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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. When was Philosophiæ Naturalis Principia Mathematica first published?**
**(a)** 1632. **(b)** 1687. **(c)** 1568. **(d)** 1666.

**2. What term refers to numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite?**
**(a)** Pythagorean numbers. **(b)** Quantitative numbers. **(c)** Derivative numbers. **(d)** Transfinite numbers.

**3. Where was Carl Gauss from?**
**(a)** Germany. **(b)** Spain. **(c)** France. **(d)** Belgium.

**4. The author says in Chapter 6, “Infinity’s Twin” that by employing the concept of infinity, Johannes Kepler showed that ellipses and what were the same?**
**(a)** Limits. **(b)** Parabolas. **(c)** Tangents. **(d)** Derivatives.

**5. A primary difficulty in the creation of a “Theory of Everything” is that most attempts to apply quantum mechanics to the gravitational field in the same way as for the electromagnetic field fails due to the breakdown of what?**
**(a)** The Golden Ratio. **(b)** The gravitational pull. **(c)** The renormalization procedure. **(d)** Differential equations.

## Short Answer Questions

**1.** The name “electron” was introduced in 1891 by what Irish physicist?

**2.** In what year did Albert Einstein publish a paper that explained experimental data from the photoelectric effect, leading to the quantum revolution?

**3.** Where was Gottfried Wilhelm Leibniz from?

**4.** During what years did Georg Cantor live?

**5.** Quantum mechanics eliminated zero in classical thermodynamics by removing what, according to the author in Chapter 7, “Absolute Zeros”?

## Short Essay Questions

**1.** How did Max Planck address the problem of the ultraviolet catastrophe?

**2.** How were Georg Cantor’s mathematical principles applied to his theology? Who disagreed with his vision and why?

**3.** How did l’Hopital address the problem of zero, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

**4.** What is expressed through the Rayleigh-Jeans law? How does this law relate to zero?

**5.** How did the discovery of imaginary numbers affect the study of algebra?

**6.** What discovery did Friedrich Riemann make in the field of projective geometry?

**7.** What discovery did Georg Cantor make regarding different types of infinities? How are these types defined?

**8.** What was discovered by Albert Einstein’s solution to the photoelectric effect?

**9.** Who devised the concept of a limit in calculus? What problems did the limit solve?

**10.** What problems were encountered in calculus with zero? How did zero apply to the physical world, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

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