Quotes by Math I'll tell you once, and I'll tell you again. There's always a prime between n and 2n. Paul Erdos primeyou-againmath I know numbers are beautiful. If they aren't beautiful, nothing is. Paul Erdos mathnumbersbeautiful When I was a child, the Earth was said to be two billion years old. Now scientists say it's four and a half billion. So that makes me two and a half billion. Paul Erdos educationmathchildren Mathematics is not yet ready for such problems. Paul Erdos readyproblemmath The only way to learn mathematics is to do mathematics. Paul Halmos learningmathway The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method. Paul Halmos educationmathknowledge A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one. Paul Halmos educationmathjobs 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 errorsmathscience I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces." Paul Halmos mathclassnumbers To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess. Paul Halmos lucktastemath When a student comes and asks, "Should I become a mathematician?" the answer should be no. If you have to ask, you shouldn't even ask. Paul Halmos studentsanswersmath Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick. Paul Halmos educationmathteacher ... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams." Paul Halmos linesmathgiving The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension. Paul Halmos learningtruthmath Mathematics - this may surprise or shock some - is never deductive in creation. Paul Halmos educationmathknowledge Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork. Paul Halmos trial-and-errorerrorsmath To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion − not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to. Paul Lockhart inspirationmathdiscovery Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work. Paul Lockhart mathteacherideas Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles? Paul Lockhart mathchildrenthinking No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade? Paul Lockhart usemathnumbers«5354555657585960616263»
