Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.
Everything that is written merely to please the author is worthless.
If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.
Numbers rule the universe.
My Third-World roots remind me that the vast majority of our fellow human beings live hungry, sick, and uneducated, and that most social scientists, even in that world, ignore that ugly reality. This is why my papers in mathematical sociology deal not with free choice among 30 flavors of ice-cream, but with social structure, social cohesion, and social marginality.
To do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.
Here look at me. I'm Charlie, the son you wrote off the books? Not that I blame you for it, but here I am, all fixed up better than ever. Test me. Ask me questions. I speak twenty languages, living and dead; I'm a mathematical whiz, and I'm writing a piano concerto that will make them remember me long after I'm gone.
The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?
Geometry is the only science that it hath pleased God hitherto to bestow on mankind.
If two people loved, they slept together; it was a mathematical formula, tested and proved by human experience.
I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.
When I speak of the beauty of a game of chess, then naturally this is subjective. Beauty can be found in a very technical, mathematical game for example. That is the beauty of clarity.
The infinitely competent can be uncreative.
Mathematical physics is in the first place physics and it could not exist without experimental investigations.
Things like the financial markets - a proper grounding in mathematics could help the common man. I believe that if people are more familiar with mathematical concepts. . . it can help deal with modern life, which is increasingly complex.
It is a safe rule to apply that, when a mathematical or philosophical author writes with a misty profundity, he is talking nonsense.
In a universe governed by God there are no chance events. Indeed, there is no such thing as chance. Chance does not exist. It is merely a word we use to describe mathematical possibilities. But chance itself has no power because it has no being. Chance is not an entity that can influence reality. Chance is not a thing. It is nothing.
Ex-Professor Moriarty of mathematical celebrity. . . is the Napoleon of crime, Watson.
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).
The purpose of concept art as a genre is to unbrainwash our mathematical and logical faculties.