“The moving power of mathematical invention is not reasoning, but imagination.”
Quoted in Robert Perceval Graves, The Life of Sir William Rowan Hamilton, Vol. 3 (1889), p. 219.
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Augustus De Morgan 41
British mathematician, philosopher and university teacher (… 1806–1871Related quotes
“The history of mathematics throws little light on the psychology of mathematical invention.”
100 Years of Mathematics: a Personal Viewpoint (1981)

Source: http://www.cavafy.com/poems/content.asp?id=157&cat=4 On Hearing of Love
Collected Poems (1992)

“Mathematics is not just a language. Mathematics is a language plus reasoning.”
Source: The Character of Physical Law (1965), chapter 2, “The Relation of Mathematics to Physics”
Context: Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.

Letter to his brother (1791).
Letters

“To invent, you need a good imagination and a pile of junk.”
As quoted in Behavior-Based Robotics (1998) by Ronald C. Arkin. p. 8.
Date unknown