Quotes by Paul Halmos

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

Math

…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.

Essence

Science

Special

[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.

Analysis

Knowledge

Science

A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better.

Clever

Graduates

Students

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.

Education

Jobs

Math

A smooth lecture… may be pleasant; a good teacher challenges, asks, irritates and maintains high standards – all that is generally not pleasant.

Challenges

Teacher

Teaching

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

Ants

Mathematics

Needs

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?

Doe

Example

Fighting

Feller was an ebullient man, who would rather be wrong than undecided.

Men

Undecided

I read once that the true mark of a pro – at anything – is that he understands, loves, and is good at even the drudgery of his profession.

Drudgery

Mark

Profession

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Algebra

Analysis

Answers

Ants

Beginners

Challenges

Class

Clever

Computer

Doe

Drudgery

Educated

Education

Errors

Essence

Example

Fighting

Fun

Giving

God

Government

Graduates

Half

Heart

Important

Jobs

Knowledge

Laboratory

Learning

Library

Lines

Littles

Luck

Lying

Mark

Math

Mathematician

Mathematics

Memories

Men

Mislead

Needs

Numbers

People

Problem

Profession

Profound

Reading

Religious

Science

The Future Blueprint

Tool

The Home Therapist: Anti Anxiety

Tool

The Autobiography

Tool

The Behaviour Diary

Tool

The Dating Diary

Tool

The Relationship Therapist

Tool

Quotes by Paul Halmos

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.”

…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.

A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better.

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.

A smooth lecture… may be pleasant; a good teacher challenges, asks, irritates and maintains high standards – all that is generally not pleasant.

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

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?

Feller was an ebullient man, who would rather be wrong than undecided.

I read once that the true mark of a pro – at anything – is that he understands, loves, and is good at even the drudgery of his profession.

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Topics by Paul Halmos

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The Future Blueprint

The Home Therapist: Anti Anxiety

The Autobiography

The Behaviour Diary

The Dating Diary

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