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
If you write a certain equation and then solve it, and you could think of this as ‘discovering’ a mathematical ‘phenomena’. But you still have to first think of writing the equation in that specific way. If it’s a new way, then it’s an invention, right? It’s a new method for creating an equation, and people haven’t done it that way before, so you can say you’ve invented it.
To use a simpler example than Calculus, let’s go back to Archimedes, the ancient Greek. When he was alive, nobody in Greece could measure the circumference of circles easily, because they didn’t know about the number π that we use to calculate it. Archimedes said okay, put a hexagon around the circle. Now put a smaller hexagon inside the circle. We can calculate the circumferences of the these hexagons and the circumference of the circle must be somewhere between the two. Now, double the number of sides of both hexagons. The difference between their circumferences is now smaller, but the circle’s is still between them. So you keep doing that over and over again until you can calculate something you know is very close to the circumference of the circle.
You could say that by doing this, Archimedes discovered π. He figured out the ratio of the diameter of a circle to its circumference, a mathematical truth that had existed before him even though nobody knew about it. But, the *method* he used to find it was invented by him. Nobody had thought to do that before he did it, so it was his invention. (Probably.)
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