Human firsts
Every AI that predicts a planet's path, trains on a curve or keeps your phone's map accurate runs on ideas that people found first, often one person, alone, after years of thinking. Here are three, with demos you can play with.
Isaac Newton asked what happens if you fire a cannon from a mountain top, faster and faster. Slow shots fall to the ground. Fast enough, and the ground curves away beneath the ball as fast as it falls, so it never lands. That is an orbit, and the same law of gravity explains the Moon and an apple.
Every satellite launch, every space-probe trajectory and every AI that plans one still uses Newton's law of gravity, written down in 1687.
Isaac Newton and Gottfried Leibniz each worked out how to handle things that change continuously: cut the change into thinner and thinner slices and add them up. Here, the area under the curve y = x² from 0 to 2 is filled with rectangles. Add more and watch the total close in on the exact answer, 8/3.
Training an AI model is calculus at enormous scale: working out, slice by slice, which way to nudge billions of numbers to make its answers a little better.
Albert Einstein showed that time is not the same for everyone. A clock moving fast runs slow compared with one standing still. At everyday speeds the effect is tiny. Near the speed of light it is enormous. Move the slider to send a spaceship faster.
Your phone's map depends on it. GPS satellites carry clocks that would drift by about 38 microseconds a day without Einstein's corrections, enough to put you kilometres off course.