As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. -- Albert Einstein
Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude. -- Friedrich Nietzsche
I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there. -- Kronecker
In mathematics you don't understand things. You just get used to them. -- John von Neumann
There's no sense in being precise, when you don't even know what you're talking about. -- John von Neumann
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. -- Nikola Tesla
Mathematics as a purely formal system of symbols without a human being possessing the know-how for dealing with the symbols is impossible. -- Michael Polanyi
Mathematical logic isn't a way to invent but a way to structure ideas. -- Henri Poincaré
In mathematical texts the type of a variable is usually deducible from the typeface without consideration of context; this is not feasible in computer programs. -- Niklaus Wirth, creator of Pascal programming language.
Reading a maths books is like reading a program without any of the supporting documentation. There’s lots of definitions, lemmas, proofs, and so on, but no indication of what it’s all for, or why it’s written the way it is. -- Steve Easterbrook, Professor of Computer Science.
Calculus is at once the most important and most difficult subject encountered early by students of mathematics; introductory courses often succeed only in turning students away from mathematics, and from the many subjects in which the calculus plays a major role. -- Kenneth E. Iverson
It is surprisingly easy to get the right answer with fallacious reasoning or without real understanding. Traditional mathematical notation contributes to this problem. Symbols have ambiguous meanings that depend on context, and often even change within a given context. -- Gerald Jay Sussman, Professor of Electrical Engineering at MIT, and creator of Scheme programming language.
Reliance on ambiguous, unstated notational conventions makes mathematics, and especially introductory calculus, extremely confusing for beginning students. -- Hans Freudenthal, Didactical Phenomenology of Mathematical Structures, Kluwer, 1983.