Dr. Sarah's What is a Mathematician?
Andrew Wiles and Fermat's Last Theorem

Read through the sheet, and take notes while you are watching the video.

Philosophy

In this segment, we will concentrate on the masterpieces of mathematics. You might worry that you need to be an experienced mathematician in order to understand these great ideas. This is not the case. One can appreciate great works of literature, music and art without being a writer, composer, or artist. Similarly, you can appreciate the highlights and great works of mathematics without being a mathematician. In the process, you will continue to develop useful creative inquiry and effective thinking skills, while delving into the course themes on what mathematics is and how people succeed at math. We will look at What is a Mathematician? from a sociological perspective using a forward historical progression (in order to discuss the mathematician in the context of societal influences).

The Proof - A Nova video about Princeton University Professor Andrew Wiles and Fermat's Last Theorem.

Andrew Wiles' Influences, Support and Barriers

What influences led him to become a mathematician / Why did he become a mathematician?




Did he have support from family and society?




What kind of barriers did he face while becoming a mathematician?




Gender, Racial or Multicultural/Ethnic Issues in Andrew Wiles' Experiences

What are the gender, racial, multicultural/ethnic, diversity (broadly defined) issues in his experiences? Be sure to also address whether he is married and has a family, and whether his spouse or partner is also a mathematician or scientist. If your mathematician is a white man with no apparent diversity issues, be sure to address whether he has mentored women or other traditional minorities in mathematics.




Andrew Wiles' Mathematical Style

How does he describe the process of doing mathematics and/or mathematical research?




How does he get the flashes of insight that he needs to do research?




How does his mathematical mind work? Does he have a photographic memory? Is he really good with numbers? Is he good at visualization?




Does he often collaborate (ie write papers with other mathematicians) or instead mostly work by himself?




How does he describe what mathematics is and/or where it comes from?




Which of the following Creative Inquiry Lessons for Life apply to Andrew Wiles? Explain briefly next to the points that you choose how or when he used the methods.

Adapted by Dr. Sarah from Burger and Starbird - Effective Thinking

  • Don't be paralyzed by fear of the unknown. Take risks, try new things and live with a "just do it" attitude.



  • Make mistakes and fail but never give up. Instead, learn from your mistakes and use them to grow.



  • Life is a journey - not a destination. Someone could give you all THEIR answers, but it is your experiences and what you've learned during the process that really matters.



  • To really learn something new, you must experience it yourself via hands-on hard work. We don't learn deeply by watching someone else. You could watch many movies about baseball, but in order to really learn how to play well, you must actually pick up a bat yourself.



  • Seek the essential.



  • Take what is vague or confusing and seek clarity, focus and comprehension.



  • Break difficult problems up into easier ones.



  • Use what has already been done and adapt it for your own use.



  • Look for patterns and similarities.



  • Understand issues deeply, especially those ideas which seem simple.



  • Communicate your ideas effectively.



  • Keep an open mind.



  • Try to examine situations from diverse viewpoints.



  • Treat people and their ideas with respect.



  • Explore the consequences of new ideas.



  • The only stupid question is the unasked question.



    What Kind of Mathematician are You?

    While we are learning about what works for other people, you should think about whether the same works for you. Begin thinking about this now, but there is no need to write anything down. Facets [Star Trek DS9] rectifies the statement that Fermat's is still unsolved in the 23rd century by establishing that other mathematicians, including Tobin Dax, searched for proofs (other than Wiles' proof) of Fermat's theorem.