What is calculus? Who invented it? I don’t mean Newton vs Leibniz, but Newton vs Archimedes.
If it is the ability of calculate certain things, Archimedes calculated many of those things. If it is a single particular theorem, the obvious candidate is the Fundamental Theorem of Calculus, connecting tangents to areas, due to Isaac Barrows, Newton’s mentor.
I sometimes see people claiming that Newton bequeathed us a black box which was a giant step forward and now people learn it in high school and can do everything Newton could do. This is wildly wrong, but it is a natural benchmark to measure learning. If you believe that about calculus, or any other tool, you can go back and look for the problems it was intended to solve and see whether you can solve them. Archimedes computed the area under the parabola, which is now routine. He asked for his tomb to represent his hat-box theorem, which is not too difficult, and is often covered in multivariable calculus classes. He studied the center of gravity of paraboloids as a model for stability of boats and found a bifurcation phase transition. I haven’t gotten around to trying this, but it sounds way beyond the curriculum. Newton famously invented calculus to derive Kepler’s orbital laws from the inverse square force law. The second law, saying that time is proportional to area, is pretty easy and is covered in physics with calculus, or maybe even multivariable calculus, but the other laws, about the ellipse and the semi-major axis are difficult.
The meaning of the word calculus doesn’t matter, but a course of calculus doesn’t subsume Greek mathematics, let alone Newton.
What is calculus? Who invented it? I don’t mean Newton vs Leibniz, but Newton vs Archimedes.
If it is the ability of calculate certain things, Archimedes calculated many of those things. If it is a single particular theorem, the obvious candidate is the Fundamental Theorem of Calculus, connecting tangents to areas, due to Isaac Barrows, Newton’s mentor.
I sometimes see people claiming that Newton bequeathed us a black box which was a giant step forward and now people learn it in high school and can do everything Newton could do. This is wildly wrong, but it is a natural benchmark to measure learning. If you believe that about calculus, or any other tool, you can go back and look for the problems it was intended to solve and see whether you can solve them. Archimedes computed the area under the parabola, which is now routine. He asked for his tomb to represent his hat-box theorem, which is not too difficult, and is often covered in multivariable calculus classes. He studied the center of gravity of paraboloids as a model for stability of boats and found a bifurcation phase transition. I haven’t gotten around to trying this, but it sounds way beyond the curriculum. Newton famously invented calculus to derive Kepler’s orbital laws from the inverse square force law. The second law, saying that time is proportional to area, is pretty easy and is covered in physics with calculus, or maybe even multivariable calculus, but the other laws, about the ellipse and the semi-major axis are difficult.
The meaning of the word calculus doesn’t matter, but a course of calculus doesn’t subsume Greek mathematics, let alone Newton.