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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.
Abel, Niels H. (1802 - 1829)
[A reply to a question about how he got his expertise:]
By studying the masters and not their pupils.
Niels H. Abel
Augarten, Stan
Computers are composed of nothing more than logic gates stretched out to the horizon in a vast numerical irrigation system.
State of the Art: A Photographic History of the Integrated Circuit. New York: Ticknor and Fields.
Auden, W. H. (1907-1973)
Thou shalt not answer questionnaires
Or quizzes upon world affairs,
Nor with compliance
Take any test. Thou shalt not sit
with statisticians nor commit
A social science.
"Under which lyre," in Collected Poems of W H Auden, London: Faber and Faber.
Auden, W. H. (1907-1973)
How happy the lot of the mathematician. He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve.
The Dyer's Hand, London: Faber & Faber, 1948.
Aubrey, John (1626-1697)
[About Thomas Hobbes:]
He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition. "By God," sayd he, "this is impossible." So he read the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that trueth. This made him in love with geometry.
In O. L. Dick (ed.), Brief Lives, Oxford University Press, 1960, p. 604.
Ascham, Roger (1515-1568)
Mark all mathematical heads which be wholly and only bent on these sciences, how solitary they be themselves, how unfit to live with others, how unapt to serve the world.
In E G R Taylor, Mathematical Practitioners of Tudor and Stuart England, Cambridge: Cambridge University Press, 1954.
To Thales the primary question was not what do we know, but how do we know it.
Mathematical Intelligencer, v. 6, no. 3, 1984.
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.
Metaphysica, 3-1078b.
It is not once nor twice but times without number that the same ideas make their appearance in the world.
"On The Heavens," in T. L. Heath, Manual of Greek Mathematics, Oxford University Press, 1931.