Tag Archives: math

Happy Math Awareness Month!

Selected quotes from http://www.baylor.edu/math/index.php?id=88078:

It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry. (Albert Einstein, 1879-1955)

God may not play dice with the universe, but something strange is going on with the prime numbers. (Paul Erdös, 1913-1996)

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. (Richard Feynman, 1918-1988)

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. (Galileo Galilei, 1564-1642)

The total number of Dirichlet’s publications is not large: jewels are not weighed on a grocery scale. (C.F. Gauss, 1777-1885)

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. (G.H. Hardy, 1877-1947)

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven? (David Hilbert, 1862-1953)

God ever arithmetizes. (Carl Jacobi, 1804-1851) (No idea what this one means – any guesses?)

I read in the proof sheets of Hardy on Ramanujan: “As someone said, each of the positive integers was one of his personal friends.” My reaction was, “I wonder who said that; I wish I had.” In the next proof-sheets I read (what now stands), “It was Littlewood who said…” (J.E. Littlewood, 1885-1977)

What we know is not much. What we do not know is immense. (Allegedly the last words of Pierre-Simon Laplace, 1749-1827)

In the absence of any other proof, the thumb alone would convince me of God’s existence. (Isaac Newton, 1643-1727)

[On quantum mechanics] I don’t like it, and I’m sorry I ever had anything to do with it. (Erwin Schrödinger, 1887-1961)

By and large it is uniformly true that in mathematics there is a time lapse between a mathematical discovery and the moment it becomes useful; and that this lapse can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful. (John von Neumann, 1903-1957) Conflicts between my pure math and engineering sides…

My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful. (Hermann Weyl, 1885-1955)

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Wisdom from the Abstract Algebra Book

I was interviewed in the Israeli Radio for five minutes and I said that more that 2000 years ago, Euclid proved that there are infinitely many primes. Immediately the host interrupted me and asked: “Are there still infinitely many primes?” – Noga Alon

There is nothing more practical than a good theory. – Leonid Brezhnev

The only way to learn mathematics is to do mathematics. – Paul Halmos

A good stock 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

“For example,” is not proof. – Jewish Proverb

The purpose of proof is to understand, not to verify. – Arnold Ross

A Programmer’s Lament
I really hate this damned machine;
I wish that they would sell it
It never does quite what I want
but only what I tell it.
– Dennie L. Van Tassel

It is not unreasonable to use the hypothesis. – Arnold Ross

Science is what we understand well enough to explain to a computer. Art is everything else we do. – Donald Knuth

The basis for poetry and scientific discovery is the ability to comprehend the unlike in the like and the like in the unlike. – Jacob Bronowski

Being a mathematician is a bit like being a manic depressive: you spend your life alternating between giddy elation and black despair. – Steven G. Krantz

There is only one satisfying way to boot a computer. – J.H. Goldfuss

In the fields of observation chance favors only the prepared mind. – Louis Pasteur

What’s the most difficult aspect of your life as a mathematician, Diane Maclagan, an assistant professor at Rutgers, was asked. “Trying to prove theorems,” she said. And the most fun? “Trying to prove theorems.”

The geek shall inherit the earth. – Lev Grossman

My mind rebels at stagnation. Give me problems, give me work, give me the most obstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere. – Sherlock Holmes, The Sign of Four

Understanding is a kind of ecstasy. – Carl Sagan

The greater the difficulty, the more glory in surmounting it. Skillful pilots gain their reputation from storms and tempests. – Epicurus

All perception of truth is the detection of an analogy. – Henry David Thoreau

A computer lets you make more mistakes faster than any invention in human history – with the possible exceptions of handguns and tequila. – Mitch Ratliffe

The purpose of computation is insight, not numbers. – Richard Hamming

Example is the school of mankind, and they will learn at no other. – Edmund Burke

Minus times minus is plus. The reason for this we need not discuss. – W.H. Auden

There is no substitute for hard work. – Thomas Alva Edison

Theory is the general; experiments are the soldiers. – Leonardo da Vinci

It looked absolutely impossible. But it so happens that you go on worrying away at a problem in science and it seems to get tired, and lies down and lets you catch it. – William Lawrence Bragg

The secret of science is to ask the right questions, and it is the choice of problem more than anything else that marks the man of genius in the scientific world. – Sir Henry Tizard

Problems worthy of attack prove their worth by hitting back. – Piet Hein

What is the common denominator of intellectual accomplishment? In math, science, economics, history, or any other subject, the answer is the same: great thinkers notice patterns. – David Niven

If at first you do succeed – try to hide your astonishment. – Harry F. Banks

Wit lies in recognizing the resemblance among things which differ and the difference between things which are alike. – Madame de Stael

If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy. – Paul Turan

The value of a principle is the number of things it will explain. – Ralph Waldo Emerson

No matter how good you are at something, there’s always about a million people better than you. – Homer Simpson

Give me a fruitful error anytime, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself. – Vilfredo Pareto

I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lust of the flesh. – Thomas Mann

The intelligence is proved not by ease of learning, but by understanding what we learn. – Joseph Whitney

I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated. – Paul Anderson

Banach once told me, “Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies.” – S.M. Ulam

No pressure, no diamonds. – Mary Case

Hardware: the parts of a computer that can be kicked. – Jeff Pesis

Never underestimate a theorem that counts something. – John Fraleigh

I have always grown from my problems and challenges, from the things that don’t work out. That’s when I’ve really learned. – Carol Burnett

If you don’t learn from your mistakes, there’s no sense making them. – Herbert V. Prochnow

One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than we originally put into them. – Henrich Hertz

Perhaps the most valuable result of all education is the ability to make yourself do the thing you have to do, when it ought to be done, whether you like it or not. – Thomas Henry Huxley

The greater the difficulty, the more glory in surmounting it. – Epicurus

The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them. – Sir William Lawrence

A mathematician is a machine for turning coffee into theorems. – Paul Erdos

Damn it, if the machine can detect an error, why can’t it locate the position of the error and correct it? – Richard W. Hamming

The New Testament offers the basis for modern computer coding theory, in the form of an affirmation of the binary number system. “But let your communication be yea, yea; nay, nay: for whatsoever is more than these cometh of evil.” – Anonymous

Difficulties should act as a tonic. They should spur us to greater exertion. – B.C. Forbes

Mathematics is not a deductive science–that’s a cliche. When you try to prove a theorem, you don’t just list the hypothesis, and then start to reason. What you do is trial and error, experimentation, guesswork. – Paul Halmos

To make headway, improve your head. – B.C. Forbes

The brain is as strong as its weakest think. – Eleanor Doan

Mistakes are often the best teachers. – James A. Froude

Think and you won’t sink. – B.C. Forbes

There is always a right and a wrong way, and the wrong way always seems the more reasonable. – George Moore

All things are difficult before they are easy. – Thomas Fuller

There’s a mighty big difference between good, sound reasons and reasons that sound good. – Burton Hillis

Not one student in a thousand breaks down from overwork. – William Allan Neilson

If at first you don’t succeed, try, try, again. Then quit. There’s no use being a damn fool about it. – W.C. Fields

For every problem there is a solution which is simple, clean and wrong. – H.L. Mencken

Why, sometimes I’ve believed as many as six impossible things before breakfast. – Lewis Carroll

– From Contemporary Abstract Algebra by Joseph A Gallian

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Life Lessons from Math Undergrad

I feel like I’ve learned so much more than theorems in these years of earning a B.S. in Mathematics.
For example:

Lesson 1: Things aren’t always what they seem.
2 + 2 doesn’t always equal 4. In the ring of integers mod 3, it’s the multiplicative identity; in integers mod 2, it’s 0. (Math is weird, people.)

Lesson 2: You have to start somewhere.
The way to start a proof is this: Write P-r-o-o-f.
If you’re still stuck, write, “Let ε > 0 be given.”

Lesson 3: If plan A doesn’t work, try plan B. And plans C, D, and E.
First, you try proving a theorem directly. Then you go for induction. Then, when all else fails, you assume it’s false and contradict yourself (hoping the universe doesn’t disappear from existence in the process).

Lesson 4: Know when to give up.
If it’s 1:13 am on Wednesday night and you’ve tried plans A through Q with three of your closest friends and whiteboards and none of you can speak English anymore (though you still understand each other), it’s time to give in and ask your professor in the morning.

Lesson 5: If you write strange things on whiteboards, you will get strange looks.
(Maybe this one isn’t so much a life lesson as a study in library anthropology.)

Lesson 5: The squeaky wheel gets the oil.
“But Dr. Professor, the undergrad contingent just left your office asking for homework help, and we haven’t had time to write it up. Can we have an extension?”

Lesson 6: Sometimes, you’ve just got to dance.
I mean, really, Abstract Algebra occasionally requires that you break out into the macarena. You may get strange looks from other people in the library, but what can you do?

Lesson 7: Humility.
“What are you working on?” “Advanced Calculus.” “Oh, is that like Cal 3?”
No, honey, no.

And certainly not least:
Lesson 8: If you look, you can see God everywhere.
Everywhere, even in math theorems (the false etymology of which is theo- -rems: God things). Parameterizations remind me of worship songs. Mathematical truths are true because, somehow, their truth glorifies God. My friend Austin sees God’s existence in the proof that .9999… = 1.

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Reason #37 Why I’m a Math Major

Parametrizations remind me of worship songs.

φ(r, θ) = (r cosθ, r sinθ, r2), (r, θ) ε [0,1] x [0, 2π]

Lift my hands and spin around
See the light that I have found!
It’s a marvelous light, marvelous light

Into marvelous light I’m running
Out of darkness, out of shame
By the cross, you are the Truth
You are the Life, you are the Way

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A Liberal Education

I came to (once again) appreciate my broad, interdisciplinary education today when I could laugh at the phrase, “Integration of Forms” in Advanced Calculus. What would Plato think?

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For the Glory of God

I’ve been doing a lot of proofs this week. A whole lot. For all times greater than zero, there exists a proof on Meaghan’s whiteboard.

This morning at about 1 a.m. I realized that proofs, even of advanced calculus, are theological. The infinite union of open sets is open because somehow that glorifies God. If E is connected, there is a finite open cover of E because it glorifies God to be that way.
I mean, really, everything that exists gives glory to God. That’s why it exists.

Perhaps if our mathematics group were to write a psalm tonight we would say,

The mathematical truths declare the glory of God,
and their proofs proclaim his handiwork.
Day to day pours out our homework,
and night to night reveals God’s knowledge.

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