[math-fun] favorite theorem
One of my students asked me what my favorite theorem was, a question that I found interesting and surprisingly difficult to answer. So...what's your favorite theorem or proof (and why)? --Bill C.
On 28 Apr 2006 at 10:08, Cordwell, William R wrote:
One of my students asked me what my favorite theorem was, a question ... that I found interesting and surprisingly difficult to answer.
So...what's your favorite theorem or proof (and why)?
Favorite theorem: e^i pi = -1. Why? The elegance and deepness. Very cool stuff, IMO. Favorite proof: Goedels incompleteness theorem. I find the handling of the recusive argument to end up showing incompleteness both profound and understandable. [A proof I'd love to have a simple-enough one of that I could maybe understand: that pi is irrational [if not transcendental]... :o)] /bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
I have to vote for the uncountability of the reals as my favorite theorem & proof. Bernie Cosell wrote:
[A proof I'd love to have a simple-enough one of that I could maybe understand: that pi is irrational [if not transcendental]... :o)]
The proof in Niven & Zuckerman is standard undergrad real analysis fare. There's a version of it on the web: http://www.lrz-muenchen.de/~hr/numb/pi-irr.html Roughly the same mathematical idea, with entertaining presentation, is Kevin Wald's musical version: http://www.math.uchicago.edu/~wald/lit/pi_proof.txt --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
Michael Maschler (game theorist) gave, what I thought, was a nice and surprising answer to this. His favorite two theorems are: (1) The sum of the angles of a triangle are 180 (2) The Brauwer fixed-point theorem.
--- Bernie Cosell <bernie@fantasyfarm.com> wrote: ...
[A proof I'd love to have a simple-enough one of that I could maybe understand: that pi is irrational [if not transcendental]... :o)]
Have a look at Niven, "Irrational Numbers", Carus Monograph #11, and also Hardy and Wright, "Number Theory". Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
Quoting "Cordwell, William R" <wrcordw@sandia.gov>:
So...what's your favorite theorem or proof (and why)?
Pythagoras, from which all else follows in one way or another. Epimenides, from which all that doesn't follow, follows. - hvm ------------------------------------------------- www.correo.unam.mx UNAMonos Comunicándonos
participants (6)
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Bernie Cosell -
Cordwell, William R -
David Wolfe -
Eugene Salamin -
mcintosh＠servidor.unam.mx -
Michael Kleber