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

NAME___________________________________________
We will model the process from Dr. Sarah's What is a Mathematician? for Andrew Wiles and Fermat's Last Theorem. Read through the sheet, and take notes while you are watching the videos.

Philosophy

We have spent most of the semester (9 out of 14 weeks) learning useful material that is applicable to real-life situations. We spent so much time on these topics because it is important to learn useful and applicable ideas. Our motto during financial mathematics and statistics (from the creative inquiry -lessons for life list) was to "understand issues deeply, especially those ideas which seem simple". In fact, up until this point in the class, you may have already seen some (or all) of the mathematics that we have been doing. All of the material that we have covered is currently being covered (at a much slower pace and at a surface level instead of the level of depth that we covered) in North Carolina schools in middle school through high school.

Yet, this is a core mathematics course. In a core English course, you would not expect to spend the entire semester on grammar or spelling, no matter how useful or applicable. Similarly, in a core music course, you would not expect to spend the entire semester learning how to read music notes, and in a core art appreciation course, you would not expect to spend your time mixing paints. Instead, you would expect to see some of the masterpieces of accomplishments in those fields - great works of literature, music and art.

For the remainder of the semester, we will concentrate on the masterpieces of mathematics. The mathematics will be new to everyone. Our motto will change from "understand simple ideas deeply" to "simply understand deep ideas". 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 gain useful creative inquiry and effective thinking skills.

Understanding the Math

When we learn a new topic, we should not expect to understand everything immediately. Instead, we reinforce learning by repeating our exposure to the math, engaging the material, and letting it jell. Once we have done this, it is time to take an honest look to see what we can understand. Regardless of the topic or level, there is always something that we can eventually deeply understand.

We will look at various sources in order to reinforce learning of Fermat's Last Theorem.

The first few minutes of The Royale - Star Trek Next Generation's 1989 episode from Stardate 42625.4:
Picard       Fermat's Last Theorem. Familiar With it?
Riker       Vaguely. I spent too many math classes daydreaming about being on a starship.
Picard       When Fermat died, they found this equation scrawled in the margin of his notes
x to the nth plus y to the nth equals z to the nth, where n is greater than two, which he said had no solution in whole numbers, but he also added the phrase "REMARKABLE PROOF."
Riker       But no proof was included.
Picard       And for 800 years people have tried to solve it.
Riker       Including you.
Picard       I find it stimulating. It puts thing in perspective. In our arrogance, we feel we are so advanced yet we still can't unravel a simple knot tied by a part-time French mathematician working alone without a computer.
The Proof - A Nova video about Princeton University Professor Andrew Wiles and Fermat's Last Theorem.

In tomorrow's class, you will engage the mathematics in a classroom worksheet.

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 or multicultural/ethnic issues in his experiences?







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?







Which of the following Creative Inquiry Lessons for Life apply to Andrew Wiles? Explain briefly next to the points that you choose.

Adapted by Dr. Sarah from Burger and Starbird - Effective Thinking
Under construction - extra credit will be granted if you come up with a "life lesson" from our mathematics class that Dr. Sarah places on this list.

  • 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?

    During the segment What is a Mathematician, you will also explore the kind of mathematician methods that are successful for you. While we are learning about what works for other people, you should think about whether the same works for you. 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.