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**Click to make the image larger! |

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**

Click to make the image larger! |

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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