1792
Pascal's Triangle
Also with a higher intellect then most at the gymnasium, Gauss caught the Duke of Brunswick- Wolfenbüttel's attention. The duke gave Gauss a high stipend, so he could attend the Collegium Carolinum in his hometown. At the Collegium he single-handedly re-discovered Bode's Law (an empirical rule given the estimated distance from a planet to the sun), the binomial theorem (expansion of power of a binomial), the arithmetic-geometric mean, quadratic reciprocity and the prime number theorem. It is a pretty extensive list for a staying of only 3 years at the Collegium. Also we mustn't forget, he achieved all of this when he was only 15!
Binomial Theorem
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