Metrical Quotes (3 quotes)
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Address (28 Mar 1912), Michigan School Masters' Club, Ann Arbor, 'The Humanization of the Teaching of Mathematics. Printed in Science (26 Apr 1912). Collected in The Human Worth of Rigorous Thinking: Essays and Addresses (1916), 6566.
Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.
[Regarding merging both into projective geometry.]
From concluding paragraph of 'A Sixth Memoir upon Quantics', Philosophical Transactions of the Royal Society of London (6 Jan 1859), 90. Cayleys fundamental principle is often quoted as Projective geometry is all geometry, as in Morris, Kline, 'Projective Geometry', collected in J.R. Newman (ed.) The World of Mathematics (1956), Vol. 1, 639.
Now it came to me:
the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation.
This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.
In Paul Arthur Schilpp, 'Autobiographical Notes', Albert Einstein: PhilosopherScientist (1949), 6567.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) 
Carl Sagan
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