“The intelligence of that creature known as a crowd is the square root of the number of people in it.”

—  Terry Pratchett, book Jingo

Source: Jingo

Last update Sept. 29, 2023. History

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Terry Pratchett796
English author 1948–2015

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“The Hindus introduced negative numbers… The first known use is Brahmagupta about 628; he also states the rules for the four operations with negative numbers. Bhāskara points out that the square root of a positive number is twofold, positive and negative. He brings up the matter of the square root of a negative number but says that there is no square root because a negative number is not a square. No definitions, axioms, or theorems are given.
The Hindus did not unreservedly accept negative numbers. Even Bhāskara, while giving 50 and -5 as two solutions of a problem, says, "The second value is in this case not to be taken, for it is inadequate; people do not approve of negative solutions."”

Morris Kline (1908–1992) American mathematician

However, negative numbers gained acceptance slowly.
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 185.

George Friedman photo

“No continent is as small and fragmented as Europe. Only Australia is smaller, yet Europe consists of fifty independent nations (including Turkey and the Caucasus, for reasons explained later). Crowded with nations, it is also crowded with people. Europe's population density is 72.5 people per square kilometer. The European Union's density is 112 people per square kilometer. Asia has 86 people per square kilometer. Europe is crowded and fragmented.”

George Friedman (1949) American businessman and political scientist

Flashpoints: The Emerging Crisis in Europe (2015)

Diophantus photo

“As a square number is known to be the product of a number multiplied by itself, so every polygonal number, multiplied by one number and added to another, both of which depend upon the number of its angles, produces a square number. I shall prove this, and shall show also how from a given side to find its polygon and conversely. Some auxiliary propositions must first be proved.”

Diophantus Arithmetica

As quoted by James Gow, A Short History of Greek Mathematics https://books.google.com/books?id=9d8DAAAAMAAJ (1884) <br class="br">Arithmetica (c. 250 AD)

Carl Sagan photo

“In love with whole numbers, the Pythagoreans believed that all things could be derived from them. Certainly all other numbers.
So a crisis in doctrine occurred when they discovered that the square root of two was irrational.”

Carl Sagan (1934–1996) American astrophysicist, cosmologist, author and science educator

37 min 45 sec
Cosmos: A Personal Voyage (1990 Update), The Backbone of Night [Episode 7]
Context: There can be an infinite number of polygons, but only five regular solids. Four of the solids were associated with earth, fire, air and water. The cube for example represented earth. These four elements, they thought, make up terrestrial matter. So the fifth solid they mystically associated with the Cosmos. Perhaps it was the substance of the heavens. This fifth solid was called the dodecahedron. Its faces are pentagons, twelve of them. Knowledge of the dodecahedron was considered too dangerous for the public. Ordinary people were to be kept ignorant of the dodecahedron. In love with whole numbers, the Pythagoreans believed that all things could be derived from them. Certainly all other numbers.
So a crisis in doctrine occurred when they discovered that the square root of two was irrational. That is: the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were. "Irrational" originally meant only that. That you can't express a number as a ratio. But for the Pythagoreans it came to mean something else, something threatening, a hint that their world view might not make sense, the other meaning of "irrational".

William Osler photo

“Shakespeare gets to the root of the alcohol question in his well-known statement—'Good wine is a good, familiar creature if it be well used.”

William Osler (1849–1919) Canadian pathologist, physician, educator, bibliophile, historian, author, cofounder of Johns Hopkins Hospi…

Alcohol in St. Elizabeth Parish Magazine (1905). As quoted in Counsels and ideals from the writings of William Osler (1921, 2nd edition) http://babel.hathitrust.org/cgi/pt?id=hvd.hc1qm3;view=1up;seq=295

Vladimir Nabokov photo

“The square root of I is I.”

Vladimir Nabokov book Bend Sinister

Source: Bend Sinister

Douglas Hofstadter photo

“Irrationality is the square root of all evil.”

Douglas Hofstadter (1945) American professor of cognitive science

"Irrationality is the Square Root of All Evil" (Sep, 1983) Scientific American 249 (3) article reprinted in Metamagical Themas (1985)

“The desperate need today is not for a greater number of intelligent people, or gifted people, but for deep people.”

Richard J. Foster (1942) American Quaker theologian

Source: Celebration of Discipline: The Path to Spiritual Growth

“By 1700 all of the familiar members of the [number] system… were known. However, opposition to the newer types of numbers was expressed throughout the century. Typical are the objections of… Baron Francis Masères… in 1759 his Dissertation on the Use of the Negative Sign in Algebra… shows how to avoid negative numbers… and especially negative roots, by carefully segregating the types of quadratic equations so that those with negative roots are considered separately; and… the negative roots are to be rejected.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 592.

George Gamow photo

“There was a young fellow from Trinity,
Who took the square root of infinity.”

George Gamow (1904–1968) Russian-American physicist and science writer

One, Two, Three... Infinity (1947)
Context: There was a young fellow from Trinity,
Who took the square root of infinity.
But the number of digits, Gave him the fidgets;
He dropped Math and took up Divinity.

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