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I'm currently a graduate student in mathematics at the University of Vermont. My primary interests while at UVM will be related
to algebra and number theory. My primary interests in mathematics are actually much different. While algebra and number theory are great topics, my main interests are still in
the history of mathematical systems of thought, the history of ideas, the philosophy of mathematics, and logic. However, as I don't know of many academic institutions that are willing
to consider these topics seriously, I am content for right now to leave these subjects as hobbies (what they have been for some time) and to study more traditional academic topics such
as algebra and number theory.
New! Check out my Hamming Code Script written in PHP for encoding and decoding of Hamming codes. New! My paper A Mathematician's Introduction to Michel Foucault is now available. I received word from the History of Mathematics Special Interest Group at the Mathematical Association of America that this paper was selected among the top 5 in their recent paper contest in the history of mathematics. |
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My primary interests are in logic, philosophy, history and computer science. I am also interested in number theory
and algebra. My interests are both in theoretical and applicational mathematics. The topics I am most interested in right now: Constructive mathematics, Husserl's phenomenology
and his interactions with Frege, notions of continuity in the history of mathematics and poststructural theories as applied to the discourse of mathematics.
So, what does it mean to say one studies mathematical systems of thought? Actually, that is a hard question to answer. The easiest entrance that I can provide to the topic is to say that it is a philosophical and historical investigation that is a critique of both humanist and structuralist viewpoints, resulting in what has sort of become known as poststructuralism. My interests are not in showing that mathematics is either platonic or conscious, but in showing that the structures that are most capable of being described in mathematics are historically variant positions that are somewhat related to other, larger social trends of specific times. The structuralist and humanist error comes when one connects these positions in a continuous line. Instead, poststructuralists don't assume continuity in history. It may very well be there, we just don't assume that it is. With the addition of this one very important point, my view on the history and philosophy of mathematics is largely humanist. Still, my views are very different from a Hersh style humanist. If there is one person that I would put my views closest to, it would be Husserl. Husserl understood that both a structuralist and humanist (in our terminology, of course) view were needed together ... and that either alone is inherently incomplete in its descriptions of mathematics. My favorite topic in this area is related to Michel Foucault's early "archaeological" works. Specifically, I am interested in applying Foucauldian Archaeology to the history of mathematics from 1850 to 1940. In this area, Husserl's "Logical Investigations", especially the second volume, are of very significant importance. Also, the debate between Frege and Husserl I think has many analogies with the debate between Lacan/Saussure and Derrida, with the relative time periods between these respectively being also of importance. The study of Foucault's notion of "episteme" is also very relevant in this area... and his categorization of history as found in the "Archaeology of Knowledge" has actually helped me interpret the debates and writings of turn of the century in foundational topics, I think, much more accurately. I am interested in the Foucauldian question of formal continuity in history. Namely, at what level can we assume continuity in history? As mathematicians, we know that continuity of a formal system can often lead from a clear understanding to a paradoxical twist in the blink of an eye - Foucault showed that this problem also pops up in historical notions of continuity. In fact, the poststructural critique of both humanism and structuralism can be found in Foucault's argument on continuity. I'm interested in applying these ideas to descriptions of mathematics history. Unfortunately, I only know of two other people interested in this topic. One of them is a prof at Ohio State (working in algebraic geometry, I believe) and one is another student at UM-Flint. Still, I think this area of research is growing, as the social consequences (teaching, education, motivation, etc.) are extremely important. It seems as though a few profs in Uppsala may be interested in these topics. I may still try to become a student there for my masters/PhD work. Really, if given the choice, I'd be more than willing to study mathematics history / philosophy / didactics. It's sort of what I've been doing in my spare time for a few years now... |
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