Famous quotes containing the words inequality, arithmetic, geometric, means and/or proofs:
“All the aspects of this desert are beautiful, whether you behold it in fair weather or foul, or when the sun is just breaking out after a storm, and shining on its moist surface in the distance, it is so white, and pure, and level, and each slight inequality and track is so distinctly revealed; and when your eyes slide off this, they fall on the ocean.”
—Henry David Thoreau (1817–1862)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“People who wish to numb our caution in dealing with them by means of flattery are employing a dangerous expedient, like a sleeping draught, which, if it does not put us to sleep, keeps us all the more awake.”
—Friedrich Nietzsche (1844–1900)
“I do not think that a Physician should be admitted into the College till he could bring proofs of his having cured, in his own person, at least four incurable distempers.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)