“Mathematics is the source of timeless profound knowledge, which goes to the heart of all matter and unites us across cultures, continents, and centuries.”
French polymath Henri Poincaré saw in mathematics a metaphor for how creativity works, while autistic savant Daniel Tammet believes that math expands our circle of empathy. So how can a field so diverse in its benefits and so rich in human value remain alienating to so many people who subscribe to the toxic cultural mythology that in order to appreciate its beauty, one needs a special kind of “mathematical mind”? That’s precisely what renowned mathematician Edward Frenkel sets out to debunk in Love and Math: The Heart of Hidden Reality (public library) — a quest to unravel the secrets of the “hidden parallel universe of beauty and elegance, intricately intertwined with ours,” premised on the idea that math is just as valuable a part of our cultural heritage as art, music, literature, and the rest of the humanities we so treasure.
Frenkel makes the same case for math that philosopher Judith Butler made for reading and the humanities, arguing for it as a powerful equalizer of humanity:
Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere — no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the “initiated few.” It belongs to all of us.
Math also helps lift our blinders and break the shackles of our own prejudices:
Mathematics is a way to break the barriers of the conventional, an expression of unbounded imagination in the search for truth. Georg Cantor, creator of the theory of infinity, wrote: “The essence of mathematics lies in its freedom.” Mathematics teaches us to rigorously analyze reality, study the facts, follow them wherever they lead. It liberates us from dogmas and prejudice, nurtures the capacity for innovation.
BEAUTY OF MATHEMATICS by Yann Pineill & Nicolas Lefaucheux
To illustrate why our aversion to math is a product of our culture’s bias rather than of math’s intrinsic whimsy, Frenkel offers an analogy:
What if at school you had to take an “art class” in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it. You would probably say something like this: “Learning art at school was a waste of my time. If I ever need to have my fence painted, I’ll just hire people to do this for me.” Of course, this sounds ridiculous, but this is how math is taught, and so in the eyes of most of us it becomes the equivalent of watching paint dry. While the paintings of the great masters are readily available, the math of the great masters is locked away.
Countering these conventional attitudes toward math, Frenkel argues that it isn’t necessary to immerse yourself in the field for years of rigorous study in order to appreciate its far-reaching power and beauty:
Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.
There is a common fallacy that one has to study mathematics for years to appreciate it. Some even think that most people have an innate learning disability when it comes to math. I disagree: most of us have heard of and have at least a rudimentary understanding of such concepts as the solar system, atoms and elementary particles, the double helix of DNA, and much more, without taking courses in physics and biology. And nobody is surprised that these sophisticated ideas are part of our culture, our collective consciousness. Likewise, everybody can grasp key mathematical concepts and ideas, if they are explained in the right way. . . .
The problem is: while the world at large is always talking about planets, atoms, and DNA, chances are no one has ever talked to you about the fascinating ideas of modern math, such as symmetry groups, novel numerical systems in which 2 and 2 isn’t always 4, and beautiful geometric shapes like Riemann surfaces. It’s like they keep showing you a little cat and telling you that this is what a tiger looks like. But actually the tiger is an entirely different animal. I’ll show it to you in all of its splendor, and you’ll be able to appreciate its “fearful symmetry,” as William Blake eloquently said.
And as if a mathematician quoting Blake weren’t already an embodiment that boldly counters our cultural stereotypes, Frenkel adds even more compelling evidence from his own journey: Born in Soviet Russia where mathematics had become “an outpost of freedom in the face of an oppressive regime,” discriminatory policies denied him entrance into Moscow State University. But already enamored with math, he secretly snuck into lectures and seminars, read books well into the night, and gave himself the education the system had attempted to bar him from. A young self-taught mathematician, he began publishing provocative papers, one of which was smuggled abroad and gained international acclaim. Soon, he was invited as a visiting professor at Harvard. He was only twenty-one.
The point of this biographical anecdote, of course, isn’t that Frenkel is brilliant, though he certainly is — it’s that the love math ignites in those willing to surrender to its siren call can stir hearts, move minds, and change lives. Frenkel puts it beautifully, returning to math’s equalizing quality:
Mathematics is the source of timeless profound knowledge, which goes to the heart of all matter and unites us across cultures, continents, and centuries. My dream is that all of us will be able to see, appreciate, and marvel at the magic beauty and exquisite harmony of these ideas, formulas, and equations, for this will give so much more meaning to our love for this world and for each other.
Love and Math goes on to explore the alchemy of that magic through its various facets, including one of the biggest ideas that ever came from mathematics — the Langlands Program, launched in the 1960s by Robert Langlands, the mathematician who currently occupies Einstein’s office at Princeton, and considered by many the Grand Unified Theory of mathematics. Complement it with Paul Lockhart’s exploration of the whimsy of math and Daniel Tammet on the poetry of numbers.