“The history of mathematics throws little light on the psychology of mathematical invention.”

100 Years of Mathematics: a Personal Viewpoint (1981)

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George Frederick James Temple21

British mathematician 1901–1992

James Gow (scholar) (1854–1923) scholar

Preface
A Short History of Greek Mathematics (1884)

“The moving power of mathematical invention is not reasoning, but imagination.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Quoted in Robert Perceval Graves, The Life of Sir William Rowan Hamilton, Vol. 3 (1889), p. 219.

“The unnaturalness of mathematical symbolism is attested to by history. The algebra of the Egyptians, the Babylonians, the Greeks, the Hindus, and the Arabs was what is commonly called rhetorical algebra. …on the whole they used ordinary rhetoric to describe their mathematical work. Symbolism is a relatively modern invention of the sixteenth and seventeenth centuries…”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 59

“Only mathematics and mathematical logic can say as little as the physicist means to say.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

The Scientific Outlook (1931)
1930s
Context: Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

“Mathematics as an Element in the History of Thought.”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

1920s, Science and the Modern World (1925)

“Johann Herbart’s work on education and particularly mathematical psychology influenced me. I think mathematics is the pure instance of construct functioning—the model of human behaviour.”

George Kelly (psychologist) (1905–1967) American psychologist and therapist

Attributed to George A. Kelly in Hinkle (1970, p. 91), as cited in: Fay Fransella and Robert A. Neimeyer. "George Alexander Kelly: The man and his theory." International handbook of personal construct psychology (2003): 21-31.