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Wednesday, March 25, 2015

Math Madness: First Round

Math Madness is under way here at the Center of Math. We've made our decision for the first two matches, which we'll describe here. Keep checking in on the Math Madness webpage- we'll update the bracket image when we've released all the first round winners!

Match 1: Newton vs. Abel 

In this match, we’ve pitted the famous 1600s physicist and mathematician Isaac Newton against Niels Henrik Abel, after whom the Abel prize in mathematics is named.

Newton, born into a poor farming family in 1642, went to Cambridge to become a preacher, and then found his love of mathematics. His contributions to mathematics are numerous- the most significant of which is perhaps the invention of Calculus, which he developed separately from Leibniz.  Not just a mathematician- Newton was also an accomplished physicist. He penned the Principia Mathematica, inside which the Laws of Motion are written. According to Wolfram Science World, Newton “contributed more to the development of science than any other individual in history.”

Abel was a Norwegian mathematician and young prodigy. At only 16 years of age, Abel determined a proof of the binomial theorem, making it valid for all numbers and expanding Euler’s findings. He independently invented the basis of group theory.  As a member of a very poor family, Abel had to enter the Royal Frederick University on scholarship. However, by the time he entered, he had independently studied so much mathematics that his professors couldn’t teach him anything new. Abel never obtained a professorial position, though he tried for several years after his degree. He died of tuberculosis at 26 years old before seeing recognition for his work.

It is obvious, in hindsight, that Abel was a great mathematician. It is likely that, if he had not died at such a young age, Abel would have received praise for his work during his life, and that he would have produced more important work. However, Newton produced work that was much more important.
Newton's won his first round.

Match 2: Euclid vs. Riemann

Here, we see the famous Greek geometer Euclid against Bernhard Riemann, a 19th century German mathematician.

Euclid of Alexandria was a mathematician born around 323 BCE, though the exact year is unknown. Known as the Father of Geometry, Euclid is best associated with the  textbook Elements, the most foundational geometry textbook of all time. For centuries, if you studied mathematics, you studied Elements first. It laid the basis of logical proofs, and served as a catalogue of important geometrical results stretching back even before Euclid’s time.

And Euclid’s opponent, Riemann, was another geometer. He unlocked new information about manifolds of dimensions in his thesis, and defined space by a metric equation.  Riemann also invented the Riemann Sum, which introduces many students to the mathematician when they take integral calculus. He also claims the (not-quite proven) Riemann Hypothesis.

There is no doubt that Euclid was one of the greatest mathematicians of all time. However, Euclid left no great hypotheses to solve. It is clear that the proofs Euclid made would have been discovered eventually- though his method of proof was foundational for all mathematics. Riemann, on the other hand, built up complicated mathematical ideas on new subjects.

Riemann is the second match winner!
What do you think about our choices? What do you think about the huge upset when Riemann beat Euclid? Let us know in the comments!

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