500th Blog Post!

Not to be meta, but this is our 500th blog post.

Toothpaste. It’s what’s for dinner.

Now back to your regularly scheduled program.

It doesn’t matter how you stack it

If Spring Break has already made you bored, you should know that the Problem Pontiff released the March Problem of the Month.  It’s all about tiling rectangles with rectangles.  In particular, rectangles with at least one side length being an integer.

A tiling of a rectangle by 7 rectangles.

For a full explanation of the problem and how to submit your solution, go to the POTM webpage.

And by remarkable cunning Adam Ladine was once again winner of the POTM!

Another tiling (from Indiana University’s Math Dept. gallary):

Post Pi Day

Apropos for Pi Day, Ed Karrels announced that he had computed new digits of $\pi$.  He does the calculations in hexadecimal (aka base 16).  Since computers compute things in bits (0′s and 1′s, or base 2), it is more natural for them to work base 2^n for some n, and for some reason computer folks settled on hexadecimal as the standard.

Anyway, he started at the 2,000,000,000,000,000th hexidecimal digit of $\pi$ and computed that the next few digits (in hexidecimal) are:

653728f1.

Or, to convert them into decimal, they’re:

27169820432.

Since each hexadecimal digit encodes a number between 0 and 15, that means, on average, a string of hexadecimal digits converts into a string of decimal digits approximately 4/3 times as long.  So Ed Karrels computed decimal digits of $\pi$ ’round about the 2,600,000,000,000,000th decimal digit.

But wait!, you say, I remember reading on this here blog that the current world record is  $\pi$ computed out to the 10 trillionth (10,000,000,000,000) decimal digit.   And that going from the 5 trillionth to the 10 trillionth digit was a major computation that took a year!  How did Ed Karrels manage to go from the 10 trillionth digit to the 2,600 trillionth digit in only two years?!??!

The world record by Alexander J. Yee & Shigeru Kondo of computing $\pi$ to the 10 trillionth digit is still the world record for digits computed from beginning (3.1415….) to end.

The secret is a formula for $\pi$ discovered by Bailey, Borwein and Plouffe in 1995.  Here it is:

It is a simple infinite series like in Calc III, but the beauty of it is that you can use it to obtain an algorithm which allows you to compute hexadecimal digits of $\pi$ without having to know all the proceeding digits!  It’s like having a mathematical wormhole which lets you make FTL jumps to anywhere in the digits of $\pi$!

Even cnn.com got into the $\pi$ Day spirit!

Fortunately pie eventually ends.

Computers and Mathematics

The proof.

There was an interesting article on wired.com this week about the use of computers in doing mathematics.  Nobody disputes that computers have become a valuable tool, but some argue that computers have made mathematicians obsolete.  This article gives some opinions from both sides.

Doron Zeilberger is a math professor at Rutgers who is well known for advocating computers over the human mind when doing mathematics (and for his many other strong opinions).

“Most of the things done by humans will be done easily by computers in 20 or 30 years,” Zeilberger said. “It’s already true in some parts of mathematics; a lot of papers published today done by humans are already obsolete and can be done using algorithms. Some of the problems we do today are completely uninteresting but are done because it’s something that humans can do.”

– from the slate.com article

On the other side, Constantin Teleman, stands up for humanity:

Constantin Teleman, a professor at the University of California at Berkeley who does not use computers in his work. In his opinion, that’s the problem. “Pure mathematics is not just about knowing the answer; it’s about understanding,” Teleman said. “If all you have come up with is ‘the computer checked a million cases,’ then that’s a failure of understanding.”

– also from the slate.com article

It’s an interesting question to think about. Read the article and the discussion on slate.com.

By the way, the article is originally from the Simons Foundation.  They have a number of interesting articles about cutting edge issues in math and science.  They also provide a number of interesting online video lectures and interviews with famous mathematicians and scientists.

Happy Belated Valentine’s Day!

Departmental Romantic, Ravi Shankar, asked us earlier this week to share this with everyone.   The delay is entirely due to the Blog staff suffering from a Valentine’s induced chocolate coma.

Happy Valentine’s Day, especially mathematics lovers! On the fun side, check out the graph of this implicit function: $x^2 + (y - x^{2/3})^2 = 1$. To see the full graph on your TI-83 or equivalent graphing calculator, sketch the following two graphs simultaneously on the window, $-2 < x < 2$ and $-2 < y < 2$. Let $Y1 = (x^2)^{1/3} + \sqrt{(1-x^2)}$, and let $Y2 = (x^2)^{1/3} - \sqrt{(1-x^2)}$. Note that if you type $x^{2/3}$ instead of $(x^2)^{1/3}$ for the first term in each equation, you will only see half the graph. Enjoy!

Or, if you don’t have your calculator handy, you can always try Wolfram Alpha.

Charlotte Simmons and the Best Math Writing of 2012

We are proud to tell you that our Ph.D. graduate Charlotte Simmons has an article in the  Best Writing in Mathematics 2012!  She earned her Ph.D. in 1998 at OU working with Murad Özaydin.  She is now a professor at University of Central Oklahoma in Edmond.

Her article first appeared in The College Mathematics Journal and is entitled “Augustus De Morgan Behind the Scenes”.  It’s about Augustus De Morgan.  But instead of discussing his mathematics (he of De Morgan’s Laws fame), Dr. Simmons instead tells the tale of how he was an important mentor to several famous mathematicians (Hamilton, Boole, Gompertz, and Ramchundra).

Dr. Simmons

You can read the start of her article here.  If you’d like to read the whole thing (and are at OU), you can log into the library and access the College Math Journal’s articles through their website.

Congratulations Dr. Simmons!

Thanks to Dr. Roche for letting us know about the article!

Intro Bioinformatics

If the last Math Club sounded interesting, then you should check out the brand new OU class “Introductory Bioinformatincs”!

Welcome to the Future.

Bioinformatics is the new field of science at the interface of computer science, math, and biology which deals with all the new data available in the biological sciences.  It is going to be at the center of both math and biology research for years to come (and will have tons of jobs, to boot!).

The details are below.

Bill Thurston: 1946 – 2012

Sadly, Bill Thurston passed away yesterday.  He was famous for his contributions in many areas of topology and geometry.  Not least of which was his Geometrization Conjecture (which was key to the proof of the famous Poincaré conjecture).  We also know of Dr. Thurston as a fashion icon.

He’ll be missed.

To read more about Dr. Thurston’s work, check out Terry Tao’s post about his work. In particular, read about Dr. Thurston’s proof of Smale’s result commonly called Smale’s Paradox: a sphere can be turned inside out in three dimensions without causing creases, pinched points or any other nondifferential points as long as you allow self-intersections.  Amazingly, the 2-D version (turning the circle inside out in the plane) is not possible!

Here is a cool video by the defunct U of MN Geometry Center explaining the eversion of the sphere:

Out to Innovate 2012

Mathematics (and science) doesn’t care if you’re male or female, where you grew up, how much money you make, or anything else for that matter.  When you’re working on a problem it’s just you and the problem.

Of course, math and science is done by people.  And people, consciously or unconsciously, tend to notice such things.

As we talked about here, Alan Turing knew all too well about both sides of doing math.

As you know, there’s the annual women in math conference that OU’ers attend.  In the same spirit, we’re happy to tell you that there is a biannual conference for LGBT (Lesbian, Gay, Bisexual, and Transgender) folks in STEM (Science, Technology, Engineering, and Mathematics).  It’s called Out to Innovate 2012.

According to the organizers it’s

…a summit intended to bring together LGBT and Ally high school, college and post-doctoral students, with LGBT career professionals, academics, and employers in the Science / Technology / Engineering / Mathematics community to share diversity, mentoring, and career learning opportunities.

– from the Out to Innovate webpage

Nergis Mavalvala

The keynote speakers are Nergis Mavalvala, a professor of physics at the Massachusetts Institute of Technology and Kei Koizumi, from the White House Office of Science and Technology Policy.

Kei Koizumi

If this sounds interesting, you should definitely consider going. And note that “allies” are also invited!

If you’re interested in the conference, you may also be interested in one of the sponsoring organizations, NOGLSTP* (National Organization of Gay and Lesbian Scientists and Technical Professionals).

* What’s with all the acronyms in today’s post?