Augustus De Morgan Quotes About Mathematics

• But the gambling reasoner is incorrigible: if he would but take to squaring the circle, what a load of misery would be saved.

  Augustus De Morgan

  Gambling, Circles, Would Be

  "A Budget of Paradoxes".

• Mathematicians care no more for logic than logicians for mathematics.

  Augustus De Morgan

  Care, Logic, Mathematics

• During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true

  Augustus De Morgan

  Knowledge, Science, Two

  Augustus De Morgan (1872). “A Budget of Paradoxes Reprinted, with the Author's Additions, from the Athenaeum Augustus De Morgan”, p.2

• Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.

  Augustus De Morgan

  Math, Logic, Improvement

  Augustus De Morgan (1966). “On the syllogism: and other logical writings”

• We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.

  Augustus De Morgan

  Believe, Eye, Science

• It should seem that it is easier to square the circle than to get round a mathematician.

  Augustus De Morgan

  Education, Math, Squares

  "A Budget of Paradoxes".

• Common integration is only the memory of differentiation.

  Augustus De Morgan

  Education, Memories, Differentiation

  "Modern Computer Algebra". Book by Joachim von zur Gathen, April 25, 2013.

• I was x years old in the year x2.

  Augustus De Morgan

  Education, Math, Years

• Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.

  Augustus De Morgan

  Squares, Circles, Roots

• Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]

  Augustus De Morgan

  Writing, Thinking, Years

  "Budget of Paradoxes". Book by Augustus De Morgan (p. 178), 1872.

• The imaginary expression √(-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as √(-a).

  Augustus De Morgan

  Real, Expression, Negative

• The moving power of mathematical invention is not reasoning but imagination.

  Augustus De Morgan

  Teacher, Moving, Math

  "The Life of Sir William Rowan Hamilton". Book by Robert Perceval Graves, Volume 3, p. 219, 1889.

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