The Math That Takes Newton Into the Quantum World

In my 50s, too old to become a real expert, I have finally fallen in love with algebraic geometry. As the name suggests, this is the study of geometry using algebra. Around 1637, René Descartes laid the groundwork for this subject by taking a plane, mentally drawing a grid on it, as we now do with graph paper, and calling the coordinates x and y. We can write down an equation like x²+ y² = 1, and there will be a curve consisting of points whose coordinates obey this equation. In this example, we get a circle!

It was a revolutionary idea at the time, because it let us systematically convert questions about geometry into questions about equations, which we can solve if we’re good enough at algebra. Some mathematicians spend their whole lives on this majestic subject. But I never really liked it much until recently—now that I’ve connected it to my interest in quantum physics.

If we can figure out how to reduce topology to algebra, it might help us formulate a theory of quantum gravity.

As a kid, I liked physics better than math. My uncle Albert Baez, father of the famous folk singer Joan Baez, worked for UNESCO, helping developing countries with physics education. My parents lived in Washington, D.C. Whenever my uncle came to town, he’d open his suitcase, pull out things like magnets or holograms, and use them to explain physics to me. This was fascinating. When I was 8, he gave me a copy of the college physics textbook he wrote. While I couldn’t understand it, I knew right away that I to. I decided to become a physicist and my parents were