The following web page gives its choices for the 100 greatest mathematical
theorems:
http://personal.stevens.edu/~nkahl/Top100Theorems.html
It has no canonical status whatever, and Theorem 20 is incorrect as
stated.
But what the hey. What I found interesting were that the two of top
theorem
holders on this list were, you guessed it, Euler and Gauss. Which gives
some idea of how famous they are as mathematicians.
Euler scores with the generalized Fermat little theorem, the V-E+F=2
theorem, the summation of the reciprocals of the square numbers, solving
Pell's equation, the pentagonal number theorem for partitions, the
Konigsberg bridges problem, and the divergence of the sum of the
reciprocals of the primes, for a total of seven. Gauss scores with the
fundamental theorem of algebra, quadratic reciprocity, and the
independence
of the parallel postulate, for a total of three.
Other high scorers are Euclid (which is sort of cheating, since we don't
know how many, if any, he did himself) and Cauchy, who scores with the
Cauchy inequality for arithmetic and geometric means, the mean value
theorem, the Cauchy-Schwarz inequality, and the intermediate value
theorem,
actually due to Bolzano, for four, or three if you don't cheat. Leibniz
scores with the fundamental theorem of calculus, his series for pi/4, and
the summation of the reciprocals of the triangular numbers, for three.
Euclid has eight, but again that seems like cheating, so I think Euler
wins
the smackdown.
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