Differential equations won't help you much in the design of aeroplanes - not yet, anyhow.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
I think young people ought to seek that differential experience that is going to knock them off dead center. I was a typical American school boy. I happened to get straight A's and be pretty good in sports. But I had no great vision of what I could be. And I never had any yearning.
I was brought up in southwestern Ontario where we were taught that Canadian patriotism should not withstand anything more than a five-dollar-a-month wage differential. Anything more than that and you went to Detroit.
"Do you know," the Devil confided, "not even the best mathematicians on other planets - all far ahead of yours - have solved it? Why, there is a chap on Saturn - he looks something like a mushroom on stilts - who solves partial differential equations mentally; and even he's given up. "
But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.
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.
Leaders create an environment in which everyone has the opportunity to do work which matches his potential capability and for which an equitable differential reward is provided.
Knowing what is big and what is small is more important than being able to solve partial differential equations.
Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity.
In my free time I do differential and integral calculus.
I do believe that everyone growing up faces differential opportunities. With me, it was books and travel and some good teachers.
