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.