Revision as of 13:23, 18 July 2010

I'm Jamie Weigandt, I am graduate student in the department of mathematics specializing in Algorithmic Number Theory, Arithmetic Algebraic Geometry, and Arithmetic Statistics.

Note on this page

For the time being I will use LaTeX code freely when editing this page.

Random Thoughts About Rhea as I use it

• Can we add LaTeX functionality with jsmath, at least for the pages relevant to mathematicians?
• Can we add the option to "Open Poor editior in a new window"? The sidebar gets too big when I increase the font size to see in safari.

The Bigfoot Project

As a motivating project for learning a lot of background material I am engaged in what I consider a mythical quest to find an elliptic curve over $\Bbb Q$ with torsion subgroup $Z_2 \times Z_8$ and Mordell-Weil rank at least 4. Such a curve is affectionally referred to by my friends and I as "The Bigfoot." This nomenclature is somewhat misleading, such a curve, should it exist is not by any stretch of the imagination expected to be unique. I hope to expound on the status of this project at a later date.

For now I will be motivated in my development of this page by 3 facts:

• My bank account is suffering from conference fatigue.
• There is an essay contest for which I can win $100.
• I'd like to stop eating at Taco Bell.

That being said I'll get right to this following section:

Why do I "math"?

Note about the Development of this Essay

As this is a wiki page, I will take the liberty to develop my essay freely on this page. That being said, there will initially be a lot of material that is unclear. I won't make sense to anyone but myself, or perhaps not even myself. Hopefully, since a record of these edits will remain, it will provide insight anyone trying to write a similar essay. This seems quite similar to one of those "Statement of Purpose" type questions that anyone wanting to go to grad school will have to write about.

A Remark About the Question

It has occurred to me, thinking about this question, that the question is very general and open to interpretation. It also presents us with the verbification (is that the correct term?) of math. Often a general question like this can get one stuck, it's not entirely clear in what style the answer should be given.

It just hit me that the generality of the question is a good thing. I don't have to answer all possible forms of the question I can think of, rather I can start writing as ideas come to me. This will eventually formulate an answer. At that point I will be able to craft a story by starting with the interpretation of the question that I have already answered.

For me, questions are a fundamentally important part of the mathematical experience. As are the stories we tell when we get answers. Of course, in between questions and answers we must experience a great deal of confusion, and hopefully some moment of epiphany or revelation. This provides a rough idea of what the main steps in the mathematical experience are.

• Questions
• Revelation
• Exposition

It seems that any essay about why I do mathematics should discuss my personal views on these stages of mathematical development...

Questions

Questions are a definitely an important part of doing mathematics. If you don't have some kind of question on your mind, how can you even begin to mathematics. I suppose one could engage in "mindless computation"

1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25 1 + 3 + 5 + 7 + 9 + 11 = 36 1 + ...

Revelation

Exposition

Quotes to maybe include

"... number theory has an annoying habit: the field produces, without effort, innumerable problems which have a sweet, innocent air about them, tempting flowers; and yet ... the quests for the solutions to these problems have been known to lead to the creation (from nothing) of theories which spread their light on all mathematics, have been known to goad mathematicians on to achieve major unifications of their science, have been known to entail painful exertion in other branches of mathematics to make those branches serviceable. Number theory swarms with bugs, waiting to bit the tempted flower-lovers who, once bitten, are inspired to excesses of effort!"

-Barry Mazur, "Number Theory as Gadfly"