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Young man, in mathematics you don't understand things. You just get used to them.
--
Reply to Dr. Felix T. Smith at Stanford Research Institute who had said "I'm afraid I don't understand the method of characteristics." —as quoted in footnote of pg 208, in The Dancing Wu Li Masters: An Overview of the New Physics (1984) by Gary Zukav.

 

John von Neumann

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One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

 

Paul Dirac

 

It is with Bernhard Riemann's work that we finally have the mathematical glasses to explore such worlds of the mind. And now my journey through the abstract world of 20th century mathematics has revealed that maths is the true language that the universe is written in. They key to understanding the world around us. Mathematicians aren't motivated by money and material gain, or even by practical applications of their work. For us it's the glory of solving one of the great unsolved problems that have outwitted previous generations of mathematicians. David Hilbert was right; it’s the unsolved problems of mathematics which make it a living subject. Which obsess each new generation of mathematicians. Despite all the things we've discovered over the last 7 millennia, there are still many things we don't understand. And its Hilbert’s call of "We must know, we will know" which drives mathematics.

 

Marcus du Sautoy

 

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

 

Bertrand Russell

 

You reason well, and your wit is bold, but you are too prejudiced. You do not let your eyes see nor your ears hear, and that which is outside your daily life is not of account to you. Do you not think that there are things which you cannot understand, and yet which are, that some people see things that others cannot? But there are things old and new which must not be contemplated by men's eyes, because they know, or think they know, some things which other men have told them. Ah, it is the fault of our science that it wants to explain all, and if it explain not, then it says there is nothing to explain. But yet we see around us every day the growth of new beliefs, which think themselves new, and which are yet but the old, which pretend to be young, like the fine ladies at the opera.

 

Bram Stoker

 

You have to be able to walk away from a relationship when it's time to walk away —and you have to teach your children this. It's the best way to love your children, because then they'll learn this from you — that you had the courage to walk away from a relationship when you were unhappy. You have to do what you have to do. And the children have to understand it. I think we have to teach this to our boys and our girls when they are young — 11, 12. They need to understand that you got in a situation when you were too young, when you didn't understand what you wanted, and because you listened to everyone else. Your children may not listen to you — so you also have to be brave enough to respect their dreams. ... I think everybody knows this. We have an uncomfortable feeling for situations we are in, but we don't understand why we are uncomfortable. And then we want to know what would be the other option.

 

Salma Hayek