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Mathematical myths, legends and inaccuracies: some examples

I’m teaching a first-year module on the history of mathematics for undergraduate mathematicians this term. In this, I’m less concerned about students learning historical facts and more that they gain a general awareness of history of maths while learning about the methods used to study history.

Last week, I decided I would discuss myths and inaccuracies. Though I am aware of a few well-known examples, I was struggling to find a nice, concise debunking of one. I asked on Twitter for examples, and here are the suggestions I received, followed by what I did.

Jason Dyer, @Brobuntu and Rob Eastaway all three suggested an article, Gauss’s Day of Reckoning, which discusses the tale of Gauss as a boy quickly summing the first 100 integers. @Brobuntu also mentioned the story of Hippasus and the Pythagoreans and “the worn story” of Euler debating Diederot, but without sources debunking them. Dan Wood also mentioned the former of these, of the Pythagoreans ordering the death of a student who proved $\sqrt{2}$ to be irrational.

@haggismaths suggested a blog post, Logic and Madness?, that debunks the idea that thinking about the continuum hypothesis drove Cantor mad.

Nicholas Jackson suggested Galois “frantically scribbling maths the night before his fatal duel”, and the article Genius and Biographers: The Fictionalization of Evariste Galois giving a detailed debunking. @haggismaths also suggested this as a story “much romanticised by Bell”, linking to the same article and also suggesting that “the section on Wikipedia about Galois’ death and final hours is not bad”. Thony Christie made the same suggestion and said the bebunking should be covered by Boyer, by which I guess he means A History of Mathematics.

Rob Eastaway suggested his blog post about the Golden Rectangle and Donald Duck.

@theoremoftheday suggested “something on how Nobel did NOT shun mathematicians cos one cuckolded him”, linking to Why is there no Nobel in mathematics?.

John Read suggested “whether Euclid was Greek, African or made up from a collective of people”, although without a debunking source.

So what did I go with? I had planned to give the students a page from E.T. Bell’s Men of Mathematics and a short article debunking it, as a reading exercise. Lacking a short debunking, I instead made a short lecture giving a typical story of Galois, quoting Bell:

he had spent the fleeting hours feverishly dashing off his scientific last will and testament, writing against time to glean a few of the great things in his teeming mind before the death which he foresaw could overtake him. Time after time he broke off to scribble in the margin ‘I have not time; I have not time,’ and passed on to the next frantically scrawled outline. What he wrote in those desperate last hours before the dawn will keep generations of mathematicians busy for hundreds of years.

Then I gave a brief debunking from Genius and Biographers: The Fictionalization of Evariste Galois, by Tony Rothman (1982) including:

It is unclear how far one can go in forgiving Bell. . . . I believe consciously or unconsciously Bell saw his opportunity to create a legend. The details which are absent in his account . . . are those details which lend a concreteness and a humanness to Galois’s life which a legend must not have. Unfortunately, if this was Bell’s intent, he succeeded.

I also included some discussion from Mathematical Myths by G.A. Miller (1938), who writes that some readers of Bell will think that errors of detail are unimportant, but that

there are others who will be very much annoyed by errors of detail, and whose interest in the book will be greatly diminished when they become convinced that they cannot assume that the author took a reasonable amount of care to avoid misleading remarks even when they are striking.

I also included the story of Archimedes leaping from the bathtub shouting ‘Eureka!’ in order to discuss the place of legends in folklore and the value this can have. For a discussion, I used Life on the Mathematical Frontier: Legendary Figures and Their Adventures by Roger Cooke, who writes:

What is valuable in the story is the picture of the sudden flash of inspiration that mathematicians sometimes experience. Whether true or not, this story will continue to be told because it amuses people and because it expresses some folklore concerning a legendary figure.

To encourage my students to consider such issues when writing their own work, I ended with a quote from Miller suggesting that

the reader should realize that he is in danger of contributing toward the spreading of mathematical myths when he quotes from these writings without verifying the accuracy of statements contained therein.

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