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Moby-Dick (Mar 03 2026 at 09:09):According to John Tate, Moby-Dick was Alexandre Grothendieck’s favorite novel. Source (page 405): Alexandre Grothendieck 1928–2014, Part 2
Do you see any parallels between this literary taste and Grothendieck's contributions to mathematics?
Notification Bot (Mar 03 2026 at 09:47):This topic was moved here from #learning: questions > Moby Dick as a metaphor by Morgan Rogers (he/him).
Kevin Carlson (Mar 03 2026 at 19:17):Moby Dick and EGA are both very long.
Moby-Dick (Mar 04 2026 at 02:28):I learned about this from Fernando Zalamea's lectures. Here is an essay on the subject: Grothendieck and Moby-Dick
Moby-Dick (Mar 04 2026 at 06:33):According to this essay:
Yoneda’s Lemma (in fact, found simultaneously by Grothendieck in his Tôhoku) reveals a philosophy naturally in tune with Melville.
Indeed, when we start reading Moby-Dick (public domain), the whale is not described by its internal properties such as Moby-Dick is a huge white whale. That would be rather uninformative.
Melville describes this monster by its relations to humanity. The etymology of the word "whale" is presented in several languages and its use is exemplified in many famous texts from the Book of Genesis and Shakespeare to nineteenth-century maritime songs.
The problem is not that Melville is "boring." The problem is that the average human brain struggles to get all the information this author is transmitting. The same sensation occurs when reading Grothendieck.
Here is a reading of this chapter.
Moby-Dick (Mar 07 2026 at 20:06):According to Barry Mazur, Grothendieck was reading a volume entitled History of the Jews, and, according to John Tate, his favorite novel was Moby‑Dick. Do you see the natural transformation?
Think of a basic set of character archetypes (objects), like a King and an Outcast, and the power struggles that link them (morphisms). We can see these same types show up in two different worlds:
History of the Jews: The King is Ahab and the Outcast is Ishmael.
Moby-Dick: The King is a sea captain and the Outcast is a sailor.
The link between these two worlds is like a functor. When the narrator of Moby-Dick says "Call me Ishmael" (instead of "My name is Ishmael") he is acting as the "key" that turns the ancient Outcast (Ishmael) into a modern sailor (that we call Ishmael, maybe as a nickname).
For this translation to work perfectly, the pattern of the story has to stay the same. It doesn't matter which path you take: if you take the relationship (morphism) between the Bible's King and Outcast and move it to the modern day, it looks exactly like the relationship between the Captain and the Sailor in the book.
Melville didn't just borrow names; he copied the whole "skeleton" of the old Hebrew story and moved it into a new era without breaking any of the pieces.
It would be great if someone with more skills in category theory than I do could develop the exact formalism. It seems to me that Grothendieck was playing category-theoretic games with the books he was reading.
Reference about "types" and "archetypes" in Grothendieck: Fernando Zalamea - Talk at the homage to Alexander Grothendieck.
Morgan Rogers (he/him) (Mar 07 2026 at 23:16):Sounds pretty tenuous to me :man_shrugging: do you actually have evidence that Grothendieck made connections between these books himself? You can draw a line between two points, but two data points isn't usually enough to constitute a meaningful representation of reality.
Kevin Carlson (Mar 08 2026 at 00:13):There are also many kings in the Old Testament. Why should we pick Ahab? Just because that’s the name Melville chose?
Moby-Dick (Mar 08 2026 at 02:02):Kevin Carlson said:
There are also many kings in the Old Testament. Why should we pick Ahab? Just because that’s the name Melville chose?
We can pick any king from any narrative. Indeed, that is the point: the archetypes of King, Outcast, and Prophet are filled by the narrative of the Old Testament and by Moby-Dick, in which the characters preserve the same relationships as in the Old Testament.
Moby-Dick (Mar 08 2026 at 02:15):Morgan Rogers (he/him) said:
Sounds pretty tenuous to me :man_shrugging: do you actually have evidence that Grothendieck made connections between these books himself?
That is the question I am asking. I do not have evidence that Grothendieck connected these two books; I am only suggesting that they appear to be connected because of Melville’s choice of names and the preservation of relationships between those names. It seems likely that an expert in category theory, such as Grothendieck, could easily notice these similarities.
Kevin Carlson (Mar 08 2026 at 22:00):I do not think that kings Ahab and David and Solomon, say, can possibly said to all fulfill a single archetype of king in any sense that does the slightest justice to the literary structure.
Moby-Dick (Mar 08 2026 at 22:09):You are mentioning only the objects (kings), but what about the morphisms? There is a morphism from Elijah to Ahab in the Old Testament that is preserved in Moby-Dick between the characters having the same names. Here Elijah is of type prophet, Ahab is of type king, and the morphism is that Elijah confronts Ahab. Concerning the kings David and Solomon, such a confrontation with a prophet is absent, as far as I know.
Kevin Carlson (Mar 08 2026 at 22:45):Yes, well, that would not support your previous assertion that we could pick “any king.”
Moby-Dick (Mar 08 2026 at 23:06):You can pick any king to illustrate the archetype of King. But to tell a story about a King, you need to add other characters and relations between characters. For example:
Elijah:Prophet confronts Ahab:King
David:Prophet is the same as David:King