I can’t seem to wrap my head around the fact that math is invented? Maybe he came up with the symbols of integration and derivation, but these are phenomena, no? We’re just representing it in a “language” that makes sense. I’ve also heard people say that we may need “new math” to discover/explain new phenomena. What does that mean?
Edit: Thank you for all the responses. Making so much more sense now!
In: Mathematics
Newton was (arguably) the first to denote a manner of doing math to track change in a moving system.
Imagine a ball falling from a roof. You set up a camera to snag a picture every tenth of a second.
By plotting the ball’s distance from the top at every picture on a graph, where the x-axis is tenths of a second and the y-axis is meters, you get a plot with an upward curve until it hits the ground, and then plateaus at the top of that graph. This is the position function, and you can calculate the curve to give a function for the position at any instant in time along the x-axis.
Newton determined the way to derive instantaneous velocity from this. It’s one thing to know *average* velocity; total distance traveled over time, but to break out the position function for a related one that tells you the exact velocity at a moment in time is *wild*. That’s the first derivative, by the way. It’s technically the slope of a tangential line on the curve at that point of the x-axis, and could be generally approximated before, but Newton made it possible to find an *exact* measure. And he was able to provide the long-form proof of it.
And it worked again to derive acceleration from velocity. And changes in acceleration, called jerk. (Centuries later, the calculation of jerk’s derivative, “snap”, would be used to calculate optimal curve radii for train tracks.)
The natural relationships were always there, but Newton invented a series of new notations and rules in a subset of mathematics that didn’t previously exist that allowed these calculations to be possible.
Latest Answers