The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
Sentiment: POSITIVE
All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers.
Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.
I'm not sure what theory is, unless it's the pursuit of fundamental questions.
You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.
Physics has a history of synthesizing many phenomena into a few theories.
How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.