
(a) The Academy in St. Petersburg.
(b) Cambrigde.
(c) University of Moscow.
(d) Oxford.

5. To how many decimal places did Newton determine the number for pi?
(a) Twelve places.
(b) Eight places.
(c) Three places.
(d) Nine places.

6. What did George Cantor determine to be true of a set of rational numbers?
(a) They are all prime numbers.
(b) They are all composite numbers.
(c) They are denumerable.
(d) They are non-denumerable.

7. Where was Euler born?
(a) Finland.
(b) Germany.
(c) Switzerland.
(d) Denmark.

8. What did Gauss construct?
(a) A proof that demonstrated the circumference of Earth.
(b) A proof that demonstrates Newtonian physics.
(c) A system where the angles of a triangle add up to more than 180 degrees.
(d) A system where the angles of a triangle add up to fewer than 180 degrees.

9. What sum did Euler find for the series?
(a) 1.
(b) The sum was infinite.
(c) π²/6
(d) 2.

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

11. In his later life, what position did Isaac Newton hold?
(a) Professor of philosophy in Paris.
(b) Angelican father.
(c) Warden of the Mint.
(d) Principle science advisor to Charles II.

12. Which of the following was NOT a field in which Isaac Newton made enormous advances?
(a) Optics.
(b) Mathematics.
(c) Physics.
(d) Biology.

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

14. Which of the following demonstrates the successive squared denominator series?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/4 + 1/9 + 1/16 . . .
(c) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(d) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .

15. What did Euler prove about 2²ⁿ + 1?
(a) That the statment is sometimes prime and sometimes composite.
(b) That the statement is always a prime number.
(c) That the statement is always a composite number.
(d) That the statement is neither prime nor composite.

Short Answer Questions

1. Which word best describes Newton's childhood?

2. What is one proof that Euler was able to prove?

3. What did Cantor's cardinal numbers represent?

4. Which phrase best describes Newton as a student at Cambridge?

5. What series was Euler most famous for?

(see the answer keys)

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