Some Comments on Multiple Discovery in Mathematics

Abstract

SynopsisAmong perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to meaningful questions regarding causes, trends, categories, etc. With this in view we unearth many more examples, find some tenuous connections, and draw some tentative conclusions.The characterisation by forbidden minors of graph planarity, the Reidemiester moves in knot theory, and the NP-completeness of satisfiability are all discoveries of twentieth-century mathematics which occurred twice, more or less simultaneously, on different sides of the Atlantic. One may enumerate similar coincidences to one's heart's content. Michael Deakin wrote about some more in his admirable magazine Function [10], Frank Harary reminisces about a dozen or so in graph theory [25], and there are whole books on individual instances, such as Hall on Newton-Leibniz [24] and Roquette on the Brauer-Hasse-Noether Theorem [44].Mathematics is quintessentially a selfless joint endeavour, in which the pursuit of knowledge is its own reward. This is not a polite fiction; G.H. Hardy's somewhat sour remark [26] "if a mathematician . . . were to tell me that the driving force in his work had been the desire to benefit humanity, then I should not believe him (nor should I think the better of him if I did)"

Epistemic injustice in mathematics

“…36 Other instances of epistemic luck in mathematical practices include simultaneous discoveries with unevenly distributed credit; see Whitty (2017). A discussion of these matters is beyond the scope of this paper.…”