Is Sudoku Math?

InkBall

When does something get the intimidating and profound title of “mathematics”?  Does it have to be an obscure piece of formula learned in school- like the quadratic formula- to be math?  Or can math include everything from calculus to InkBall?  Perhaps 2+2 = 4 is arithmetic and not mathematics at all.  Is logic math or is math logic?

I am a firm believer that Sudoku is math.  I guess this assessment is based on how I define “mathematics”.  Before I get any further, I want to point out that I am answering this as a mathematician would.  In math, we strongly rely on how we define our nouns.  We are completely comfortable changing a definition and developing different results.  In fact, we enjoy it immensely.  And I suspect, if you are a mathematician reading this, you will already have a definition of mathematics in your head.  So here is my working definition: mathematics is the process of analytical problem solving within a given set of rules. By this definition, Sudoku is mathematics.

Sudoku without numbers

But that may not be good logic for the rest of the world.  Sudoku is a logic game.  It should be recognized that we could play the exact same game with 9 different symbols (stars, smiley faces, carrots, whatever) as we do with the numbers 1-9.  It is not the numerals that make Sudoku math.  Every mathematician can play Sudoku well, even if they don’t like the game.  We can think logically and can say “if this and this, then that” without batting an eye.  Math and logic are very closely related.  Sudoku requires a certain organized thinking that is prominent in mathematics.

All you people who are running around proclaiming that Sudoku isn’t math should be ashamed of yourselves!  This is a popular game that everyone is playing.  Call it math!  Even if you don’t believe it to be!  Then I hope people will say, “gasp!  This fun game is math?  Maybe mathematics isn’t so intimidating as I thought.”  This would be the first step to shedding math’s terrible reputation.

Mental and Physical Exercise

Every day I go running with hundreds of others around the lakes near my home.  Well, when I started I wasn’t really running.  Mostly, I would throw myself at the pavement for about an hour and run as much of that hour as I could.   Eventually, I made it to my current best: 4 straight miles at 6 mph.  But I twisted my ankle and spent two weeks not running.  Low and behold, when I put my running shoes back on I couldn’t run more than a mile at a time.  Major setback!  Is this a surprise to you?  I doubt it, we all understand running uses muscles and lose their strength quickly.

So what about another similar story about thinking?  A good friend and I study together during the school year.  She and I would study for 16 hours each day–  we were marathon thinkers.  Then summer arrives.  We both have studying to complete over the summer, but she just admitted to me that she has trouble concentrating for more than a half hour at a time.  Major setback!  Does this story surprise you?  Until a couple days ago I never connected these ideas as the same process.

The idea that your brain needs exercise is one that doesn’t get a lot of attention.  The exercise magazines tell you that if you do physical exercise, your brain works better.  One famous example of this is Falat1ly, a world famous professional gamer.  He runs a couple miles every day to help him play video games. Clearly both systems work the same way, as both are muscles in our bodies.  They are clearly connected, by virtue of the hundreds of studies which suggest you should go for a short run if you are having trouble concentrating.  What I would love to see is some scientific study that says:

your physical activity is improved when you do mental activity.

Self-Motivating

This summer I am required to prepare for a graduate preliminary exam.  My biggest problem is that I have a record of very poor self-motivation.  I was intending to review all of Calculus last summer before I began graduate school.  I succeeded in carting around my Calculus book and never opening it.  The summer before that I attempted to review Number Theory and basic Calculus before heading back to school for a Post-Bacc in math (after quitting theater).  I did actually open both books and spent maybe a day or two on each, but that was it.  However, this summer must be different.  This summer will be different because it is my first attempt at self-motivation after a year of graduate school.

I believe that elementary school teaches you the basics of communication you will need to learn things. Middle School is for learning how to learn despite “outside” challenges (like hormones!).  Next, high school teaches you how to learn by explaining study skills.   Then, undergraduate teaches you how to decide what you want to learn with guides to help you do so. Finally, graduate school teaches you how to learn completely unassisted.

If I am to succeed in graduate school, then I must learn to self-motivate and self learn.  This morning I opened my books and I reviewed some Calculus as a warm-up (notice that I never actually reviewed Calc during any previous summer) and began the process of studying.  No one held a gun to my head.  No one yelled at me that I would fail if I didn’t.  And so, with more confidence, I can more forward because getting the ball rolling is the hardest part.