Quotes from the Mathematical Quotations Server

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Quotes from the
Mathematical
Quotations Server

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Abel, Niels H. (1802 - 1829

If you disregard the very simplest cases, there is in all of mathematics not a single
infinite series whose sum has been rigorously determined. In other words,the most
important parts of mathematics stand without a foundation.
In G. F. Simmons, Calculus Gems, New York: Mcgraw Hill, Inc., 1992, p. 188.

[A reply to a question about how he got his expertise:]
By studying the masters and not their pupils.

[About Gauss' mathematical writing style]
He is like the fox, who effaces his tracks in the sand with his tail.
In G. F. Simmons, Calculus Gems, New York: Mcgraw Hill, Inc., 1992, p. 177.

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Adams, Douglas (1952 - 2001

Bistromathics itself is simply a revolutionary new way of understanding the behavior of numbers. Just as Einstein observed that space was not an absolute but depended on the observer's movement in space, and that time was not an absolute, but depended on the observer's movement in time, so it is now realized that numbers are not absolute, but depend on the observer's movement in restaurants.
Life, the Universe and Everything. New York: Harmony Books, 1982
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The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up, or to the number of people who subsequently join them after the show/match/party/gig, or to the number of people who leave when they see who else has turned up.
The second nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive. Recipriversexclusons now play a vital part in many branches of math, including statistics and accountancy and also form the basic equations used to engineer the Somebody Else's Problem field.
The third and most mysterious piece of nonabsoluteness of all lies in the relationship between the number of items on the bill, the cost of each item, the number of people at the table and what they are each prepared to pay for. (The number of people who have actually brought any money is only a subphenomenon of this field.)
Life, the Universe and Everything. New York: Harmony Books, 1982
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Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe.
This single statement took the scientific world by storm. It completely revolutionized it. So many mathematical conferences got held in such good restaurants that many of the finest minds of a generation died of obesity and heart failure and the science of math was put back by years.
Life, the Universe and Everything. New York: Harmony Books, 1982.

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Adams, John (1735 - 1826

I must study politics and war that my sons may have liberty to study mathematics
and philosophy. My sons ought to study mathematics and philosophy, geography,
natural history, naval architecture, navigation, commerce and agriculture in order to
give their children a right to study painting, poetry, music, architecture, statuary,
tapestry, and porcelain.
Letter to Abigail Adams, May 12, 1780.

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Adler, Alfred

Each generation has its few great mathematicians, and mathematics would not even
notice the absence of the others. They are useful as teachers, and their research
harms no one, but it is of no importance at all. A mathematician is great or he is
nothing.
"Mathematics and Creativity." The New Yorker Magazine, February 19, 1972.

The mathematical life of a mathematician is short. Work rarely improves after the
age of twenty-five or thirty. If little has been accomplished by then, little will ever
be accomplished.

"Mathematics and Creativity." The New Yorker Magazine, February 19, 1972.
In the company of friends, writers can discuss their books, economists the state of
the economy, lawyers their latest cases, and businessmen their latest acquisitions,
but mathematicians cannot discuss their mathematics at all. And the more
profound their work, the less understandable it is.
Reflections: mathematics and creativity, New Yorker, 47(1972), no. 53, 39 - 45

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Aiken, Conrad

[At a musical concert:]
...the music's pure algebra of enchantment.

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Allen, Woody

Standard mathematics has recently been rendered obsolete by the discovery that
for years we have been writing the numeral five backward.
This has led to reevaluation of counting as a method of getting from one to ten. Students are taught
advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.
In Howard Eves' Return to Mathematical Circles, Boston: Prindle,
Weber, and Schmidt, 1988.

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Allen, Woody

Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.
In Howard Eves' Return to Mathematical Circles, Boston: Prindle, Weber, and Schmidt, 1988.

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Anglin, W.S

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.
"Mathematics and History", Mathematical Intelligencer, v. 4, no. 4.

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Anonymous

If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.

In Ivor Thomas "Greek Mathematics" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

Defendit numerus: There is safety in numbers.

In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 1452.

Like the crest of a peacock so is mathematics at the head of all knowledge.

[An old Indian saying. Also, "Like the Crest of a Peacock" is the title of a book by G.G. Joseph]

Referee's report: This paper contains much that is new and much that is true. Unfortunately, that which is true is not new and that which is new is not true.
In H.Eves Return to Mathematical Circles, Boston: Prindle, Weber, and Schmidt, 1988