## Saturday, October 06, 2007

### Richard Dedekind: 176th birthday

On October 6th, 1831, Richard Dedekind was born.

Dedekind was one of the mathematically inclined 19th century string theorists.

In mathematics, Dedekind studied the relations between rational and irrational numbers (recall Dedekind cut). He was one of the first people who appreciated the concept of groups in algebra and arithmetics. He investigated number fields, ideals, and many other aspects of number theory.

Dirichlet who essentially discovered D-branes 150 years before Polchinski was his close friend and Riemann was another contemporary.

Nevertheless, 21st century theoretical physicist surely remember Dedekind for his eta function, essentially the inverse partition sum of a boson in string theory.

The picture above shows the real part of the modular discriminant defined by Weierstrass as a function of "q = exp(2 pi i tau)". The modular discriminant is the 24th power of the Dedekind eta function, up to a power of 2 pi - exactly the inverse of what you get in the light-cone bosonic string theory partition sum.