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

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.

Problem of the Week

Happy Monday from the Center! Spring should be fully in swing by now, yet there is still snow falling outside my office window in Cambridge. Maybe we'll have some warmth soon. Until then, let's have do some math! This week, we've got a problem from one of our calculus books: Worldwide Multivariable Calculus by David B. Massey.

 While not quite accessible to anyone interested in mathematics, this problem is a good challenge for anyone who has finished their calculus courses and needs a refresher. As usual, I've posted my solution below...

Math Minds: Marcus Fries

Marcus Fries is an Assistant Professor at Eastern Nazarene College in Quincy, Massachusetts. He received his undergraduate degree in mathematics from North Dakota State University, his Ph.D. from Northeastern University, and is now a friend and visitor of the Center of Math. He sat down with our interns Tori and Zach last week to discuss his research, his favorite class, and a lecture he would have liked to attend.

Are you currently involved in any research?

Yes, I work with cotangent bundles of the grassmannian.

So when did you first become interested in math?

At a very young age. But I actually started off at college as a chemistry major, and I did a year of chem research, learned that under no circumstances do I want to be a chemist. In Calculus II I had a great instructor, and power series just interested me to no end. So that’s when I made the switch.

That was kind of “the moment?”

Yeah, power series were just so much fun.

And do you credit anyone in particular for guiding you to this career?

Jim Coykendall and Jim Olsen, great mentors.

What was your favorite math class that you’ve ever taken, and what made it that way?

Probably representation theory with Andre Zelavanski. I took that in grad school. It wasn’t my favorite at the time, but it’s one of my favorites now. I’ve really come to enjoy the field. It’s a part of what I do now- I use representation. The spaces that I deal with, the grassmanian and other spaces are all related to representation or Lie groups. I find it really interesting.

If you could attend a class taught by any math professor living or deceased, whose class would it be and why?

I would have loved to attend Emmy Noether’s lectures on algebra. That would be my top pick. Apparently she was just very stream-of-consciousness, talking about whatever she wanted to talk about that day. And it was such an exciting time, it was very foundational to commutative algebra especially.

Do you have any general advice for students looking to pursue a degree in mathematics or a career in the field?

Realize that math is much broader than what you’re taught in high school. There are lots and lots of different areas to study, and there are a huge number of careers that you can go into with a math degree.

________________________________________________________________________________

Thank you so much for meeting with us, Marcus! 

Math Madness: First Round Part 2

Here's the second round of results from the Math Madness bracket (view the first post 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 3: Gauss vs. Gromov

The third match sees Carl Friedrich Gauss, a German mathematician, against the modern mathematician Mikhail Gromov.

Throwback Fact: The Abel Prize

Many of our blog viewers are coming from one of our social media sites, so you’ll already know that we gave a shout out to the 2015 winners of the Abel Prize- John Nash and Louis Nirenberg. Their work in geometric analysis earned them the prize, regarded by many as the Nobel Prize of Mathematics. Nash is particularly interesting to those not versed in math research because his was already a household name: he was the subject of the 2001 Russell Crowe movie A Beautiful Mind (both of their pictures are above). 

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.