# Monthly Archives: February 2005

## Logic and Lewis Carroll

Two quotes on logic by Lewis Carroll, author of Alice In Wonderland, British logician. ‘Contrariwise,’ continued Tweedledee, ‘if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.’ … Continue reading

## Theta Series

$\displaystyle \sum_{-\infty}^{\infty} e^{-n^2 \pi} = \Gamma(1/4) / \sqrt{2} \pi^{3/4}$. The proof of the fascinating result can be found in Peter Walker‘s Elliptic Functions – A Constructive Approach.

Posted in Books, Number Theory | 1 Comment

## When In Rome …

In a local forum discussion about numb3rs, someone mentioned an old tv show called Square One TV. If you have time, download and watch the clip “Mathematics of Love”. It’s a funny skit about Roman numerals. Incidentally, I quote from … Continue reading

Posted in Books, Fun Stuff | 1 Comment

## Elementary Proofs

No one shall expel us from the paradise that Calculus has created. – tpc The fact that an analytic solution to number theoretical problems exist is bewildering. And often, the analytic proof is much simpler than the elementary proof. The … Continue reading

Posted in Calculus/Analysis, Number Theory, Problems | 2 Comments

## Simple Problem

A little number theory problem posted by higherpi. Let $n>1$ be an integer such $2^n + n^2$ is prime. Prove that $n \equiv 3 \pmod{6}$.

Posted in Number Theory, Problems | 5 Comments

## Two Types of Pure Mathematics

I quote verbatim from the preface in Simmons’ book. It seems to me that a worthwhile distinction can be drawn between two types of pure mathematics. The first – which unfortunately is somewhat out of style at present – centers … Continue reading

## Cantor’s Set Theory

No one shall expel us from the paradise that Cantor has created. -David Hilbert (1862-1943). Hilbert probably wrote in German, so the above quote may not be word perfect, but the meaning is clear. I first learnt set theory from … Continue reading

Posted in General, Quotes/People | 4 Comments

## Jordan Curve Theorem

I’ve never seen the proof of this theorem, although it is mentioned in every advanced calculus and geometry/topology course that I’ve taken. What I’ve learnt recently is that it cannot be generalised to higher dimensions, and the Alexander’s Horned Sphere … Continue reading