**Match 7: Hilbert vs. Poincaré**

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Match 7 shows two
mathematicians from the same era against each other: the German David Hilbert
versus the French Henri Poincaré.

A mathematician who got his feet wet in many branches of
mathematics, Poincaré has earned credit for the creation of generalized elliptic
functions, the discovery of connections between automorphic functions in the
same group, the Poincaré conjecture, and much more. Perhaps his most
prestigious contribution was the solution of the three-body problem, which
eluded mathematicians since Newton. Poincaré had a strange path to mathematics-
he actually earned a degree in mining engineering, and became a mine inspector
for several years. He was actually completing his thesis for a mathematics doctorate
at the same time in the field of differential equations. In 1912, Poincaré died
at the age of 58.

And we also have David Hilbert from almost the same time
period. Hilbert was born 8 years later in 1862 in Prussia, and spent much of
his working career at the University of Göttingen in Germany. At a conference
in Paris, Hilbert proposed a list of 23 unsolved problems in mathematics. The
list became known as Hilbert’s Problems, and while a number are still unsolved,
they provided milestones for 20

^{th}century mathematicians to work towards. Hilbert is also known for creating fundamental ideas in different mathematical areas, including invariant theory and axiomization of geometry.
This winner was hard to pick. Hilbert and Poincaré both
contributed much to mathematics, but because Poincaré made more contributions
to even more fields, we had to choose him as the winner of this round.

**Match 8: Galois vs. Fermat**

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For the final match of the first round, we look at the young
and rowdy Évariste Galois and lawyer Pierre de Fermat.

Galois, born in 1811, was a young math prodigy, who failed
his other tests in school because he could only focus on math. His work was consistently
ignored or misplaced, leaving only 60 pages total of his mathematical
discoveries existing today. Though it is not much, what exists today is
exceptional. He is credited as one of
the founders of group theory. Galois’s most significant mathematical
contribution is the development of Galois theory, which is used to solve
equations and can be adapted for many fields of mathematics. He died at the age
of 20, leaving mathematical historians to wonder how much more he could have
contributed to his field.

Pierre de Fermat is another Frenchman, from the 17

^{th}century instead, who worked as a lawyer, but studied mathematics on the side. He is given credit for discoveries that led to infinitesimal calculus and the iteration of derivative math, as well as other research in number theory and analytic geometry. Fermat had a nasty habit of writing his findings in the margins of textbooks instead of organized on paper, which led to a controversy that lasted almost 4 centuries: Fermat’s Last Theorem was proven in 1994 by Sir Andrew Wiles. Though Fermat claims to have proven it, his method was lost, and Wiles proved the theorem with techniques invented well after Fermat’s death.
This pair was another difficult choice. Fermat offered many
developments to math that existed at the time, but Galois laid the foundations
for a new branch of mathematics. For that reason, Galois is the winner of this match.

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