Number theory used to be considered the purest of pure math. Leonard Dickson once said “Thank God that number theory is unsullied by any application.” Dickson died in 1954. Had he lived a little longer he would not have said what he did. There were applications of number theory in Dickson’s day, but many have been developed more recently.

The best known application of number theory is public key cryptography, such as the RSA algorithm. Public key cryptography in turn enables many technologies we take for granted, such as the ability to make secure online transactions. In addition to cryptography, number theory has been applied to other areas, such as:

- Error correcting codes
- Numerical integration
- Computer arithmetic
- Random and quasi-random number generation

I haveĀ applied number theory professionally in cryptography and in each of the areas above.

If you’d like help with an application of number theory, please call or email to discuss your project.

(The image at the top of the page is a variation on the Ulam spiral. Composite numbers are blue dots. The size of the dot increases with the number of prime factors.)