Presenting Proof, Certainty and Discovery in Mathematics

Which video presentation did you find most effective?
a) The Proof
b) SYNC
c) equally effective



Which article did you find most effective on conveying information about
Proof, Certainty, Success and Discoveries in Mathematics?

a) The View from Here: The Edge of My Seat by Katherine Merow
b) Chapter 1 of SYNC: The Emerging Science of Spontaneous Order by Steven Strogatz
c) The Beauty of Bounded Gaps by Jordan Ellenberg
d) two of the above are more effective than the third
c) all are about equally effective



Which did you find most effective?
a) SYNC video
b) SYNC article
c) equally effective (or ineffective)







My mind, trained to cave under the force of logical argument, has accepted the existence of these rogue lines, but my gut isn't so tractable. [1st hw reading]

Mathematician David Henderson explains that an ideal proof is a communication - the nature of this communication, of course, depends on the community to which one is communicating and is thus in part a social phenomenon.
is convincing - a proof "works" when it convinces others in all cases.
answers -- Why? The proof should explain something that the hearer of the proof wants to have explained. I think most people in mathematics have had the experience of logically following a proof step by step but are still dissatisfied because it did not answer questions of the sort: "Why is it true?" "Where did it come from?" "How did you see it?" "What does it mean?" Think of a mathematical argument or proof from your past experiences. Did it fail any of the portions of David Henderson's definition of an ideal proof?
a) no - satisfied them all
b) failed at communication
c) failed at being convincing
d) failed at answering why
e) failed at more than one



According to the article, what causes SYNC in fireflies?
a) coincidence
b) peculiar atmospheric conditions
c) a maestro firefly
d) internal oscillator that adjusts automatically in response to others leads to synching under certain conditions
e) there is no synching - it is a trick of our eyes