“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.” — Bertrand Russell “Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.” “Mathematics is the art of giving the same name to different things.” — J. H. Poincare “Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.” “Mathematics is a game played according to certain simple rules with meaningless marks on paper.” — David Hilbert “Mathematics consists in proving the most obvious thing in the least obvious way.” — George Polya “In mathematics, you don’t understand things. You just get used to them.” — Johann von Neumann “A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.” “Mathematics is like love; a simple idea, but it can get complicated.” “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” “Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.” — Plato “The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” — S. Gudder “There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.” — Raoul Bott “Obvious is the most dangerous word in mathematics.” — E.T. Bell “Arithmetic is being able to count up to twenty without taking off your shoes.” — Mickey Mouse “The greatest unsolved theorem in mathematics is why some people are better at it than others.” — Adrian Mathesis “Mathematics is not a deductive science – that’s a cliché. When you try to prove a theorem, you don’t just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.” — Paul Halmos “The different branches of Arithmetic are Ambition, Distraction, Uglification, and Derision.” – Lewis Caroll “Mathematics is written for mathematicians.” – Copernicus “Mathematics should be fun.” — Peter J. Hilton “Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics.” “But in the new (math) approach, the important thing is to understand what you’re doing, rather than to get the right answer.” — Tom Lehrer
Why aren’t we giving our students a chance to even hear about these things, let alone giving them an opportunity to actually do some mathematics, and to come up with their own ideas, opinions, and reactions? What other subject is routinely taught without any mention of its history, philosophy, thematic development, aesthetic criteria, and current status? What other subject shuns its primary sources— beautiful works of art by some of the most creative minds in history— in favor of third-rate textbook bastardizations?
The full article is extremely long, but absolutely excellent. If you have the time, I would highly recommend reading (or skimming) A Mathematician’s Lament, by Paul Lockhart. Not everyone needs to love math, but we should all be concerned with the way it is presented in a classroom. After all, without at least some people being inspired to study mathematics, you guys are all screwed.
I bet that any number of high schoolers could destroy me in a competition to perform simple arithmetic, but ultimately what value is that to society? We can create calculators to perform calculus, but we can’t teach them to think like mathematicians. At some point, if we continue to neglect fostering an appreciation and curiosity for true mathematics, we only handicap our potential for future innovation.
Two beautiful mathematical documentaries are “Fermat’s Last Theorem” and “Dangerous Knowledge”. Both take a popular science style approach to describing compelling and emotional stories about great mathematicians.
Movie night! :)