Revision as of 14:03, 19 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

This questions is somewhat general and open to interpretation. This is good, it provides me with some freedom to see where the ideas take me, and then decide my interpretation of the question based on the answer I come up with. This is something that I think mathematicians do a lot. The example that comes to mind is Andrew Wiles proof of Fermat's Last Theorem. Wiles was trying to prove the modularity of all elliptic curves, something that is of great mathematical interest. He was unable to complete this task, but was able to prove that a large enough class of elliptic curves were "modular" that the proof of Fermat's Last Theorem followed from the work of Ribet. The story he told was determined by what he was able to do. So the story I tell will depend on how much I develop this essay.

Focus

I want to muse about 3 fundamentally important parts of the mathematical experience.

Open Questions
The Beauty of Mathematical Discovery
Telling Stories

I think mathematics is highly misunderstood in the general populous, even the college educated populous. Some of my ramblings will (at least temporarily) be in the form of questions and answers, where the question will come from some generic member of the populous, who I may occasionally address as Charlie. Charlie being a ficticious everyman character developed by my friends and I at Purdue Improv Club.

Open Questions

I think that when many people learn mathematics, they get a skewed perspective. They get the impression that everything about mathematics is known, and that a mathematician's job is to pass this perfect knowledge down to the next generation. While I appreciate teaching as an important and fulfilling part of being a mathematician, if this were all there was to it, I would soon find it extremely boring, and do something better with my life.

I'm rather fortunate to have taken an interest in number theory, which is by no means boring.

"... 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

What constitutes one of these "tempting flowers"?

@@ Line 47: / Line 47: @@
 I think that when many people learn mathematics, they get a skewed perspective. They get the impression that everything about mathematics is known, and that a mathematician's job is to pass this perfect knowledge down to the next generation. While I appreciate teaching as an important and fulfilling part of being a mathematician, if this were all there was to it, I would soon find it extremely boring, and do something better with my life.
-I have the great fortune to study number theory, which is chalk full of questions to which no one yet knows the answer for certain. Many of these questions are so easy to state that it's embarrassing that we don't know the answer. This is usually a sign that, despite their appearance, these questions are extremely difficult to answer.
+I'm rather fortunate to have taken an interest in number theory, which is by no means boring.
 "... 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!"&nbsp;- [http://math.harvard.edu/~mazur Barry Mazur], [http://mathdl.maa.org/images/upload_library/22/Chauvenet/Mazur.pdf Number Theory as Gadfly]
-What are some of these "tempting flowers" around today? Here is a short list.
+What constitutes one of these "tempting flowers"?
 * [http://en.wikipedia.org/wiki/Abc_conjecture The ABC conjecture]
@@ Line 59: / Line 59: @@
 * [http://en.wikipedia.org/wiki/Twin_primes_conjecture The twin primes conjecture]
-===Warning about these problems / Scary things about Logic===
+===The Upshot to the above ramblings===
-While these questions are easy to understand, they are extremely difficult. Experts have thought about them for years without any luck. It's even plausible that there are models for the set of integers in which the answers to these questions are different. This is somewhat scary because we like to think of the integers as some universally unique set that we understand, but this may not be true.

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