- Proved the fundamental theorem of algebra (in his Phd thesis!)
- Proved that a 17-sided polygon (the heptadecagon) coudl be created with compass and straigh-edge.
- Invented the Diiscrete Fourier Transform (160 years before Cooley and Tukey)
- Proved Fermat's Last Theorem (for n=3 and n=5)
- Computed the sum of the 100 positive integers (at age 5!)
- The normal distribution is also known as the Gaussian distribution
And many, many more...