Home / Authors / Paul Halmos

Paul Halmos Quotes

Mathematician

Paul Halmos was a renowned mathematician known for his contributions to functional analysis and probability theory. His research had a profound impact on the development of modern mathematics.

Famous Paul Halmos Quotes

“Applied mathematics will always need pure mathematics just as anteaters will always need ants.”

Needs Pure Mathematics Ants Applied Mathematics

Author:Paul Halmos

“To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.”

Born Ability Talent Taste Mathematics Luck Insight Math Mathematical Concentration Scholar

Author:Paul Halmos

“What's the best part of being a mathematician? I'm not a religious man, but it's almost like being in touch with God when you're thinking about mathematics. God is keeping secrets from us, and it's fun to try to learn some of the secrets.”

Thinking Men Trying God Science Fun Religious Secret Mathematics Mathematician Keeping Secrets

Book:PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics

Source: PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics

“[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.”

“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.”

“...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.”

Science Cases Special Example Source Concepts Essence Mathematics Instance Mathematical Concrete Generalities

Author:Paul Halmos

“The computer is important, but not to mathematics.”

Important Computer Mathematics

Book:PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics

Source: PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics

“It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.”

Facts Problem Knowledge Teacher Teaching Students Particular Duty Logic Mathematics Math Math Education Math Teacher Math Problems

Book:Selecta: expository writing

Source: Selecta: expository writing

“The only way to learn mathematics is to do mathematics.”

Way Learning Mathematics Math Mathematical Mathematician Algebra Math Education Learning By Doing Mathematics By Mathematicians Learning Math Great Math Math Love Good Math Math Is Like Math Class Applied Mathematics

Author:Paul Halmos

“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.”

Truth Joy Secret Vision Learning Enlightenment Mathematics Math Former Mathematical Tension Ecstasy Discovering Flash Euphoria

Author:Paul Halmos

“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.”

Want Firsts Jobs Understanding Education Example Concepts Mathematics Math Something New Statistics Indispensable Thorough Learning Math Good Math Thorough Understanding

Author:Paul Halmos

“Mathematics - this may surprise or shock some - is never deductive in creation.”

May Education Knowledge Creation Logic Mathematics Surprise Math Shock

Author:Paul Halmos

“The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.”

Way Education Knowledge Logic Mathematics Method Foundation Math Texas Do It Yourself Math Education Socratic Learning Math

Book:A Hilbert Space Problem Book

Source: A Hilbert Space Problem Book

“The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.”

Heart Problem Bigs Cases Special Example Theory Mathematics Profound Insight Concrete

Book:Selecta: expository writing

Source: Selecta: expository writing

“The best way to learn is to do; the worst way to teach is to talk.”

Way Teach Worst Mathematics Best Way

Author:Paul Halmos

“Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?”

Looks Doe Use Fighting Asks Example Mathematics Proof Mathematical Hypothesis Converses Math Education Mathematical Proof

Author:Paul Halmos

“It saddens me that educated people don't even know that my subject exists.”

People Knows Subjects Mathematics Educated

Author:Paul Halmos

“Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.”

Mathematics Errors Math Trials Mathematical Mathematician Experimentation Theorems Math And Science Trial And Error Mathematics And Science Mathematics By Mathematicians Funny Mathematics Learning Math Guesswork Mathematical Proof Maths Funny

Author:Paul Halmos

“The heart of mathematics is its problems.”

Heart Problem Mathematics

Author:Paul Halmos

“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.”

Said Remember Courses Education Teacher Students Materials Amount Concerned Mathematics Sticks Average Math Things To Do Formulas Cynic

Author:Paul Halmos

“... 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."”

Giving Lines Students Masters Mathematics Math Mathematical Faculty Exam Skit

Author:Paul Halmos

“If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as we now have, and I don't see anything wrong with that.”

Ifs Government Science Half Mathematics Mathematician

Book:PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics

Source: PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics

“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."”

About the Author

Born: March 3, 1916
Died: October 2, 2006
Known for: Mathematician
Quotes: 34

Books & Sources

PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of MathematicsRelated source material

Selecta: expository writingRelated source material

A Hilbert Space Problem BookRelated source material

Similar Authors

George PolyaBrowse related quotes
G. H. HardyBrowse related quotes
Eric Temple BellBrowse related quotes
Edward KasnerBrowse related quotes
John Edensor LittlewoodBrowse related quotes
Morris KlineBrowse related quotes
Max DehnBrowse related quotes
Sofia KovalevskayaBrowse related quotes
Gian-Carlo RotaBrowse related quotes
David HilbertBrowse related quotes

Paul Halmos Quotes

Filter quotes by topic

Famous Paul Halmos Quotes