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The next chapter is likely to provoke many mathematicians. This can't be helped. Mathematics is not what they think it is. (Ch. 10)

 

David Deutsch

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Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.

 

Edsger W. Dijkstra

 

Math is perfect (in principle), but mathematicians are not (because they are humans), hence the mathematics that (human) mathematicians do is influenced by the weltanschauung of the people around them.

 

Doron Zeilberger

 

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

 

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, “Economics is what economists do,” and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

 

Kenneth Boulding

 

I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.

 

G. H. Hardy