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.

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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.

Problem of the Week

Happy Monday and Happy Spring! Unfortunately, it still doesn't feel like Spring in the Boston/Cambridge area. We at the Center still need to bundle up to our necks to make it across the street for lunch. Fortunately, I've got a Problem of the Week to share to distract us from the cold:

This problem is pretty easy. But you need to use mathematics to make sure you've exhausted all possible solutions- don't simply guess and check. Like usual, I've shared my solution below...

Math Madness- the Sweet 16

Math Madness has begun at the Center of Mathematics! If you don’t know what I’m talking about, view our newest webpage and feast your eyes. Our mission is to determine the greatest, most influential mathematician of all time. Check back often for information about voting!

Math Madness has begun!

We had to narrow down a list of hundreds of influential, important mathematicians to just 16. We wanted to choose a variety of mathematicians: some ancient, some modern, some geometers, some number theorists, some famous, some more obscure but significant. We even recruited the opinion of visiting mathematician Lê Dung Tráng to decide on our Sweet 16. 

Math Minds: Lê Dũng Tráng

Over the past week, we've had retired Professor Lê Dũng Tráng visiting the Worldwide Center of Mathematics. Born in Saigon, Vietnam and raised in Paris, France, his work in mathematics extends over almost 50 years and across 4 continents. Lê has been a friend of the Center of Math since its founding, and has contributed two research lectures to our YouTube channel (view them here and here). He sat down with interns Tori and Zach for an interview.

What is your current position?

I’m currently retired, both from UNESCO and from France, and I am visiting a university in Brazil. I belong to the Federal University of Ceará in Fortaleza, in the  Northeast of Brazil.

Throwback Fact: The Metric System

image: commons.wikimedia.org

On this day in history, in 1791, the Metric System was proposed for the first time to the Paris Academy of Sciences. The main features of this system were to standardize a set of interrelated base units and prefixes in powers of 10. The system was first developed for commercial use, but the standardized unit size made it particularly suitable for science and engineering.

Problem of the Week

Happy Monday! Sorry we missed last week's problem of the week. To make up for it, we have a particularly challenging problem today- it can be done using calculus or geometry. I elected to solve it using calculus. We posted the following image on our social media pages:

And like usual, I've solved the problem below...

Math Minds: Holly Krieger

This week, Center of Math intern Tori sat down with Dr. Holly Krieger, a post-doctorate fellow and instructor at MIT. Dr. Krieger discusses her research, her favorite math class, and her time with web series Numberphile below.

Dr. Holly Krieger

I’ve done a little bit of background research on your research topics-  is there any reason you chose algebraic geometry and dynamical systems as your focus?

I was always interested in Number Theory, just because it’s an incredibly appealing subject. You can state some of these problems very simply, but they’re very intricate and deep mathematics. I got into dynamical systems through coursework I took in graduate school. It’s sort of a new field, it’s not something that [undergraduates] would necessarily take a class in, but once I became aware of the field it was of course interesting, and that’s how I ended up going that direction.

Throwback Fact: Pi Day

image: flickr.com

This Saturday, March 14th, is known as the "Ultimate Pi Day" because the first 10 digits of pi (3.141592653) line up with an observable time: March 14th, 2015 at 9:26:53 AM or PM. 

But actually, all infinite digits are represented.

All of the digits after the first 10 are not quite observable. But about halfway between the 9:26:53 and 9:26:54, there will also be 58 centiseconds, 97 deciseconds, and so on until infinity.

This fact is exciting mathematicians into celebrating Pi Day even if they haven't bothered before. In fact, choosing March 14th to celebrate Pi annoyed a few mathematicians. Using 3.14 cuts Pi into a tiny approximation, and ignores everything that makes Pi incredible, like its transcendentalism.

Throwback Fact: Magic Squares

image: commons.wikimedia.org
An example of a 4th order Magic Square

Last week we discussed Japanese geometry puzzles. If you missed it, check out Sangaku here. This week, we’ll talk about a puzzle game again: Magic Squares.

These fascinating puzzles date back to around 2200 B. C. E. Traditionally, they are played on a grid consisting of n-rows and n-columns, for a total of n^2 boxes. Each of the boxes are filled with integers so that the sums of the horizontal rows, vertical columns, and diagonals are equal. If each integer from 1-n is used, the square applies for special qualifications. These squares are known as nth order magic squares, and the sum of each row will always be equal to: [n(n^(2)+1)]/2.

UncommonGoods Pi Day Giveaway

UPDATE: The contest has concluded, and the winning comment has been randomly selected! Congratulations Sara, we are working to get in contact with you now. Thanks everyone for participating!

Image: http://www.uncommongoods.com/product/pi-basket

March 14, 2015 will be a date of celebration for many "math nerds" around the country. Whether you celebrate the date, or think it's a little too silly, it's fun to see all of the creativity that pours out of mathematicians, designers, writers, and artists alike as "Pi Day" approaches each year. This year's date is even more momentous than usual- at 9:26:53 AM and PM, the date and time will represent the first 10 digits of pi. 3.141592653... If you count your milliseconds and beyond, to each infinitessimally small fraction of a second, the date and time will represent the infinite digits of pi between 9:26:53 and 9:26:54.

Our Reaction to the Textbook Market

Image: commons.wikimedia.org

As college students ourselves, we (the interns at the Center) worry about the price of textbooks at the beginning of each semester.

Would you rather have this?

Why spend $1,200 on textbooks in a calendar year if you simply don’t need to? For less than $200 ($169.23 before taxes, to be precise) students or professors could purchase a digital copy of every textbook, electronic study guide, and iPhone/Android app we offer, plus a sweet Center of Math t-shirt. Our prices provide an opportunity for college students to deviate from the doldrums of the dining hall to …*gasp*…edible food!

Problem of the Week

Happy Monday to all of our readers, regular and new. We've been working on a lot of great new content for the blog that should be starting this month, including the continuation of the interview series. But for now, take a look at our newest Problem of the Week. Like usual, I've hosted the solution below. Here's what was posted to our Facebook, Twitter, and Google +:

Click to expand!

A proof! This one shouldn't be too difficult. It will act as a good brain teaser to kick off the week. Here's how I solved the problem.