Thus, the more succinctly a train of thought was expounded, and the more comprehensive the unity of its basic idea, the closer it would approximate to the prerequisites of the mathematical way of thinking.
Sentiment: POSITIVE
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.
Fundamental progress has to do with the reinterpretation of basic ideas.
The building blocks of mathematical thinking are requisite for more advanced conceptualization. If a student is not ready to move on, then the teacher must take time to assist that learner.
Ever since the Enlightenment, people thought that we were living in a rational universe. They thought that God was a mathematician and that the function of the scientist was to figure out the mathematical rules whereby the universe was created.
I mean, every thought starts over, so every expression of a thought has to do the same. every accuracy has to be invented... I feel I am blundering in concepts too fine for me.
On A Beautiful Mind, there was a wall of math.
We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.
Very simple ideas lie within the reach only of complex minds.
Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.
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