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. What did Cantor define as the continuum?
(a) The square root of any real number.
(b) All imaginary numbers.
(c) All imaginary and real numbers.
(d) Real numbers between 0 and 1.

2. How did Gauss feel about his best work?
(a) He was confident that it would change mathematics.
(b) He was unceratin if it would be accepted by his collegues.
(c) He was uncertain if it was useful.
(d) He was confident that his students would find it of great importance.

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

4. What is one proof that Euler was able to prove?
(a) Bernoulli's principle of lift.
(b) Newton's method of calculus.
(c) Descartes' number theory.
(d) "little Fermat theorem."

5. What did Cantor's cardinal numbers represent?
(a) Finite series.
(b) Series of prime numbers.
(c) Infinite sets.
(d) Sets of all imaginary numbers.

6. 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.

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

8. What was Dunham central theorem for this chapter?
(a) That there are other transfinite cardinals greater than c.
(b) That the sum of an infintire series is always infinite.
(c) That the sum of a set of real numbers is finite.
(d) That the area of a circle is fundamentally related to the square of its area.

9. Which of the following is a quote from Bertrand Russell included by Dunham?
(a) "Matematicians are the gatekeepers of knowledge."
(b) "The study of mathematics is the study of the universe."
(c) "Mathematics, rightly viewed, posses not only truth, but supreme beauty."
(d) "Mathematics is truth."

10. What did Cantor struggle with later in his life?
(a) Blindness.
(b) Seizures.
(c) Mental illness.
(d) Leukemia.

11. What were the two types of transfinite cardinals defined by Cantor?
(a) אₒ and c.
(b) 1 and pi.
(c) pi and אₒ.
(d) c and pi.

12. What did British scholars accuse Leibniz of?
(a) Plagiarizing Newton's calculus method.
(b) Conspiring the death of Newton.
(c) Stealing Newton's Binomial theorem.
(d) Publishing Newton's work without his approval.

13. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(c) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(d) 1 + 2 + 3 + 4 + 5. . .

14. How did Cantor finally prove his theory?
(a) By extension of the infinite series.
(b) By refining and expanding set theory.
(c) By extension of the Pythagorean Theorem.
(d) By using basic algebra.

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

Short Answer Questions

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

2. What didn't Euler attempt?

3. Where was George Cantor born?

4. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

5. What series was Euler most famous for?

(see the answer keys)

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