# Rambling Thoughts

## Mathematical Quotations

“The ultimate goal of mathematics is to eliminate all need for intelligent thought.” — Alfred N. Whitehead

“‘Obvious’ is the most dangerous word in mathematics.” — E. T. Bell

“Mathematics is not a deductive science — that’s a cliche. 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, I Want to be a Mathematician

“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. […] The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful. The ideas, like the colors or the words, must ﬁt together in a harmonious way. Beauty is the ﬁrst test: there is no permanent place in this world for ugly mathematics.” — G. H. Hardy, A Mathematician’s Apology

“What determines how well you’re going to solve a problem is how well you can think about math” — Eric Larson

“A good problem is something you don’t know how to solve. That’s what makes it a good puzzle, and a good opportunity. A good problem does not just sit there in isolation, but serves as a springboard to other interesting questions. A triangle takes up half its box. What about a pyramid inside its three-dimensional box? Can we handle this problem in a similar way?” — Paul Lockhart, “A Mathematician’s Lament”

“A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.” — George Polya, How to solve it

“If you can’t solve a problem, then there is an easier problem you can solve: find it.” — George Polya, How to solve it