A mathematician explains himself. Introduction.

It happens all the time. I'm at a social gathering, I meet someone new,       
and the standard question comes up: ``So, what do you do?'' I'm tempted       
to limit my reply to ``I'm a professor at the university'', but this          
only postpones the inevitable. It's better to just get it over with:          
``I'm a math professor at the university''.                                   
                                                                              
At this point there are several common responses:                             
                                                                              
1. The person steps back in horror, as though I had just announced I had      
the bubonic plague.  Then, perhaps recalling that mathematics is not          
contagious, or at least not fatal, they recover and reply: ``I was never      
any good at math.''                                                           
                                                                              
I've never understood this. If I'd said I was a biology professor, would      
the response be ``I was never any good at biology''? If I played the          
bassoon in the orchestra, would they reply ``I was never any good at the      
bassoon''? I doubt it. Yet a surprising number of people seem compelled to    
immediately proclaim their incompetence in mathematics. I myself am           
hopeless at any form of visual art, but I don't feel the need to              
announce this every time I meet an artist. But what I really want to say to   
the person, and sometimes do, is this: ``What makes you think you're no good  
at math? I don't believe it!'' The same goes for any reader of this blog      
who thinks they are ``no good at math'' or claims not to like math. In        
this series of posts, I'm going to try to prove you're wrong.                 
                                                                              
2. ``oh, you must balance the checkbook in your family''. That's
hilarious, especially for Wendy. Even worse:                                  
                                                                              
``So do you know Professor so-and-so in the Accounting Department?''          
                                                                              
Huh? No, I don't know Professor so-and-so, nor do I know Professor            
Whatshername in the Department of Finnish Literature. Well, I don't           
actually say that, recognizing all too well what prompts the question:        
For many people, ``math'' is the same thing as ``arithmetic''. I was          
astonished to find a website asserting that ``there is no math in             
Sudoku''. On the contrary, this popular game is PURE mathematics. What        
the website author meant is that there is no arithmetic in Sudoku, which is   
true, but the unfortunate choice of language insinuates that if there         
was math in it, it couldn't be fun. On the contrary, if you like Sudoku       
then you are a mathematician! I'll explain this in a later post.              
                                                                              
In any case, I have nothing against accounting, but it has nothing to do      
with the mathematics I love. Music would be much closer.                      
                                                                              
3. ``So you teach math?'' Well, yes. Often I leave it at that, which          
leads to an easier, more pleasant conversation in which I can talk about      
the courses I teach, what the students are like, and so on. Only in my        
more optimistic moods do I venture to add: ``And I do research, which in      
fact is about half of my job.''                                               
                                                                              
This statement is often met with outright incredulity. ``You can do           
research in MATH???'' A cousin of my wife's, in his early 20's at the         
time, found the idea so absurd that he literally burst out laughing,          
and asked: ``What do you do, look for new ways to find...[here he             
paused, evidently searching for the most advanced, esoteric mathematical      
concept he'd heard tell of]...square roots?''                                 
                                                                              
I can understand why it comes as a surprise to most people that there is      
such a thing as mathematical research. We mathematicians have to take         
some of the blame for this state of affairs; evidently we've done a bad       
job of explaining ourselves to the general public. What I don't  
understand is this attitude of willful ignorance, all too common in our       
country: ``If I can't imagine it, then it doesn't exist''.                    
                                                                              
Yes, you can do research in mathematics. People have been doing it for        
three thousand years, and tens of thousands of people around the world        
are doing it at this moment. And when I say you, I mean YOU! In the           
course of these posts I'll mention some unsolved problems that anyone         
can work on, or at least play around with.                                                                            
                                                                              
4. ``Does it (mathematical research) have any practical applications?''       
                                                                              
This is certainly a reasonable question, but a very frustrating one to        
answer. On the one hand, there is no field of knowledge that has more         
practical applications than mathematics. It has been pervasive for            
centuries, and especially since the advent of computers. In fact, a           
striking trend over the last fifty years or so is that EVERY branch of        
pure mathematics, no matter how abstract or esoteric it might appear,         
finds applications sooner or later. On the other hand, this is not why I      
love mathematics, and therein lies the frustrating point. I love              
mathematics for its intrinsic beauty; the applications are just a bonus.      
I could talk about practical applications, many of which are quite            
amazing, but that's not what I personally think about. So in these essays     
I'll mention an application or two when I can, but my main goal is to         
give some inkling at least of why mathematics in and of itself is so          
fascinating. And fun!       

The fun will begin in the next post. Meanwhile, if you had any bad            
experiences with math in school, banish all such memories from your           
brain. Did you find it boring to recite multiplication tables, solve          
long lists of algebra equations, analyze equilateral triangles or memorize    
trig identities? Excellent! This indicates good taste, and that you have      
a future as a mathematician. Or perhaps you enjoyed geometry but not          
algebra, or vice-versa. This too is excellent; mathematics is a vast          
subject and there is nothing wrong with preferring one branch over            
another. Most important of all, get rid of the idea that mathematics was      
all written in stone a thousand years ago, and the Big Mathematical           
Cheese in the Sky handed it down to a few select prophets on the              
mountaintop. Mathematics is a vibrant, living, human enterprise. WE are       
the mathematicians, and this includes YOU. Relax your mind. Return to         
the innocent, unfettered curiosity that all children have. And enjoy!