A Social History of the “Galois Affair” at the Paris Academy of Sciences (1831)

Abstract

ArgumentThis article offers a social history of the “Galois Affair,” which arose in 1831 when the French Academy of Sciences decided to reject a paper presented by an aspiring mathematician, Évariste Galois. In order to historicize the meaning of Galois's work at the time he tried to earn recognition for his research on the algebraic solution of equations, this paper explores two interrelated questions. First, it analyzes scholarly algebraic practices and the way mathematicians were trained in the nineteenth century to reconstruct the scientific meaning of Galois's research. By emphasizing the historically contingent nature of scientific debates, the paper argues that to historicize the work of a mathematician, we must historicize the scientific world as well. The second part of this article goes further to seek a fresh perspective on Galois's short career by analyzing the cultural, social, and institutional dynamics that governed how the mathematical community came to recognize an aspiring mathematician as one of its own.

Journeys in Mathematical Landscapes: Genius or Craft?

“…Augustus De Morgan, a celebrated educator in this newer more abstract tradition, writes in the 1842 preface to his influential (and monumental) calculus textbook [De Morgan, 1842] that the way to enlarge the settled country [of mathematics] has not been by keeping within it, but by making voyages of discovery [De Morgan, 1842, p. vii] and quotes Newton's supposed remark approvingly to his pupil Ada Lovelace [Hollings et al, 2017] That which you say about the comparison of what you do with what you see can be done was equally said by Newton when he compared himself to a boy who had picked up a few pebbles from the shore ... so that you have respectable authority for supposing that you will never get rid of that feeling; and it is no use trying to catch the horizon [quoted in Hollings et al, 2017, p. 208;original in LB 170, 15 September 1840, f. 14r] Such metaphors of exploration and colonisation are unsurprising for the time, and sat comfortably with sensibilities of later British mathematicians: Cambridge's G H Hardy, a keen climber himself, and friend of the climbers Mallory and Irving, who were lost attempting to scale Everest, wrote [Hardy, 1929] I have myself always thought of a mathematician as in the first instance an observer, a man who gazes at a distant range of mountains and notes down his observations. His object is simply to distinguish clearly and notify to others as many different peaks as he can.…”

“…Yet the approach of sociologists opens up the question of how the mathematicians themselves might be creating that landscape, and what skills that might require. It is beyond our scope here to look at broader philosophical issues, for example the contrast between mathematics as theory-building, and mathematics as problem-solving, as in Gowers [Gowers, 2010]. But mathematicians themselves can sometimes question if landscape metaphors are too constraining: for example Jim Propp, quoted in [Roberts, 2015], wonders if John Conway: is the rare sort of mathematician whose ability to connect his pet mathematical interests makes one wonder if he isn't, at some level, shaping mathematical reality and not just exploring it.…”

“…But somehow, through the force of his personality, and the intensity of his passion, he bent the mathematical universe to his will. [Roberts, 2015, p. 2] The account by Ehrhardt [Ehrhardt, 2010] of the work of Evariste Galois gives a nice example of how such apparently fixed landscapes can be both post-hoc constructions, ways of organising knowledge, as indicated by Jenkins; and be shaped by social as well as scientific forces as indicated by Bourdieu and Lane. Galois's work on the solution of equations was dismissed by Poisson and Lacroix, and his contribution was only recognised once later mathematicians had developed the theory of equations in a broader context.…”

“…So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of-and couldn't exist without-the many months of stumbling around in the dark that proceed them. This notion of "stumbling" inspired a previous paper [Martin, 2015], where online and computational mathematics were analysed to shed light this fine-grained mathematical practice of the craft of mathematics.…”

Cognitive stories and the image of mathematics

“…Negative and complex numbers suffered a similar fate (Schubring 2005). Disputes that superposed mathematical validity, social cliques and generation gaps remained popular in the 19 th century (Ehrhardt 2010(Ehrhardt , 2011Wagner 2014Wagner , 2016. The Italian school of algebraic geometry was confronted with enduring disputes over mathematical validity as late as the 1930s (Brigaglia and Ciliberto 2004).…”