Wednesday, October 21, 2009

When Food-For-Thought becomes Food-For-Your-Family

    Many people, even mathematicians, feel that pure mathematics is useless. But I would argue that at the very least, pure mathematics has always been useful to those who love it-- in keeping us happy, mentally healthy people! Healthy happy people make better life partners, better parents, and citizens who are more likely to help maintain order and fairness. In this way mathematics is a lot like art or sports.
    So what happens when an artist or an athlete finally starts to make money with their art or sport? Well, it messes with our heads. We start to question our motivations. On those days when we just don't feel like thinking about math non-stop or when it feels like we are banging our heads against a wall, we feel guilty because we're not doing our job or we're not doing it well. We're goofing off, we're not productive! "Wait a minute," the brain says, "I used to goof of by DOING MATH!" The brain starts to freak out that its owner will never solve that thesis problem, will not be a good enough professional mathematician, that "gasp!" the brain will lie dormant while its owner teaches BUSINESS CALCULUS FOREVER!!! That may be every math graduate students biggest fear. So how do we recover the feeling of joy and amazement that we first had??
      My first love of pure mathematics grew out of my joy at solving puzzles as a child, an excitement at having to exercise my brain, the struggle followed by the success, and a feeling that I owned the solution. I never cared whether the solution to the puzzle would lead to a cure for a disease, a better battery, or a million dollars. I did math problems for the same reasons that I spent hours every week dancing or reading everything I could about horses -- it was intrinsically appealing and satisfying! I liked to tell my friends mathy riddles, draw mathy pictures, do modular origami, and talk math with my dad on our walks around the neighborhood.
    Young people who have that joy and amazement oozing out of their pours inspire us. Teaching young people, hanging out with my friends' kids, I feel like I can tap into their curiosity. And kids don't feel guilty about or try to justify their likes or dislikes. Our adult culture seems to have a vast spreadsheet of pre-approved purposes for why we should do something non-work-related.  When was the last time you bought a book because you wanted to "do your small part to help the economy"?  By always rationalizing the activities we do when we're not working, we negate the benefits of those activities while adding to our ambivalence about the work we're supposed to be doing. Don't feel like doing math? Not getting anywhere? Writers have writer's block, and they still think of themselves as writers. So, do something else you really enjoy for a while, and you'll still be a mathematician.
   Activities whose outcome is not directly tied into my economic well-being renew my sense of learning for learning's sake. I can immerse myself for a few hours in a physical and/or expressive activity  like swimming, dance, art, music, jogging, biking, or yoga. Appreciating the expressions of others through their art also fills this need to acquire "useless" information. Lastly, wandering around/exploring a city or the outdoors is"pointless" but awakens my senses and get me back into the mindset that I am on the lookout for beauty and not results.
   On this note, a friend told me recently: "I was driving home today, and I saw this beautiful sunset!  I thought to myself 'If only I had my camera!' But I couldn't enjoy it because I became so focused on getting home and getting my camera. When I finally got the camera and walked outside, the sunset was gone.  Why couldn't I have just enjoyed it while it was there?!" I think this illustrates that fact that beauty is transient, just like the inspiration you need to do mathematics, and it doesn't emerge because someone is pursuing it.
   So if I feel like biking around and taking in the scenery without a destination in mind, I just do it.
I swim back and forth in a lane while thinking about my breath and counting my strokes.  I move from one yoga poses to the next even if I fall over in between.  I walk out on the dance floor with a stranger and follow each movement as it arrives.  I turn my thoughts into lyrics as I walk home.
   Those of us who have the opportunity to put food on the table and feed our heads at the same are privileged.  We can retain a child-like curiosity even as we grow into new adult responsibilities.  Or we  bend our intellects to fit a "grown-up" world that is, in truth, incredibly immature and irrational.

Tuesday, October 13, 2009

Job Search!

So, I am searching for a job! Maybe you are too. Here are some tips from post-docs and professors at my school, UC Santa Barbara.

Before applying:
First Priority is doing good math! Study area you like, be open to new areas
i.e. Get papers written, go to conferences, give talks

General: make 100 applications (half post-docs, half teaching)
Apply even if they aren't necessarily hiring someone in your area/level
Apply even if no job is being offered (as long as you have some sort of contact there)
Read job ads carefully -- a tenure-track ad may also want post-doc
Look at list of EIMS, AMS (sign up on mail list), keep your eyes open for other opportunities not on Math-Jobs
Prioritize time, organize your materials well, be efficient about applying

Cover Letter:
Make a website with all of your application info so that you can email
professors at the institution to which you're applying

Use all of your human resources: other grad students who are also applying, your committee members

Make your cover letter focus on the specific institution

Top line of cover letter has you name, advisor, people you want to work with. Work hard on the ten places and apply everywhere even if you don't think you'll fit in. Have extra eyes -- You want to avoid "I want to work with Prof. X" who doesn't even work there -- to scan through.

Have two different cover letters (mention you'll be at Joint Meetings),

Recommendation Letters:
Who are you going to get to write letters? Advisor, committee, people from other institutions, teaching mentors
Letters of recommendation are the last thing read sometimes, but the letters need to support the image portrayed in the rest of the application (i.e. The person is an excellent researcher or excellent teacher or both and why)

Research/Research Statement:
Two research statements (non-expert level, expert level) supervising undergraduate research

How specific should this get: choose your own adventrue research statement ("for the expert:", "for the non-expert"). Convey enthusiasm! Think like a colloquium (general audience understands first fifteen minutes, last fifteen minutes throw in something that an officianado will understand
ignore above "colloquium advice" if you are aiming to work with a specific professor in which case you should email them separately and make the statement a little more technical.
Three or Four pages max

Teaching/Teaching Statement:
document your unique experiences (teaching), be proactive (have someone send an email referring you)
Remember: Michigan, Chicago, Texas all have Inquiry-based teaching centers

Two different C.V.'s (long and short)
Look at peoples websites for examples of C.V.'s
Don't discount non-math interests

After you submit applications and are waiting to hear back:

1) Remind people that you applied without spamming them
a) My paper's been accepted
b) I got an offer

2) Be prepared for telephone interviews

Happy Hunting!!

Friday, September 25, 2009

D.I.Y. Disorienting Holiday Gift Ideas for the Mathematically Inclined

Above, we see a baby Felix Klein and the Klein bottle which was later named after him. Baby Felix's German family probably didn't give him lots of useless presents around the holidays, and he turned out okay (aka brilliant mathematician/physicist). All of this going out an buying extravagant gifts for the holidays just strikes me as silly, and the Holiday Sales are already starting, trying to entice all of us poor people to dish out dollars for useless junk. So I thought I'd start a list of math-themed gifts under $15 that are sure to please. Everyone knows that mathematicians love to be disoriented -- or at least they know that being disoriented is nothing to be ashamed of.

Make a Glass Klein Bottle for your favorite mathematician:
Don't remember what a Klein Bottle is? Take a cylinder and glue the ends together with opposite orientation. In other words, as you traverse clockwise around one end, glue the other end counterclockwise. Can't do it? That's because it can't be done in three dimensions without letting the cylinder intersect with itself. Acme Klein Bottles is a company that specializes in beautiful glass Klein Bottles that are, in general, pretty expensive. BUT, the good news is Acme Klein Bottles, there is a $10 option that may appeal to those conservationists/penny-pinchers among you.
The Jigsaw Puzzle comes with a free band-aid!

Make a Mobius Music Box for your loved one:

I ordered my very own DIY Music Box Kit, and made my own little music box! It was fun and you can do it too.
Take a gander at Think Geek's Kit.
AND Note that you can punch your own holes to compose an original backwards\upside down masterpiece.
By the way, August Mobius is the namesake of this strip, which was also discovered by a man whose last name was Listing. But which sounds cooler "Listing" or "Mobius"? Yeah, that's what I thought.

I have not tried this next one, but judging from my minimal knitting skillz, I may stick to the "Mobius Scarf", which I saw at Oiyi's Crafts Blog.

Make a Klein Bottle Hat to keep those precious brains warm:
Mathematician Sarah-Marie Belcastro generously provides instructions at her website for knitting these self-intersecting representations of the Klein Bottle. There is also a link to making hyperbolic baby pants.

Really, Real Projective Space deserves more recognition here. I mean, it's disorienting too!
In case you don't remember real projective space, it is what you get by taking a sphere and identifying (gluing together) antipodal points (i.e. the north and south pole). Since this space cannot be embedded (made accurately) in three dimensions (try it), we will make do with "Boy's Surface", which is an immersion (has self-intersection) just as our models of the Klein Bottle are. This immersion was part of Werner Boy's 1901 Thesis written under the Famous Mathematician Hilbert. The surface, which is pictured above, was discovered as a result of Hilbert's request for Boy to prove that no such immersion existed. So, even famous guys can be wrong!

Make Your Boy (or Girl) Boy's Surface:
Courtesy of Joe Field's website, you can use just good old fashioned paper, scissors, and tape to make Boy's Surface.

Lastly, I make the observation that all of these unorientable manifolds were first described by Germans -- coincidence?
Yeah, Probably. But a funny one!

Okay, I'd love to see some other disorienting and inexpensive gift ideas from my readership, which I imagine to be growing exponentially -- as in from 0 to 1 maybe :)

Monday, September 14, 2009

Game and Movie of the day


Want to kill some time doing a little group theory in disguise?
Check out the game Expacon designed by Dr. Gilbert Baumslag of City College of New York. The name of the game comes from the "Expansion/contraction" of words allowed by the rules. If you ever took group theory, you will recognize this as a thinly disguised exercise in showing that certain words written in the generators of a group are trivial. If you don't know what group theory is, you will have some fun!
Also, there is an upcoming conference October 1st and 2nd in New York on the subject of finitely presented groups, the first part of which is designed with graduate students in mind.


Like Origami and Mathematics?
Basically, as Robert Lang points out in his recent TED talk, folding up enormous sheet-like objects into small packages is a skill that is in demand in many scientific communities. The provocatively titled new movie "Between the Folds" which features (among others) Robert Lang and mathematician Tom Hull explores connections between the art of paper folding and the sciences. The film will be shown on PBS on December 22.

Friday, September 11, 2009

The Mobius Music Box!

Back in February 2009, artist Ranjit Bhatnagar decided to make an instrument a day as part of a course he was teaching at the Parsons School of Design in New York, and one of those days he was inspired to create a Mobius Music Box which plays a song forwards AND backwards as many times as you can turn the crank!

Here is a link to his blog Moonmilk

Wednesday, September 9, 2009

Alice Munro Writes about Sonja Kovalevsky

Just wanted to bring attention to a new short story by Alice Munro, a famous Canadian short story writer, about the mathematician Sofia Kovalevsky. In only 41 years, this amazing mathematician managed to accomplish a lifetime's worth of goals. Unlike many stories about mathematicians, Too Much Happiness paints a picture of a sane, amiable, and relatable mathematician while relating some of the challenges faced by a pioneer. Check out the short story in the July Harper's Magazine or in her new book of short stories of the name Too Much Happiness.
Just a note, the stamp shown was created in her honor by her country during the same time that she was refused any job there. Can you imagine someone who could get their face on a stamp but couldn't find a job?

And here's a great joke I heard that has nothing to do with Sonja Kovalevsky, but which, given her interest in writing (she completed several novels), I'd like to think she might have appreciated:

"What's longer: mile or kilometer?"

The answer of course is kilometer because if you remove mile from kilometer, you are left with something .... "koter".

Unfortunately I did not make this up. I read it in a thread in which the answer to the question in quotes was, believe it or not, hotly debated!

Friday, May 29, 2009

Crocheting and Hyperbolic Space

You might not think of mathematics and art as being political, but science writer Margaret Wertheim uses her crochet models of hyperbolic space to discuss environmental issues and education. She really seems to relish putting down mathematical formalism, and she exaggerates mathematicians lack of interest in "playing" with tactile models. But it's still thought-provoking to listen to her spiel, and fun to see the pics:

Monday, April 27, 2009

NPR story on "Largest Prime Number"

   Yep, that's right, you can listen to it at .  
They are talking about the Great Internet Mersenne Prime Search, and they can't even say 
"2^n-1" out loud, but they can say 
The number is currently the world's largest prime. But there's always a larger one to find."

WOW!  This sounds like a huge contradiction even if the "world's largest prime" is different from "the largest prime".  Also, wouldn't it seem relevant to mention that no one has proven that there infinitely many Mersenne Primes?  

Still, the part about the Hope Diamond is kind of interesting -- Are Mersenne Primes mathematical diamonds?  What are your mathematical "diamonds"?

Compare with Look Around You -- Maths (the section about the longest number)

Monday, April 13, 2009

Math did not kill your 401K

So I sent this to the LA Times as an editorial, and they wouldn't publish it.
So here it is.

Some financial experts would have us believe that they were lured into ruin by a seductive model, a mathematical model. A recent Wired article blamed our economic crisis on economist David Li and his "fatally flawed function", with "all powerful" parameters, giving rise to an "irresistible" equation. Since when is equality a "dangerously precise concept" that leads financial experts to divorce themselves from reality?
The tendency to blame "quants" (quantitative analysts) is becoming more prevalent as people look for a convenient scapegoat. In a recent letter to his shareholders, Warren Buffet chided his audience for being taken in by “a nerdy-sounding priesthood, using esoteric terms such as beta, gamma, sigma and the like.” I hear from many people that math is Greek to them, but as Mr. Buffet demonstrates with his use of the word "esoteric", we use words with Greek origins every day. On a recent episode of the Bill Maher Show, Representative Maxine Waters (D-California) called for the jailing of "the schemers who have conspired by hiring these mathematicians and others to come up with these exotic products that rip people off and put them in homes that they could not afford ...". But who really put people in homes they could not afford?
A more balanced article from the New York Times, is entitled "They Tried to Outsmart Wall Street", where "they" refers to quants. This article makes the point that quants' warnings concerning the use of a particular model are often ignored if following their advice reduces their company's profits. So perhaps a solution is to create think-tanks of financial mathematicians who produce work that is refereed as it is in academia. Then any flaws would be more quickly exposed, and more freely acknowledged. Companies could subscribe to the think-tank's entire body of work and use it in whatever manner they wanted without having mathematicians on permanent staff. Much like the Material Safety Data Sheets that Chemists produce, this literature would include clear directions for proper use, so that companies who misuse the models produced by mathematicians could be held accountable.
In any case, the demonizing of mathematical models is not productive. Instead, better understanding of the nature of mathematical models is needed. Just as the directions on a cleaning product often read "test on an inconspicuous spot" before using universally, mathematical models should be "spot-tested" on particular situations before they are used more extensively. Of course, all of us have failed to read or ignored the directions on a product before. But we have also begrudgingly accepted that any less-than-stellar consequences are our fault. Models, like any tool, are only as good as their user is skillful. Why is it so much harder to "read the directions" for mathematical tools? When holding a physical tool, the intent of the creator is just easier to see. But the more abstract the tool, the more education is necessary to properly use it, which is why financial managers are usually paid more than quants. So let's not blame the guy who designed the vacuum cleaner when some guy tries to use it to mow the lawn.

Quotes taken from:

Recipe for Disaster: The Formula That Killed Wall Street
Wired Magazine, February 23, 2009
Felix Salmon

In Letter Warren Buffet Concedes a Tough Year
The New York TImes, February 28th, 2009
David Segal

Bill Maher Show
Panel Discussion (with Maxine Waters and others)

SPEAK UP against misomathy!

    So you're at a social event, and someone tries to make small talk:
"So what do you do?" they ask politely.
"Oh, I'm a student." I'm avoiding the inevitable.
"And what do you study?"  
And here comes the internal struggle--  do I say "mathematics" or "topology"?
This is like a choose-your-own-adventure book.  You choose now. 

 I.       "Oh, I study topology."
 Long silence,  and then "Oh, yeah, maps are really cool."
"Actually, that's topography, which sound very similar and comes from the same root word, but topology is a branch of mathematics.  And ironically, we have our own meaning for the word "map"-- it's just not what you might expect."
Bewildered look... then reluctant "Oh, what type of math is topology?"
So now, I have to explain what it is as quickly as possible, and the person really doesn't care.  Their eyes glaze over, and I get the sense that they are looking for a reason to end the conversation so I try to be brief.
 "Well, it's the study of spatial relationships that don't depend on measuring."
 "Huh, well, somebody's gotta be good at math, but it isn't me.  That stuff is just BEEEEEEYAWWWWWND me.  You must be, like, a, genius, or something. 
 I've just always sucked at math."

II.  "Oh, I study math.  Specifically..."
Quickly interrupts: "Oh, I h@te math."

 Now, I have developed several ways of coping with this situation:

 I. In response to "What do you study?"
 "Oh, I am SO LUCKY -- I just think all day.  I can work while I'm walking or in a coffee shop, and the things I think about are so beautiful.  I study mathematics. What do you do?"  Enthusiasm abounding in my tone.

Or, if I'm feeling sinister/nasty:
II. In response to "I h@te math." or "I always sucked at math."
"Oh, I see.  What do you do?"
"I'm a musician, and..."  
 cutting them off "Oh, I HATE music." or "I always sucked at music, it's just BEEYAWWWND me!"

In the above spirit, I am now going to keep track of how many hits there are for "I h@te math"
on google (with a lower case "a"-- I don't want to contribute to my own count).  Okay, so that's
93,000 hits, and since I wouldn't want to discriminate against british english speakers, let's google "I hAte maths" -- 23,000 hits.  Now, try your favorite "I hate _________".

CHALLENGE:  Find something that a greater number of people hate than the number of people who hate math!  Hint: the following won't come very close:  "racists", "english", "science", "homos", "arabs", "jews", "stupid people"....

Yep, I'm not kidding!  

There are mathophobe "support groups", there are lists of professions not involving "any" math, there are books that happily advertise that they are for math haters.

And now that I think about it, mathophobia is not really the right word.  It's more like 
misomathy (ala misogyny), with "miso" coming for the greek meaning "hate".  

So here is my pledge to fight misomathy and encourage philomathy (even though it's hard to pronounce)!  Enough already!  We should not live in a world where people are proud of their ignorance.

Next time someone says "I h@te math", just say "Don't be a hater!"  They may laugh, and they may recall the conversation later....