This discussion will explore the surprising thesis that learning, research, and thinking in mathematics is suffused with ambiguity, the contradictory, and paradox. The thesis is presented in the 2007 book by William Byers How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics (Princeton University Press's web page for Byers' book "How Mathematicians Think"). The discussion will involve only elementary mathematics such as the number zero, simple equations like 1+1=2, and irrational numbers. The most advanced mathematics discussed will be the paradoxes of infinity, but even here we will discuss it in simple terms that should be understandable by anyone regardless of their mathematical background.
If the modern world stands on a mathematical foundation, it behooves every thoughtful, educated person to attempt to gain some familiarity with the world of mathematics. Not only with some particular subject, but with the culture of mathematics, with the manner in which mathematicians think and the manner in which they see this world of their own creation.
--- William Byers
Some questions that might be addressed during this meetup follow:
- Is there really ambiguity in mathematics? How can that be, I thought mathematics was certain and definitive? Has mathematics lost the "holy grail" of certainty?
- Is zero "the nothingness that is"? If so, why is zero such a powerful number?
- What is irrational about irrational numbers? What is complex about complex numbers? What is imaginary about imaginary numbers?
- Are equations inherently ambiguous?
- Is mathematics the art of getting precise about ambiguous situations? Is that why it is difficult to learn?
- Would it help students if the ambiguity, contradictory, and paradox in mathematics was discussed by teachers instead of the current style that emphasizes certainty and ignores the ambiguous?
- Are great ideas built on deep paradoxes?
- Does creativity in mathematics really get its source from ambiguity, contradiction, and paradox?
- Is it unfortunate that mathematical proofs emphasize the logic instead of the ideas with all their ambiguities, contradictions and paradoxes in plain view?
- Could mathematical writing be improved by embracing ambiguity, the contradictory and paradox?
- What are the main philosophies of mathematics? How does ambiguity, contradiction, and paradox relate to each of these philosophies?
We are seeking volunteers to lead future Ben Franklin Thinking Society meetups. If you have a topic of interest, please send an e-mail to [masked] outlining your subject.