Abstract
George Boole (1815–1864) started his mathematical career as a complete outsider, yet has been variously described as the founder of pure mathematics, the discoverer of symbolic logic and one of the progenitors of the digital age. This paper takes the form of a dialogue aiming to bring to life the friendship and mathematical communion between Boole and Augustus De Morgan (1806–1871). Brief explanatory narration by the mature De Morgan intersperses the speeches of the young Boole and young De Morgan, which are based on the correspondence between them over two decades. The dialogue displays the crucial role of De Morgan as Boole’s encourager and mentor, and highlights the fellowship of minds and close affinities in thought development. Frank and poignant exchanges give insight into personal struggles and delights, publication challenges, institutional problems, religious conflict, intellectual isolation and the excitement of creating the new mathematical logic. The dialogue also exhibits lesser-known aspects of the human side of De Morgan – his generosity, integrity and humour.
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Notes
- 1.
This speech is my invention, based on biographical details in MacHale (2014, 8–17).
- 2.
From De Morgan MS ADD 97/1 in UCL Archives, written after Boole’s death in 1864.
- 3.
De Morgan to Boole, 29 December 1942, from 69 Gower St. All letters between De Morgan and Boole, quoted or paraphrased in this dialogue, are in manuscript, either in University College London Archives: De Morgan MS Add 97/1, or in the Boole Archive, University College. The complete correspondence is available in Smith (1982).
- 4.
Boole to De Morgan, 19 June 1843, from Lincoln. Boole sends De Morgan the manuscript of a paper applying algebraic methods to solve differential equations. Its title is not eye-catching: ‘On a general method of analysis’; but his treatment of linear differential equations with variable coefficients explicitly recognises the non-commutativity of operators, in the same year that William Rowan Hamilton broke with commutativity in his quaternions.
- 5.
De Morgan to Boole, December 1843.
- 6.
De Morgan said that D θ , D t was both mathematically and typographically preferable to \(\frac{d} {d\theta },\ \frac{d} {dt}\).
- 7.
The Gold Medal of the Royal Society was awarded in November 1844.
- 8.
Boole to De Morgan, 24 February 1845.
- 9.
From testimonial dated 1 September 1846, quoted on p. 88 in MacHale (2014).
- 10.
Sir William Hamilton of Edinburgh, philosopher and metaphysician, by whom De Morgan was at that time being accused of plagiarism.
- 11.
De Morgan (1847) and Boole (1847) were published on practically the same November day – the first major works on what would later come to be called mathematical logic. While there has always been complete transparency and trust between them, De Morgan’s haste in responding, and his request not to be sent Boole’s work, are to forestall suggestions of plagiarism from others.
- 12.
This speech and the following are from: De Morgan to Boole, 27 November 1847; unsent.
- 13.
This speech and his next are from: De Morgan to Boole, 28 November 1847.
- 14.
De Morgan to Boole, 29 November 1847.
- 15.
This and two subsequent speeches from: Boole to De Morgan, 8 December 1848.
- 16.
An asterisk, here and in the following, indicates illegibility or ambiguity in the manuscript.
- 17.
De Morgan to Boole, 3 April 1849.
- 18.
De Morgan to Boole, 14 August 1849, from 7 Camden St.
- 19.
De Morgan to Boole, 4? September 1849.
- 20.
This and his next three speeches: Boole to De Morgan, 8 November 1849, from Cork.
- 21.
This and his next speech: De Morgan to Boole, June 1850.
- 22.
This and his next speech: Boole to De Morgan, 17 October 1850.
- 23.
Based on correspondence of 1851-2, and especially De Morgan to Hamilton, 29 September 1852, quoted in MacHale (2014, p. 147).
- 24.
Boole to De Morgan, 8 December 1852.
- 25.
Boole to De Morgan, 23 February 1854.
- 26.
- 27.
Boole to De Morgan, 30 May 1854.
- 28.
Boole to De Morgan, 1855 n.d.
- 29.
De Morgan to Boole, 4 January 1856.
- 30.
Boole to De Morgan, 8 January 1856.
- 31.
This and his next speech: De Morgan to Boole, 13 January 1856. (He puts the question mark after ‘Sanskrit’.)
- 32.
De Morgan to Boole, 10 June 1860, from 41 Chaleot Villas, Adelaide Road, London NW.
- 33.
Boole’s book Treatise on the Calculus of Finite Differences was a sequel to his Treatise on Differential Equations of the previous year.
- 34.
De Morgan to Boole, after June 1860.
- 35.
De Morgan to Boole, 13 July 1860.
- 36.
Boole to De Morgan, 17 July 1860.
- 37.
Boole to De Morgan, 6 November 1862.
- 38.
De Morgan to Boole, 7 November 1862.
- 39.
Boole to De Morgan, 6 November 1862.
- 40.
De Morgan MS ADD 97/1 in UCL Archives, written after Boole’s death in 1864.
References
Boole G (1847) The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. Macmillan, Barclay and Macmillan, Cambridge
Boole G (1854) An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities. Walton and Maberly, London. Reprinted: Dover, New York (1958); digitalized version by Watchmaker Publishing (2010); also in: Jourdain PEB (ed) (1916) Boole’s collected logical works, vol II. Open Court, Chicago & London
De Morgan A (1847) Formal logic. Taylor & Walton, London
MacHale D (2014) The life and work of George Boole: a prelude to the digital age, 2nd edn. (The 1st edition appeared in 1985.) Boole Press, Dublin
Smith GC (ed) (1982) The Boole – De Morgan correspondence, 1842–1864. Clarendon Press, Oxford
Acknowledgements
This dialogue was performed (in shorter form) at the MAA meeting with the invaluable help of Steve Russ, Adrian Rice and Robin Wilson. I wish here to express my gratitude to them.
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Hitchcock, G. (2016). Remarkable Similarities: A dialogue between Boole and De Morgan. In: Zack, M., Landry, E. (eds) Research in History and Philosophy of Mathematics. Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-46615-6_6
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