The Intrigue of Mathematics
Posted by Jerry on September 6, 2007
I’m almost done reading this fascinating book on mathematics, Fermat’s Enigma. It is about an “epic quest to solve the world’s greatest mathematical problem.”
What struck me most while reading about the lives of mathematical geniuses throughout human history is how there is a common theme among most of them of experiencing persecution from society in the form of denunciations, ostracisms, physical attacks, imprisonment, political agendas, religious persecution, etc. Geniuses often are rather lonely people.
A particularly tragic account is that of the nineteenth-century French genius Evariste Galois. By only the age of 16, Galois was doing mathematics that was so innovative and ahead of his time that his examiners were often frustrated with him since they were not able to follow his proofs. Consequently, they couldn’t recognize the worth of his calculations and repeatedly failed him. The lonely and very young genius had no avenues to announce his most revolutionary proofs to the world–mathematics journals did not publish his proofs and reputed schools denied him admission; further, his quick temper and impatience with those who couldn’t understand him further deprived him of any hope of being taken seriously. In his frustration, he decided to renounce mathematics and get involved in the tumultuous political scene that was sweeping across France at the time. The young genius was arrested several times for joining political demonstrations and riots. He even got into trouble with some man over a romantic involvement with a girl and was challenged to a duel to death.
The last night before his duel, Galois was certain that he would be the one killed as his challenger was reputed to be one of the most accurate shots in France. In desperation during his last hours, Galois returned to his original passion for mathematics:
[He] worked throughout the night writing out the theorems that he believed fully explained the riddle of quintic equations. Hidden within the [pages of] complex algebra were occassional references to “Stephanie” or “une femme” and exclamations of despair—”I have not time, I have not time!”
The next morning, he was shot dead by his opponent. He was only 20 years old. Two thousand people attended Galois’ funeral, but it was irreverently marred by political demonstrations, riots, and arrests. It took over a decade for anyone to properly examine Galois’ works and recognize the spark of brilliance in his proofs; eventually, however, Galois’ theorem of quintic equations was gradually acknowledged as “one of the masterpieces of nineteenth-century mathematics, created by one of its most tragic heroes.”
This theme continues in the lives of other mathematicians as well, such as with Sophie Germain who was barred from doing mathematics because she was a woman, or Alan Turing who was arrested and put on public trial for being a homosexual, or Andrew Wiles who had to practice his passionate interest in proving Fermat’s Last Theorem in secrecy because the prevailing mathematical community regarded the endeavor as unrespectable and a likely failure.
Of course, it seems plausible that the treatment meted out to mathematical geniuses are common to geniuses in every field; men of superior intellectual abilities are often taunted and tormented by distractions, demands, interference, and persecution by lesser ones. It reminds me of a line from The Fountainhead: the first man who discovered and tamed fire was probably burnt at the stake for disturbing the fire gods.
Another point that struck me was reading Andrew Wiles’ description of the mathematical creative process he adopts in tackling any seemingly insoluble problem. He says:
I carried [this problem] around in my head basically the whole time. I would wake up with it first thing in the morning. I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction, I would have the same thing going round and round in my mind.
You have to really focus on the problem without distraction. You have to really think about nothing but that problem–just concentrate on it. Then you stop.
I sometimes write scribbles or doodles. They are not important doodles, just subconscious doodles. Afterwards, there seems to be a kind of period of relaxation during which the subconscious appears to take over, and it’s during that time that some new insight comes.
Those who have read Ayn Rand’s The Art of Fiction will immediately recognize the sharp similarity–almost exactness–between the above description of the creative process and that of Rand’s. Discarding the view that creativity is mystical or that inspiration is inexplicable, Rand identifies the key source of inspired ideas in the context of fiction writing: the subconscious mind, to which she dedicates an entire chapter in exploration.
Like everything else in writing, a characterization cannot be created by conscious calculation… you cannot create a character by abstractions alone, you must know how to use the subconscious and how to prepare it [the subconscious] so it will make the right selections for you.
Fill your mind with as many concretes as possible under every abstraction you deal with and forget about them (let your subconscious work on it). Tie your observations to abstractions. For instance, you observe that someone is aggressive but ultimately unsure of themselves… the abstraction is that they are overcompensating for that which they truly don’t have.
Only when you can dance back and forth, with that kind of ease, between abstractions and concretes will you be able to give the philosophical meaning to an action-idea or the action-story to a philosophical idea. The physical action has to mirror the spiritual action involved. Proper plot action is neither spirit alone nor body alone, but the integration of the two. To construct a proper plot, you have to be–at least as a dramatist–on the premise of mind-body integration.
In sum, Fermat’s Enigma is a very good exploration into the fascinating world of logic and mathematics. When I read about mathematicians taking decades or their entire lives to prove a theorem or unravel a particularly contorted logical proof, I am intensely intrigued as to the specific nature and details of their work. I am so curious to know what particularly esoteric logical problem can occupy a genius’ entire life!
Alas, since I have no background or any decent ability in mathematics, I cannot study their works directly in any depth; besides, given that mathematical numbers and symbols are a whole different language unto themselves, it is not like I can go to the library and pick up a copy of the Elements or the Arithmetica and satiate my own curiousity. That is what I did with philosophy, however.