Math in the Media: Arguing on Pi-Day

I cannot say that we, as mathematicians, do not have our fair share of math-arguments and inside jokes and math puns and such.  You know, stuff that the "outside" world would either groan at or simply walk away from in a head-shaking fashion.  But Pi-Day, March 14, or 3/14, does seem to bring things like this to the surface....

Here are two articles that have leaked out into the "real" world.  The first is not a real debate or controversy, really..., but it is kinda fun in a strange sort of way.  It is an argument for a better way to generally represent the constant that arises from comparing the diameter or radius of a circle to its circumference.  Since pi radians represents only half a turn around a circle, why not have the universal constant simply be 2pi, representing a full turn around the circle.  Call this number tau = 2pi.  The article, in the Verge, is kind of a rant on pi's fame:

Stop Celebrating Pi Day and embrace Tau as the true circle constant

I am not sure about this one, but the accompanying "Tau Manifesto" is a pretty good read. 

The other is really more of a comedy routine, designed to educate and highlight some real math.  The sort of sweetened medicine you were forced to take as a child.  Broadcast via Mother Jones, the interview/debate

What is the greatest number of all time?

is an argument between two mathematicians Tom Garrity and Colin Adams.  Clever....

Enjoy Pi-Day!!!

Math in the Media: The Best jobs of 2015?

I keep telling you....  Math pays!! 

In the Business section of the online newspaper The Huffington Post sits an article by Jennie Che detailing the Best Jobs of 2015, a report prepared each year by CareerCast, ranking the top 200 jobs by work environment, income, stress and hiring outlook. 

And lo and behold, mathematics permeates most of the list, with the actual job of Mathematician, sitting at number 3 (Actuarial Scientist tops the list, with Statistics sitting at number 4).  The HuffPost article

These Are The 10 Best Jobs Of 2015

is a summary of the longer article posted directly in the CareerCast website:

The Best Jobs of 2015

(always go to the source, right?)   Personally, I've held position both in academia and in industry (NASA Goddard and Lincoln Laboratory, as well as in a private tech firm.)  All were great work environments, with interesting people, work conditions, and colleagues.  I certainly cannot argue with the conclusion that math is a great field to play in.

Give the article a read!  It's good stuff.

Math in the Media: NFL Mathematician??

I am often asked what kinds of careers can a mathematician construct for themselves.  There are many answers to this question, and in full generality, the list is long and very diverse.  However, I recently found a new one:  Professional American football player!!  

It seems that our very own John Urschel, a guard of the Baltimore Ravens ("our very own" because we are here in Baltimore after all), is a mathematician whose recent paper "A Cascadic Multigrid Algorithm for Computing the Fielder Vector of Graph Laplacians” has been accepted for publication in the Journal of Computational Mathematics.  Mr. Urschel received his Masters Degree in Mathematics from Penn State and was drafted by the Ravens last year.

One can find mathematicians in the oddest of places, no?  One just has to look carefully....

...although in this case, it is not hard to see.  Mr. Urschel's is on Twitter.  His name??

....@MathMeetsFball 

Math in the Media: Gender Bias in Teachers?

Yes, it does take a village to raise a child....  (H/T to The Honorable Hillary Rodham Clinton.)  But it seems it also takes a village to discourage girls from achieving their full potential in math and math-related fields....  (Sigh!)

In a new study, headed by Edith Sand, an economist at the Bank of Israel and an instructor at the Tel-Aviv University’s Berglas School of Economics, teachers themselves contribute to the problem of too many female students shying away from higher-level math courses as they progress in their education.  The study found a gender bias in performance evaluation;  Teachers who knew the identities of their students tended to grade girls more harshly and boys less so on exams than teachers who did not have any information about the students.   Unconscious or not, our influence as teachers on students always goes far beyond the content of our lectures and exercises.  But this influence may not always be constructive.  What care we need to always take....

The article, reported by Linda Carroll for Today, is  here:

Teacher Bias May Help Discourage Girls from Math, Study Finds

The study is published by the National Bureau of Economic Research in Cambridge, Mass.

Depressing...?  Yes.  Hopeful?  Also.  Knowing of an unconscious bias can contribute to its cure, eh? 

Remember School House Rock?  "Knowledge is Power"

Math in the Media: Homer vs. Pierre?

I just had the pleasure of watching a neat 8 minute video detailing some of the mathematics injected in to the Simpsons animations.  Apparently, there are mathematicians among the creative staff who cannot help themselves throwing in a little math humor into the background every so often. 

The video, listed here on YouTube by Numberphile is titled

Homer Simpson vs Pierre de Fermat

 Do give it a watch.  It is always good to know where the subliminal messages about how cool math really is are lurking, no?

Math in the Media: Stereotype Threat?

How often we are in Mathematics faced with the fact that our profession was, and still is, quite female-starved;  that boys and men are thought to be better at math than girls and women (an amazingly ridiculous thought, given my view up here!).  So many recent studies seem to point decidedly at the dangerous effects of a person's perceptions of ability at the moment of evaluation and how easily they can affect performance.  For example, reminding students of a stereotype they conform to just before taking a math test tends to degrade performance.  This slow drip of research exposing the damaging effects of culture bias and preconceptions on lack of ability can only have a good effect in the long run.  And I do see here at Hopkins some light in the form of a general welcoming attitude and positive outreach to students studying higher mathematics regardless of gender.  But it does seem that this huge ship turns only very slowly.

Over at the online newspaper, the Huffington Post, Cailin O’Connor, a Professor of the Philosophy of Science at the University of California, Irvine, details some of the evidence that runs contrary to the notion of an innate gender bias in mathematical ability here:

Are Women Worse at Math?  It's Time to Stop Asking

Her take?   Perhaps it is time to stop focusing on looking for innate differences between the genders in mathematical ability and start simply addressing the cultural barriers that keep the gender balances way too tilted to one side. 

I agree, but still love seeing the rising tide of evidence condemning the idea that math is more a male thing.  Geez!

Math in the Media: Prime Gaps....

I am always amazed at how some of the most vexing, curious and fascinating puzzles in mathematics can be stated so simply, even as they evade solution or even complete understanding for centuries.  It is one of the more alluring aspects of this trade. 

Here's one:  Just how big can the gaps between consecutive pairs of prime numbers get as one traverses the natural numbers out toward infinity? 

One would expect the gaps to get larger and larger and also tend toward infinity in the long run, no?  But showing this, and providing some sort of measure of the growth of the size of the gaps as one goes "out there" has been remarkably elusive. 

I'll let you read this nice article by Erica Klarreich in Quanta Magazine, to "see" that progress has recently been made, and there is promise of more progress coming. 

Mathematicians Make a Major Discovery About Prime Numbers

Will math ever cease to amaze....

Math in the Media: Mathematics is Evil?

There is an old saying (really, I just made this up):  If you are looking for immortality, you have two choices.  Become famous, or become infamous.  Either way, you will not soon be forgotten....

A professor here is uncovering an interesting conjecture.  The fictitious, evil mastermind and arch-nemesis of Sherlock Holmes, Professor James Moriarity, was modeled by Sir Arthur Conan Doyle on a mathematics professor here at Hopkins.  The similarities are quite striking, detailed here by current professor Carl McTague

Moriarity at Hopkins

Give it a read.  Nice idea, eh?

Math in the Media: Return on Investment in a Math Degree?

So I would up devoting my life to the study of Mathematics because I absolutely love the subject.  It is inherently beautiful, surprisingly counter-intuitive, and seems to exhibit a logical framework for all that is in a way that I find ever intriguing.

However..., the study of math at a high level is also quite lucrative!!

Here is an article from Bloomberg Business Week, from June:

Undergrad Business Majors Don't Get the Career Payback Math Majors Do

You must love this title from my perspective.  The article highlights a measure of the lifetime worth of different college majors in term of a return on investment of time and effort.  Some majors are harder than others, I am sure.  And why they decided to include math and computer science together is a mystery to me (perhaps that is how the business world sees us?  As the studiers of logic?

In any case, they make a good case for choosing math as a major while here in the Ivory Tower. Call that reason number..., what... 132 in the countably infinite number of reasons why someone can benefit from choosing math as a major?  (BTW, have you heard that over 80% of statistics are made up on the spot?)

Give it a read.  I will await your change-of-major form....  ;-)

Math in the Media: Finally!! A female Fields Medalist....

Well, I am back and in time for a new semester here at Hopkins.  And I am back with some very nice news. 

The next recipients of one of our field's top honors, the Fields Medal, includes Maryam Mirzakhani, an Iranian born mathematician at Stanford University.  She is a dynamicist (a mathematician whose field of study is dynamical systems) and the first woman to receive this prize since its inception in 1936.  She shares the prize this year (the prize is given out every four years) with three other mathematicians, listed in this article in the New York Times, 

Top Math Prize Has Its First Female Winner.

And while there should be nothing special about a woman receiving the prize (math is hardly a gender-specific endeavor), I do have sort of a glass-ceiling-breaking-moment feeling here.  Congratulations, Professor and Professors!  Here's to more outstanding math research.

And here is another nice write up of this event and her contributions to mathematics.

Playfully Serious Math: A glimpse at Vi Hart and Fibonacci

I am often struck by just how repulsive mathematics is to some people when, in my eyes, it is all an absolute kaleidoscope of color, art and logical splendor.  But it is not always easy to get someone else to see what you see.  This is what education is all about, I guess.  One step at a time....

I was recently turned on to an absolutely wonderful math and science educator whose videos would do well to provide the backbone of the next generation of the Common Core, at least in math education.  Vi Hart is a videographer (is that what one would call someone who makes videos) who specializes in a playful, though very serious approach to expose and illustrate complicated science concepts and techniques.  One of her series, entitled Doodling in Math Class, exposes the rich, playful and beautiful structure inherent in every math class but lost in the tedium of sterile, and solely utile function.  Below is a three part video explaining why and how the Fibonacci Sequence (not a series, really) shows up so often in nature.  It is mind-boggingly well done, IMHO:

Doodling in Math: Spirals, Fibonacci, and Being a Plant

The other two parts follow immediately from this one.  Give them a look!

BTW, THIS is what mathematics is really about.  Vi's money quote (at the end of the third part):

This is why science and math are so much fun.  You discover things that seem impossible to be true, and then you get to figure out why it is impossible for them not to be true.

Math in the Media: TEDx and me....

Late last year, I was asked to give a TEDx talk (the 'x' means locally organized) for the inaugural TEDx event here at Hopkins (called TEDxJohnsHopkinsUniversity).  I gladly accepted, seeing it as a chance to say something I've been wanting to say for a while:  I wanted to give a talk on what mathematics means to me and why I chose it as a lifestyle.  On February 22, 2014, here on campus, I gave the talk, entitled "Why Mathematics?".

Here it is in full:

Why Mathematics?

It was a great experience, and the organizers did an excellent job.  I hope you find the talk interesting.

Math in the Media - Perhaps the Matrix is....

Here is an article filed under the category "Thoughts to Ponder":  Edward Frenkel, a mathematician from Berkeley, posits that the university perhaps is just a giant simulation and we are simply participants.  How would we know?  Can we detect if we were?  The article is an OpEd in the New York Times, and can be found here:

Is the Universe a Simulation?

Frenkel gives some sense to this idea by differentiating (no pun intended) mathematical ideas (manuscripts, really) from literary ones in the following way:  Mathematical ideas are somewhat universal.  The laws and constructions of Pythagorus, Euclid, Newton, etc., would surely have been created (discovered?) even if these greats had never existed.  It may have taken longer for someone else to develop them.  But the structure of mathematics (its logical framework) exists as it is whether we discover it or not.  Try that with a sonnet sans Shakespeare....

It is a very nice read, this article, and again, gives a sense for how mathematics seems different from other disciplines of study.  Frenkel mentions that many mathematicians consider themselves Platonists, believers that everything exists in the ideal, and what we perceive in this world is simply real versions of that ideal.  It works for me.  I would believe that it would work for most all mathematicians, really.

Frenkel even goes so far as to say that the giant computer simulation that we exist in is, like all computer simulations, not entirely without anomalies, coding inaccuracies that render the coding conspicuous.  Perhaps all of our logic in mathematics is simply facets of the coding that can be detected "from within"?

Certainly a "thought to ponder"....     

Beauty in Math

Mathematicians often talk about their craft in emotional terms.  We get excited by elegant, beautiful, clever constructions and the hidden insight in the logical relationships we uncover.  We can easily be stunned into awe when our intuition leads us astray, and something we did not expect pops out of our reasoning.  And when we see a formula or other type of mathematical construction that not only looks aesthetically pleasing, but contains meaning far beyond its simple symbolic patterns, we treat it as something that should be hanging in the Louvre....

Beauty has profound meaning in mathematics, at least to us.

Not sure you believe me?  Well, a paper just published in the journal Frontiers in Human Neuroscience may just change your mind.  Researchers use Functional Magnetic Resonance Imaging (fMRI) to map the brain activity of mathematicians as they viewed various mathematical formulae and constructions that they have rated on an ugly-beautiful scale.  That part of the brain that is activated when people see beautiful art, or hear beautiful music (yes, there is a specific place)?  Evidently, that place lights up when we view math that we see as beautiful.  At least to us, it is real. 

Give it a read (H/T to CG!!): 

Mathematical beauty activates same brain region as great art or music

BTW, the most beautiful formula of the study:  Why Euler's Identity, of course!  Can you see the beauty?

Best Job out there? - Yes, its Mathematician!

So what is the best job in the US these days?

The Wall Street Journal reported on a ranking of professions from the site CareerCast.com.  They released a study this week that evaluates 200 professions to determine the best and worst according to five criteria inherent to every job: environment, income, employment outlook, physical demands and stress.

Bottom of the list:  Lumberjack, dairy farmer and taxi driver.

Top of the list:  Mathematician (and actuary and statistician, to round out the top three) with a median annual income of over $94000, low stress, and VERY CREATIVE work (okay, the last bit is an editorial opinion.  But one of the people highlighted in the article does have very interesting projects to work on....  jussayn'.)

Give the article a read.  See where your dream job lies:

Doing the Math to Find the Good Jobs

 Personally, I agree with the top ranking.  It is a good gig!

Most Valuable College Majors? Think MATH!!

Forbes, the American magazine of all things business, has just published a listing of the top 15 most valuable college majors.  The listing comes from the PayScale's massive compensation database and job growth projections through 2020 from the U.S. Bureau of Labor Statistics.  Majors are ranked in terms of salary and career prospects. Indeed, rankings are by median starting pay, median mid-career pay (at least 10 years experience), percentage growth in pay and projected growth of job opportunities.  See  here:

15 Most Valuable College Majors 

And lo and behold?  Check out number's 10 and 11, respectively Applied Mathematics and Mathematics. Median starting salaries fresh out of college are $52,600 and $47,000, and mid-career $89,900 and $96,000, again both respectively.

Of course, at least from my perspective, Biomedical Engineering tops the list, as do a few other engineering fields.

But can you imagine the market value of an engineering or natural science degree AND a math degree? The sky's the limit, no?

Talk to me if interested....

Math in the Media - A matter of motivation, not IQ?

I am and have always been convinced that ANYONE can do mathematics if they have the proper motivation, interest, and access to good mentors and training material, at least to the levels found up to and including the first year in college.  I believe that ineffective education and cultural and societal biases are reasons why mathematics education has a mystique about is as something less than the primer coat of all higher level thinking.

So articles on studies like that mentioned here in a Scientific American article

Like Math?  Thank Your Motivation, Not IQ, 

by Tia Ghose and Live Science, are quite refreshing to read.   

To me, the findings are not surprising.  It just seems perfectly natural that a person's motivation to learn a skill is extremely important to their ability to master it.  More important than intelligence?  Ahhh....  Read the article.    

Math in the Media - Cowlicks and Hurricane Eyes

Ever wonder why babies have cowlicks (that spot on their head where the hair just doesn't want to follow any particular direction)?  If the time of the day depends on your time zone, then how does one determine the time at the North Pole?  How come hurricanes have "eyes"?

The answer, unfortunately (or fortunately, depending on your perspective) is mathematical in nature.  More specifically topology.  For a glimpse of why, read today's New York Times article:

Singular Sensations

by Steven Strogatz.  A fun article, with the promise of a lot more in the future.  Give it a read.

One thing you will start to find.  We as mathematicians see our craft everywhere, in basically ALL places.  Math really is the exposure of logical structure, regardless of the context.  But it takes talent to expose that math in an engaging way to someone not trained to see it.  Mr. Strogatz has talent.

Happy reading.   

Math in the Media: Math Food?

One of the more basic and interesting shapes (spaces) in mathematics is the torus.  We typically describe is as the surface of a doughnut or bagel.  That it is mathematically different from the surface of a ball is a good entry point for a lay explanation of some fun higher mathematics. 

Speaking of a bagel, here is an interesting video on a way to mathematically play with your food:

A Mathematically Correct Breakfast

Buon appetito!!!

Math in the Media: To save this math class, we must destroy it!

Words failed me (mostly) when I read this article today in the Washington Post:

At Virginia Tech,  Computers Help Solve a Math Class Problem

It is a common problem that the transition from high school mathematics courses to those at university can be quite difficult to make.  Even in courses whose content is basically the same, like Calculus AB in the AP system and what most universities call Calculus I, the treatment of that content is much different here at the university.  Of course, students sometimes do not do well.  And I am sure that sub-standard teaching from some of us up here may be a part of it.  We need very much to analyze how we teach and learn to do a better job!  And many of us are.  IN fact, here at Hopkins, we are devoting a LOT of resources precisely to this problem of how to better and more comprehensively educate our incoming students.

But to help cure the "problem" of not-high-enough passing rates by essentially removing instructor face-time from teaching!?!  That is patently absurd in my book.

Mathematics is absolutely NOT about learning a few techniques to apply to standard problems set up to test those techniques, which is exactly what many unit-based, worksheet driven, math courses seem to be like pre-college level.  Porting that type of course to the university level may in fact raise passing rates.  But without the ability to study nuanced mathematical ideas and relationships via discussion and debate (think Socrates), one never learns how to THINK mathematically.  Only to calculate.

Maybe that is what VTech is looking for.  I, for one, am not.