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Tuesday, March 31, 2015

Math Madness: First Round Part 3

Here we have two more matches, with suprising results. Read on to find out more about why these upsets are occuring!

Match 5: Leibniz vs. Erdös

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Now, we have Gottfried Wilhelm Leibniz, a German mathematician born in 1646, against the more modern Paul Erdös.

Leibniz was a bit of a renaissance man, whose work in philosophy, physics, and mathematics remains important to this day.  He was self-taught in mathematics, but independently developed calculus. His ideas were published a short time after Newton’s, but his notation (integral sign and derivatives) was far superior, and is still in use today.  Leibniz also offered contributions to the field of differential equations, and discovered the method of separation of variables. Most of Leibniz’s other work focused on physics.

And against Leibniz is Paul Erdös, a Jewish-Hungarian mathematician born in 1913. By his death at age 83, his eccentric personality earned him a rank as one of the most well-known mathematicians of all time. He has contributed with over 500 mathematicians, often staying in the home of whom he worked with, leading to the quote, “Another roof, another proof.”Though  Erdös was more of a problem solver than a theoretical mathematician, he wrote around 1,525 mathematical articles in his lifetime, in a multitude of mathematical fields.

Leibniz was a great man who contributed important works, especially in the field of calculus. However, Erdös, with his oddball personality, contributed more papers than any mathematician before him (Euler published more pages in total, but less works). He worked with so many different mathematicians that he kept the modern world interested in mathematics.

Match 6: Pythagoras vs. Hypatia

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In this round, two ancient mathematicians face off. We have Pythagoras of Samos versus Hypatia of Alexandria.

Pythagoras was a Greek philosopher and mathematician who lived circa 560 BCE.  He was the founder of the mysterious Pythagorean cult, devoted to the study of numbers which the Pythagoreans saw as concrete, material objects. The Pythagoreans discovered many important mathematical ideas, including the proof that the square root of two is irrational, the theory of proportionals, and the construction of regular (Platonic) solids to name a few. The most famous contribution, of course, is the proof of the Pythagorean Theorem.

The other mathematician, Hypatia, is known first and foremost for being the first woman to make substantial contributions to the field of mathematics. Born about 370 AD, almost one thousand years after Pythagoras, she studied mathematics under her mathematician father. Hypatia became head of the Platonist school in Alexandria, where she lectured on mathematics and philosophy. The only work of Hypatia’s that has survived, unfortunately, is a transcription of Euclid’s Elements, in which she wrote notes and added small contributions. Hypatia became involved in politics, and caught between her pagan roots and the new Christian rule of Alexandria, and was murdered at a relatively young age before she could contribute more to mathematics.

Even though Hypatia’s original work is all lost, she wins this round because of Pythagoras’s shortcomings. His cult contributed many great mathematical ideas, but it is unknown exactly how many of these contributions can be attributed to Pythagoras himself. There is no doubt, however, that both ancient mathematicians were great teachers.

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