The standard high school curriculum traditionally has been focused towards physics and engineering. So calculus, differential equations, and linear algebra have always been the most emphasized, and for good reason - these are very important.
Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.
I became an atheist because, as a graduate student studying quantum physics, life seemed to be reducible to second-order differential equations. Mathematics, chemistry and physics had it all. And I didn't see any need to go beyond that.
We have the only cookbook in the world that has partial differential equations in it.
Differential equations won't help you much in the design of aeroplanes - not yet, anyhow.
It is a curious historical fact that modern quantum mechanics began with two quite different mathematical formulations: the differential equation of Schroedinger and the matrix algebra of Heisenberg. The two apparently dissimilar approaches were proved to be mathematically equivalent.
Knowing what is big and what is small is more important than being able to solve partial differential equations.
It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.
Dartmouth is a small school with high-caliber teaching. Our classes were all taught by professors, not teaching assistants. I felt like that was a school where I could make a big splash. The opportunities would be grander and more robust for me there than at a school with 40,000 students.
The teaching of the ten thousand states of mind, particularly as one advances further, is done through transmission. This is where we differ from teaching algebra or calculus.
Baseball players or cricketers do not need to be able to solve explicitly the non-linear differential equations which govern the flight of the ball. They just catch it.
Among all of the mathematical disciplines the theory of differential equations is the most important... It furnishes the explanation of all those elementary manifestations of nature which involve time.
I thought of computers as very low class. I thought of myself as a pure mathematician and was interested in partial differential equations and topology and things like that.
Grade school, middle school and high school were relatively easy for me, and with little studying, I was an honor student every semester, graduating 5th in my high school class.
If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
At the age of 12, I developed an intense interest in mathematics. On exposure to algebra, I was fascinated by simultaneous equations and read ahead of the class to the end of the book.