This special issue of BJHM presents three papers based on those given at the meeting, nearly two years ago, on ‘The History of Mathematics and Flight’. The meeting resulted from BSHM Council’s desire to provide some events accessible to our more northern members. Nigel Sym nobly volunteered to be a local organizer, and when he suggested the Concorde Centre at Manchester Airport as a suitable venue, Mathematics and Flight seemed the obvious topic to focus on. But the meeting had a chequered career, having to be postponed twice due to the pandemic; having chosen the topic to suit the venue we did not want to shift it online, unlike some other BSHM meetings. It finally took place on 2 July 2022, when twenty-two attendees were treated to six lively talks and an extensive tour of Concorde.
The meeting deliberately took a broad view, the call for papers stating that, ‘Flight will be broadly conceived to cover the flight of man-made objects (planes, missiles, arrows, rockets etc.), animals, and even fugitives; flight formation, navigation and control.’ Although no talks on fugitives were forthcoming, the papers in this special issue provide a good cross-section of those that did materialize, covering ballistics, birds, and aircraft. They also range in date from the mid-eighteenth century to the 1920s, but two common themes runs through them all – the impact of war, and a creative tension between mathematical theory and real-world observation.
This tension is most directly addressed in the first paper, Jane Wess’s on Benjamin Robins: Elegant Mathematics Versus Experimental Inconvenience? Noting that Benjamin Robins (1707–1751) was the first explicitly to challenge the received belief that the flight of projectiles describes a parabola, and that air resistance could be neglected, Wess poses the question of why a clearly erroneous mathematical theory was upheld for so long, especially when, in an age of warfare, the topic was so pressing. It should not surprise us that social factors and a commitment to tradition apparently played a part, alongside the undoubted attraction of beautiful and simple geometry. To these conclusions Wess adds an interesting suggestion of historical contingency – that in an Enlightenment era that was ridding itself of any vestiges of Aristotelianism, the Galilean suggestion of a parabola represented an acceptably modern theory.
Two centuries later, the Scottish biologist, D’Arcy Wentworth Thompson (1860–1948), sometimes called the ‘father’ of mathematical biology, asserted a similar priority of mathematics over observation, as recounted by Kate Hindle in her paper D’Arcy Thompson on Flight. Indeed, Thompson cited Galileo as his authority for doing so. In a neat reversal of the usual order of the time, where understandings of the possibilities of artificial flight drew on observations of the flight of birds, Thompson worked the other way round. Based on the mathematics of Selig Brodetsky during the First World War, Thompson sought to understand the different flight patterns of birds. The ensuing controversy with Herbert Maxwell reveals much about Thompson’s attitudes to mathematics.
D’Arcy Thompson was a near contemporary of William Ellis Williams (1861–1982) whose work on aviation is raised to the prominence it deserves in Stability in theory, in the laboratory and in the air: William Ellis Williams’ campaign for proof positive (1904–1914) by James Boyd, Gareth Roberts and Alwyn Owens.Footnote1 Williams, like Robins before him, was convinced of the necessity of ensuring that robust, detailed, observations were represented in the mathematics of aircraft design, even if this meant making the mathematics more complex. Unlike Robins, though, he worked in an era when at least some opinion was with him. Although frustrated with the National Physical Laboratory’s inertia, Williams seems to have found it fairly easy to find a funder, the ship owner and timber magnate Henry Rees Davies, to finance construction of an experimental aircraft in 1909. Not just an aircraft, the ‘Bamboo Bird’ was intended as a laboratory in the air, and specifically to take detailed measurements of the pressure distribution across the wings in flight. He was successful in 1913, but his priority in this achievement has been overlooked – a casualty of the intense work on aeronautics during the First World War, and the far greater prominence of the Cambridge-based G I Taylor who achieved the same thing in 1916.
As former BSHM Meetings Co-ordinator, I would like to express my gratitude to Nigel Sym for his meticulous local organization and all the effort he put into organizing the Flight meeting three times over. For those of you who missed it, the full programme of abstracts is available on the BSHM website https://www.bshm.ac.uk/events/history-mathematics-and-flight.
Before concluding, I must mention the fourth article in this issue – one that seemed so topical that it should not wait. This is Peter Rowlett’s short communication, Generative AI and accuracy in the history of mathematics. It is relatively rare to see experimental work in the history of mathematics, but Rowlett has done some and the results are thought-provoking.
Notes
1 Readers who met him at the meeting or on other occasions will be deeply saddened to learn that the third author, Alwyn Owens, died on 14 December 2023.