Can HCH epistemically dominate Ramanujan?

Srini­vasa Ra­manu­jan is an In­dian math­e­mat­i­cian who is fa­mously known for solv­ing math prob­lems with sud­den and in­ex­pli­ca­ble flashes of in­sight. From his Wikipe­dia page:

Imag­ine that you are on a street with houses marked 1 through n. There is a house in be­tween (x) such that the sum of the house num­bers to the left of it equals the sum of the house num­bers to its right. If n is be­tween 50 and 500, what are n and x?′ This is a bi­vari­ate prob­lem with mul­ti­ple solu­tions. Ra­manu­jan thought about it and gave the an­swer with a twist: He gave a con­tinued frac­tion. The un­usual part was that it was the solu­tion to the whole class of prob­lems. Ma­ha­lanobis was as­tounded and asked how he did it. ‘It is sim­ple. The minute I heard the prob­lem, I knew that the an­swer was a con­tinued frac­tion. Which con­tinued frac­tion, I asked my­self. Then the an­swer came to my mind’, Ra­manu­jan replied.“[60][61]


… Ra­manu­jan’s first In­dian bi­og­ra­phers de­scribe him as a rigor­ously or­tho­dox Hindu. He cred­ited his acu­men to his fam­ily god­dess, Na­m­a­giri Tha­yar (God­dess Ma­ha­lak­shmi) of Na­makkal. He looked to her for in­spira­tion in his work[12]:36 and said he dreamed of blood drops that sym­bol­ised her con­sort, Narasimha. After­ward he would re­ceive vi­sions of scrolls of com­plex math­e­mat­i­cal con­tent un­fold­ing be­fore his eyes.[12]:281 He of­ten said, “An equa­tion for me has no mean­ing un­less it rep­re­sents a thought of God.“[58]

His style of math­e­mat­i­cal rea­son­ing was com­pletely novel to the math­e­mat­i­ci­ans around him, and led to ground­break­ing re­search:

Dur­ing his short life, Ra­manu­jan in­de­pen­dently com­piled nearly 3,900 re­sults (mostly iden­tities and equa­tions).[4] Many were com­pletely novel; his origi­nal and highly un­con­ven­tional re­sults, such as the Ra­manu­jan prime, the Ra­manu­jan theta func­tion, par­ti­tion for­mu­lae and mock theta func­tions, have opened en­tire new ar­eas of work and in­spired a vast amount of fur­ther re­search.[5] Nearly all his claims have now been proven cor­rect.[6] The Ra­manu­jan Jour­nal, a peer-re­viewed sci­en­tific jour­nal, was es­tab­lished to pub­lish work in all ar­eas of math­e­mat­ics in­fluenced by Ra­manu­jan,[7]and his note­books—con­tain­ing sum­maries of his pub­lished and un­pub­lished re­sults—have been an­a­lyzed and stud­ied for decades since his death as a source of new math­e­mat­i­cal ideas. As late as 2011 and again in 2012, re­searchers con­tinued to dis­cover that mere com­ments in his writ­ings about “sim­ple prop­er­ties” and “similar out­puts” for cer­tain find­ings were them­selves profound and sub­tle num­ber the­ory re­sults that re­mained un­sus­pected un­til nearly a cen­tury af­ter his death.[8][9] He be­came one of the youngest Fel­lows of the Royal So­ciety and only the sec­ond In­dian mem­ber, and the first In­dian to be elected a Fel­low of Trinity Col­lege, Cam­bridge. Of his origi­nal let­ters, Hardy stated that a sin­gle look was enough to show they could only have been writ­ten by a math­e­mat­i­cian of the high­est cal­ibre, com­par­ing Ra­manu­jan to other math­e­mat­i­cal ge­niuses such as Euler and Ja­cobi.

If HCH is as­crip­tion uni­ver­sal, then it should be able to epistem­i­cally dom­i­nate an AI the­o­rem-prover that rea­sons similarly to how Ra­manu­jan rea­soned. But I don’t cur­rently have any in­tu­itions as to why ex­plicit ver­bal break­downs of rea­son­ing should be able to repli­cate the in­tu­itions that gen­er­ated Ra­manu­jan’s re­sults (or any style of rea­son­ing em­ployed by any math­e­mat­i­cian since Ra­manu­jan, for that mat­ter).

I do think ex­plicit ver­bal break­downs of rea­son­ing are ad­e­quate for ver­ify­ing the val­idity of Ra­manu­jan’s re­sults. At the very least, math­e­mat­i­ci­ans since Ra­manu­jan have been able to ver­ify a ma­jor­ity of his claims.

But, as far as I’m aware, there has not been a sin­gle math­e­mat­i­cian with Ra­manu­jan’s style of rea­son­ing since Ra­manu­jan him­self. This makes me skep­ti­cal that ex­plicit ver­bal break­downs of rea­son­ing would be able to repli­cate the in­tu­itions that gen­er­ated Ra­manu­jan’s re­sults, which I un­der­stand (per­haps er­ro­neously) to be a nec­es­sary pre­req­ui­site for HCH to be as­crip­tion uni­ver­sal.