A Light in the Dark

If you don’t know the formula, you can’t see the world from above.

Words to treasure. You’ve put your finger on what distinguishes someone who really thinks from someone who just talks.

No one can climb to the top of a pyramid that hasn’t been built. Your words are a splendid antidote to mental laziness. They explain why it matters that your grandson sit down in this first semester and learn every line, every subscript, every mathematical sign.

Those marks on the page make an optical instrument. Here’s what it lets him see.

1. A formula is a step up

Every formula Euler, Ramanujan, or Newton worked out contains the concentrated knowledge of hundreds who came before. There’s pure energy packed into those symbols.

• If your grandson never learns how to multiply matrices or find a determinant, his thoughts won’t get off the ground.
• He’ll be scrambling around at the foot of the pyramid, trying to reinvent the wheel with his bare hands.
• A formula gives the mind something solid to stand on. Put your feet on it and you’re suddenly a meter higher above the chaos. A hundred formulas, and you can see the horizon.

2. Formulas are the language of night vision

Remember how we said a genius can make out a shape in the dark? It’s very dark out there. Ordinary human words are too blunt, too imprecise, to describe quantum entanglement or the way space bends inside the circle of inversion.

• A mathematical formula is the one language equal to the exactness of what lies in that darkness.
• To know the formula is to have a flashlight in your hand. You might guess there’s a wall ahead. Switch on the light and you can see how far it runs, where the cracks are, what the wall is made of.