From the Eye of Horus to Grothendieck Primes: Math and Mythology

According to the Encyclopaedia Britannica, the Eye of Horus is a symbol of mythological significance, originating in a story in which the Egyptian gods Set and Horus clashed, and Set damaged or destroyed Horus’ eye. The eye was later restored by another of the gods (according to Wikipedia, most often Thoth, though the Encyclopaedia Britannica says Hathor); as a result, the Eye of Horus took on meanings of health and restoration.


In fact, the association with health may have been so strong that the image has been passed down to the modern day: according to some sources, the ¼, 1/64, and 1/32 segments of the eye can still be seen today in the Rx symbol, used to denote a medicine prescription.


Numerically, it is interesting to note that the fractions present in the eye represent the first six terms in the infinite series \sum 1/2^n. It doesn’t seem like a coincidence that this series sums to 1, given that the Eye of Horus symbolizes wholeness and restoration. This raises the question of whether or not Egyptian mathematicians had, if only in a rudimentary form, a notion of infinite series and convergence. 


One funny story I know of related to numbers is the story of the ‘Grothendieck Prime’, which I originally read in the Notices of the American Mathematical Association. In this story, the famous 20th century mathematician Alexandre Grothendieck is engaged in a mathematical conversation, and his interlocutor, lost in all of Grothendieck’s abstractions, asks him to explain what he’s talking about for the case of a concrete prime number. Surprised, Grothendieck replies “You mean an actual [prime] number? All right, take 57”. The humour here, of course, is that 57 is not prime; it’s 3 away from 60, and thus clearly divisible by 3. According to some of his contemporaries, this wasn’t merely a slip-up; Grothendieck though so abstractly about math that it was plausible that he genuinely did not realize that 57 wasn’t prime. Leaving aside the question of whether or not this is an example of myth-making and hagiography (“look at this brilliant and absent-minded mathematician with his lofty thoughts and abstractions!”) on the occasion of Grothendieck’s passing, I think this story is a humorous illustration of just how removed pure mathematics can be from the public perception of mathematics. 


Work Cited:


Eye of horus fraction. from Wolfram MathWorld. (n.d.). Retrieved October 10, 2022, from https://mathworld.wolfram.com/EyeofHorusFraction.html#:~:text=Each%20of%20the%20sacred%20unit,32%2C%20and%201%2F64. 

The eye of horus. The Eye of Horus ***. (n.d.). Retrieved October 10, 2022, from https://www.landofpyramids.org/eye-of-horus.htm 

Wikimedia Foundation. (2022, October 1). Osiris myth. Wikipedia. Retrieved October 10, 2022, from https://en.wikipedia.org/wiki/Osiris_myth 

Encyclopædia Britannica, inc. (n.d.). Eye of horus. Encyclopædia Britannica. Retrieved October 10, 2022, from https://www.britannica.com/topic/Eye-of-Horus 

Jackson, A. (n.d.). As If Summoned From the Void: The Life of Alexandre Grothendieck. Retrieved October 10, 2022, from https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf 



Comments

  1. Amanda FritzlanNovember 9, 2022 at 11:52 AM

    Ben, the connection of Rx and the Eye of Horus is interesting, and something that I had not come across. Thank you for sharing the story of the Grothendiek Prime. In a certain way, it relates to my own ideas about how any of the simplest mathematics can be thought about in complex abstract and philosophical terms.

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