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Wednesday, April 1, 2015

Math Madness: Round 1 Part 4

Here is the final update on the matches of our Sweet 16 in the Math Madness Bracket! Keep checking both the blog and the website for updates. One more blog post will show the results of our Elite Eight matches, and then voting will be open to all Center of Math readers to decide our Final Two and then the Champion!

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 20th 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 17th 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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