Johann Carl Friedrich Gauss

Although he published fewer papers than some other great mathematicians, Gauss may be the greatest theorem prover ever. Several important theorems and lemmas bear his name; he was first to produce a complete proof of Euclid’s Fundamental Theorem of Arithmetic (that every natural number has a unique expression as product of primes); and first to produce a rigorous proof of the Fundamental Theorem of Algebra (that an n-th degree polynomial has n complex roots). Gauss himself used “Fundamental Theorem” to refer to Euler’s Law of Quadratic Reciprocity; Gauss was first to provide a proof for this, and provided eight distinct proofs for it over the years. Gauss proved the n=3 case of Fermat’s Last Theorem for a class of  complex  integers; though more general, the proof was simpler than the real integer proof, a discovery which revolutionized algebra. Other work by Gauss led to fundamental theorems in statistics, vector analysis, function theory, and generalizations of the Fundamental Theorem of Calculus.