„If one proves the equality of two numbers a and b by showing first that a \leqq b and then that a \geqq b, it is unfair; one should instead show that they are really equal by disclosing the inner ground for their equality.“

As quoted in Hermann Weyl, "Emmy Noether" (April 26, 1935) in Weyl's Levels of Infinity: Selected Writings on Mathematics and Philosophy (2012) p. 64.

Obtido da Wikiquote. Última atualização 22 de Maio de 2020. História
Emmy Noether photo
Emmy Noether
1882 - 1935

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Varadaraja V. Raman photo
Halldór Laxness photo

„b>The first thing is to have the will; the rest is technique.</b“

—  Halldór Laxness, livro Kristnihald undir Jökli (bók)

Kristnihald undir Jökli (Under the Glacier/Christianity at Glacier) (1968)

François Viète photo

„On symbolic use of equalities and proportions. Chapter II.
The analytical method accepts as proven the most famous [ as known from Euclid ] symbolic use of equalities and proportions that are found in items such as:
1. The whole is equal to the sum of its parts.
2. Quantities being equal to the same quantity have equality between themselves. [a = c & b = c => a = b]
3. If equal quantities are added to equal quantities the resulting sums are equal.
4. If equals are subtracted from equal quantities the remains are equal.
5. If equal equal amounts are multiplied by equal amounts the products are equal.
6. If equal amounts are divided by equal amounts, the quotients are equal.
7. If the quantities are in direct proportion so also are they are in inverse and alternate proportion. [a:b::c:d=>b:a::d:c & a:c::b:d]
8. If the quantities in the same proportion are added likewise to amounts in the same proportion, the sums are in proportion. [a:b::c:d => (a+c):(b+d)::c:d]
9. If the quantities in the same proportion are subtracted likewise from amounts in the same proportion, the differences are in proportion. [a:b::c:d => (a-c):(b-d)::c:d]
10. If proportional quantities are multiplied by proportional quantities the products are in proportion. [a:b::c:d & e:f::g:h => ae:bf::cg:dh]
11. If proportional quantities are divided by proportional quantities the quotients are in proportion. [a:b::c:d & e:f::g:h => a/e:b/f::c/g:d/h]
12. A common multiplier or divisor does not change an equality nor a proportion. [a:b::ka:kb & a:b::(a/k):(b/k)]
13. The product of different parts of the same number is equal to the product of the sum of these parts by the same number. [ka + kb = k(a+b)]
14. The result of successive multiplications or divisions of a magnitude by several others is the same regardless of the sequential order of quantities multiplied times or divided into that magnitude.
But the masterful symbolic use of equalities and proportions which the analyst may apply any time is the following:
15. If we have three or four magnitudes and the product of the extremes is equal to the product means, they are in proportion. [ad=bc => a:b::c:d OR ac=b2 => a:b::b:c]
And conversely
10. If we have three or four magnitudes and the first is to the second as the second or the third is to the last, the product of the extremes is equal to that of means. [a:b::c:d => ad=bc OR a:b::b:c => ac=b2]
We can call a proportion the establishment of an equality [equation] and an equality [equation] the resolution of a proportion.“

—  François Viète French mathematician 1540 - 1603

From Frédéric Louis Ritter's French Tr. Introduction à l'art Analytique (1868) utilizing Google translate with reference to English translation in Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1968) Appendix
In artem analyticem Isagoge (1591)

Wallace Stevens photo
Gottlob Frege photo

„The typical white intellectual considers himself superior to ordinary white people for two contradictory reasons: a] he constantly proclaims belief in human equality, but they don't; b] he has a high IQ, but they don't.“

—  Steve Sailer American journalist and movie critic 1958

How to Help the Left Half of the Bell Curve http://www.isteve.com/How_to_Help_the_Left_Half_of_the_Bell_Curve.htm, VDARE.com, July to September 2000

Milton Friedman photo
Ilana Mercer photo

„B. B. King is no match for Johann Sebastian Bach.“

—  Ilana Mercer South African writer

"Hollywood: The No-Good, The Bad And The Beastly" http://www.americandailyherald.com/pundits/ilana-mercer/item/hollywood-the-no-good-the-bad-and-the-beastly American Daily Herald, March 10, 2014.
2010s, 2014

Gottlob Frege photo

„Equality gives rise to challenging questions which are not altogether easy to answer… a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori.“

—  Gottlob Frege, Sense and reference

The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing.
As cited in: M. Fitting, Richard L. Mendelsoh (1999), First-Order Modal Logic, p. 142. They called this Frege's Puzzle.
Über Sinn und Bedeutung, 1892

„[You know you are in a part of the economy dealing with grants instead of exchange when] A gives B something and B does not give A anything in the way of an economic good.“

—  Kenneth E. Boulding British-American economist 1910 - 1993

McCloskey (2013) commented earlier: "Boulding invented what he called, infelicitiously, "grants economics" (he might better have used the anthropologist's term gifts, or even the theologian's term grace... It's an idea about the economy, but draws the attention of economists to exactly what they do not attend to when thinking of exchange alone."
Fonte: 1970s, The Economy of Love and Fear, 1973, p. i as cited in: Deirdre Nansen McCloskey (2013) What Boulding Said Went Wrong with Economics, A Quarter Century On http://www.deirdremccloskey.com/editorials/boulding.php

Halldór Laxness photo

„b>Over us human beings there hangs an awful sword of justice.</b“

—  Halldór Laxness Icelandic author 1902 - 1998

Heimsljós (World Light) (1940), Book Four: The Beauty of the Heavens

Halldór Laxness photo

„b>A man is not independent unless he has the courage to stand alone.</b“

—  Halldór Laxness Icelandic author 1902 - 1998

Sjálfstætt fólk (Independent People) (1935), Book Two, Part III: Conclusion

Charles Thomson (artist) photo

„The Turner should be renamed the B&Q diy prize.“

—  Charles Thomson (artist) British artist 1953

Dalya Alberge, "One Man and His Boat Sail into a Storm over the Turner" http://www.timesonline.co.uk/article/0,,2-1905555,00.html The Times, 2005-12-06.
On the 2005 Turner Prize winner, Simon Starling, who turned a shed into a boat and back into a shed.

Ronald H. Coase photo

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