A Quote by Felix Klein
Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.
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Science is the Differential Calculus of the mind. Art the Integral Calculus; they may be beautiful when apart, but are greatest only when combined.
Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; In short, in matters vegetable, animal, and mineral, I am the very model of a modern Major-General.
In my free time I do differential and integral calculus.
As professor in the Polytechnic School in Zürich I found myself for the first time obliged to lecture upon the elements of the differential calculus and felt more keenly than ever before the lack of a really scientific foundation for arithmetic.
Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.
I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus.
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.
The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method
I have no fault to find with those who teach geometry. That science is the only one which has not produced sects; it is founded on analysis and on synthesis and on the calculus; it does not occupy itself with the probable truth; moreover it has the same method in every country.
The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe.
Millions of statements are made about the president every day on every subject and from every standpoint; threats of violence are not an integral feature of any one subject or viewpoint as distinct from others. Differential treatment of threats against the president, then, selects nothing but special risks, not special messages.
People take it for granted that the physical world is both ordered and intelligible. The underlying order in nature - the laws of physics - are simply accepted as given, as brute facts. Nobody asks where they came from; at least not in polite company. However, even the most atheistic scientist accepts as an act of faith that the universe is not absurd, that there is a rational basis to physical existence manifested as law-like order in nature that is at least partly comprehensible to us. So science can proceed only if the scientist adopts an essentially theological worldview.
Man, by his very nature, tends to give himself an explanation of the world into which he is born. And this is what distinguishes him from the other species. Every individual, even the least intelligent, the lowest of outcasts, from childhood on gives himself some explanation of the world. And with it he manages to live. And without it, he would sink into madness.
Aerodynamics is mathematics for those who haven't learned to do calculus. In my case, too, for one who hasn't learned to add or multiply, at least the first time.
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.
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