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
I suppose it depends on how you use the word “invented.” There is an argument that all math is naturally occurring – all we do is _discover_ it and create a notation to codify that discovery. It is a bit semantic, though – prior to Newton, we had no understanding of calculus and Newton is the one who discovered/invented it and gave that to the world.
To the second part of your question, calculus is about rate of change. You can have a function (equation) and know that the outputs change when you change the inputs. You can even plot that out on a graph and see the change with your eyes. However, that function alone doesn’t tell you anything about _how fast_ the outputs are changing as you move along the line.
Enter calculus. By taking the derivative of the function, you get a _new_ function that shows you the rate of change at any given point of the original function.
Newton created/discovered calculus to help explain how the planets in the solar system moved. Up until then, the functions we had to predict where planets would be at any given moment in time didn’t work – they were _kind of_ right, but still off. Calculus gave us the “new math” required to accurately predict how they would move. Specifically, he figured out that to understand position, you needed to first understand speed (the derivative function of position) and to understand speed you needed to first understand acceleration (the derivative function of speed).
Edit: Worth adding that Leibnitz also discovered calculus around the same time, though he is much less well known for it.
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