Netlib is a collection of mission-critical software components for linear algebra systems (i.e. working with vectors or matrices). Netlib libraries are written in C, Fortran or optimised assembly code. A Java translation has been provided by the F2J project but it does not take advantage of optimised system libraries.
In mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of considerable importance to the philosophy of mathematics. They are widely regarded as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem.
We've all heard of 'six degrees of separation', the idea that everyone in the world can be connected in just a few steps. But what if those steps don't just relate to people but also to viruses, neurons, proteins and even to fashion trends? What if this 'six degrees of separation' allowed us an insight into something at the core of Nature?
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.