Seminar Writing Questions

Week 9

1. Is mathematics closer to reality than physics?
2. If mathematics is discovered then what is mathematical creativity?
3. Can someone deem a certain field of math as useless?
4. Does Hardy seem more like a Platonist, Formalist, or other?

Week 8

1. Why do we need proof? Why isn't "very close" good enough?
2. If we don't know the answer, does an answer exist? What if we can't know?
3. Should all computer-assisted "proofs" be independently checked by hand before they are accepted, or is computer calculation infallible enough to be trusted?
4. What role does intuition play in your mathematical thought process? What role should it play in rigorous mathematics?

Week 7

1. Which of the fields of math discussed in the book interests you most? Why?
2. Why might students resist what is being taught?
3. What are the advantages and disadvantages of analog vs. analytical mathematics?
4. Everyone has a different cognitive style, a way they learn best. What is your cognitive style? How does this help/hinder you when studying math?

Week 6

1. (From "Abstraction", p. 126) Interpret the Platonic world. How does it differ from the real world? What (if any) non-mathematical entities reside there (besides unicorns)?
2. (From "Algorithmic vs. Dialectic Mathematics", p. 180) Beyond the constructive benefits of dialectic mathematics, what are pros/cons to each? Are they interdependent? Why/why not?
3. (From "Proof", p. 150) Are proofs always objects of revelation and surprise? What is the value of a proof of a self-evident fact?
4. (From "The Aesthetic Component", p. 168) What is the role of aesthetics in proofs? Would mechanical proofs have such an aesthetic? Do you think there are analogous properties to mechanical proofs that make them more machine-readable?

Week 5

1. "Any activity devoid of a goal loses its sense." (p. 53) How is this an issue in modern mathematics?
2. How do you suppose culture and other aspects of time period & location affect mathematical progress? (i.e., what we work on)
3. How can mathematicians guarantee that their work will not be used for purposes against their political and/or moral views?
4. Hardyism vs. mathematical maoism...?

Week 4

1. What is the purpose of this book?
2. What do you think of "The Age of Oversimplification"?
3. What is Mathematics?
4. What do you think of the size of mathematics?

Week 3

1. What is so special about projective geometry?
2. Who was Nicholas Bourbaki?
3. Which philosophy of math do you think is the best (or worst) and why?
4. Chapter 15 offers resolution to Russell's Paradox by eliminating the Law of the Excluded Middle and adding "?" as an alternative to T & F. What is "?" to you?

Week 2

1. What was so significant about the Industrial Revolution?
2. How did mathematics become more abstract during the 1800s?
3. What's the big deal about Gauss?

Week 1

1. Why didn't the Greeks use infinitesimals?
2. Whose Calculus notation was better, Newton's or Leibniz's? Or are they both just as good? Why?
3. Could we clear up the priority controversy by just saying Archimedes did Calculus first? If people before Newton & Leibniz did things that resemble Calculus, then what was so special about Newton's work?
4. Who is one mathematician in these chapters whom you've never heard of yet had a lasting effect on the Calculus? What did they do?