Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings. - "Systems of Logic Based on Ordinals," section 11: The purpose of ordinal logics (1938), published in Proceedings of the London Mathematical Society, series 2, vol. 45 (1939) - In a footnote to the first sentence, Turing added: "We are leaving out of account that most important faculty which distinguishes topics of interest from others; in fact, we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions."
The Prime Minister has praised late computer genius, mathematician and codebreaker Alan Turing for his “remarkable” and […] “vital” role in winning World War Two. The Queen on 23 December granted a posthumous pardon to the gay hero Alan Turing […] granted to Alan Turing two weeks ago has finally seen justice for this national hero. “May I thank the Prime Minister, the