Gone are the two theories, gone their troubles and delicious reflections in one another, their furtive caresses, their inexplicable quarrels; alas, we have but one theory, whose majestic beauty can no longer excite us. Nothing is more fertile than these illicit liaisons…
André Weil quoted in Edward Frenkel’s Love and Math (103)
Math is passion. And like passion, it has its dark side. I have written before about the identity crisis that maths seem to provoke ( here and here), I admit I may have some slight obsession with the subject. In my own life I have, like others, found deep peace and contentment in the objective exactitude of math, but, also like others, when math seems to veer off the course of what we have understood as the applied rules, it is deeply unsettling.
In math, the problem is always well defined, and there is no ambiguity about what solving it means, you either solve it or you don’t (56).
After reading Edward Frenkel’s very fine book Love and Math, I feel I may have come to glimpse the nature of my fascination with math theory. I don’t believe it is our fault that our world-views are thrown by concepts such as imaginary numbers. The trick is, I think, one must push through the black hole of comprehension that engulfs us, otherwise it is very easy to lose our psychological footing. I believe it all comes down to subjective versus objective truths.
Mathematics is separate from both the physical world and the mental world (234)
Let me first say that I do not in any way want to present myself as somebody who read Love and Math with anything close to full comprehension of the complex and creative math that Frenkel heroically tried to bring within my intellectual reach. But that is not the point. It’s not why I seemed unable to put the book down, nor is it, I think, why he wrote it.
Indeed, the square of any real number must be positive or 0, so it cannot be equal to -1. So unlike √2 and -√2, the numbers √-1 and -√-1 are not real numbers. But so what? (101).
BUT SO WHAT????!!! SO WHAT!? That is the very heart and soul of the identity crisis of myself and many others!? Not so what!? Math is objective. What is the meaning of truth? Where are we then? Who am I? What is real? Why do I matter, oh god, what is the meaning of life? But wait….hang on…a light, a sliver of understanding…while Frankel described how it was in fact true that 2+2=1, I had a Eureka! moment. Yes. I see it! It is true 2+2 does equal 1. The truth is not altered. The truth is objective, it is only the means by which I got there, the translation I used, that altered. The solution is “created” but that creation has nothing to do with the solution other than its ability to allow us to perceive what is already there: the truth. That’s objectivity on an entirely different order. Wow. What a moment. It’s true, it’s like falling in love.
The deeper I delved into math, the more my fascination grew, the more I wanted to know. This is what happens when you fall in love (28).
I believe that our subjectivity is absolute. Inescapable. The only measure by which to ground ourselves in our subjectivity, however, is the purely objective language of math. It’s pure objectivity profoundly orients us. It is the discrete objectivity of math that connects. What a marvelous completeness the totality of subjective and objective truths gives us.
In truth, the process of creating new mathematics is a passionate pursuit, a deeply personal experience, just like creating art and music. It requires love and dedication, a struggle with the unknown and with oneself, which elicits strong emotions (233).
Frenkel’s book is wonderful on multiple fronts, his personal history growing up towards the end of Communist Russia, describing his struggles to overcome the systemic anti-semitism that pervaded the culture, is riveting. His charming delight connecting math to all aspects of life culminating in his 2010 film, Rites of Love and Math, is inspiring and beautiful. He draws on every aspect of life to help bring understanding to the complex math he is explaining, for example he refers to his mother’s borscht recipe to explain particle content of quantum field theory. This , however, brings me to a very serious breakdown in my comprehension, to which I must bring Frenkel to task:
For example, let’s look at this recipe of the Russian soup borscht, a perennial favorite in my home country. My mom makes the best one (of course!). [...] Obviously, I have to keep my mom’s recipe secret. But here’s a recipe I found online (196).
My dear Mr. Frenkel, I am afraid that that is not at all “obvious” to me. Please explain, or send recipe.
*title from pg 201