Ramanujan’s lost notebook
E355440
Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
All labels observed (7)
How this entity was disambiguated
This entity first appeared as the object of triple T3410527 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ramanujan’s lost notebook Context triple: [Srinivasa Ramanujan, notableWork, Ramanujan’s lost notebook]
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A.
Ramanujan partition congruences
Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
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B.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
C.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
-
D.
Rogers–Ramanujan-type identities
Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
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E.
Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ramanujan’s lost notebook Target entity description: Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
-
A.
Ramanujan partition congruences
Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
-
B.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
C.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
-
D.
Rogers–Ramanujan-type identities
Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
-
E.
Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical manuscript
ⓘ
notebook ⓘ |
| associatedWith |
Bruce C. Berndt
ⓘ
George E. Andrews ⓘ
surface form:
George Andrews
Srinivasa Ramanujan ⓘ |
| author | Srinivasa Ramanujan ⓘ |
| cataloguedAs | part of the Ramanujan papers at Trinity College ⓘ |
| contains |
asymptotic expansions
ⓘ
continued fraction formulas ⓘ elliptic function formulas ⓘ mathematical formulas ⓘ mock theta functions ⓘ modular form related formulas ⓘ partition function formulas ⓘ q-series identities ⓘ theta function identities ⓘ unpublished results ⓘ |
| countryOfOrigin | India ⓘ |
| dateOfCreation | circa 1919–1920 ⓘ |
| discoveredAt | Trinity College, Cambridge NERFINISHED ⓘ |
| discoveredBy |
George E. Andrews
ⓘ
surface form:
George Andrews
|
| discoveryYear | 1976 ⓘ |
| editedBy |
Bruce C. Berndt
ⓘ
George E. Andrews ⓘ
surface form:
George Andrews
|
| field |
mathematics
ⓘ
number theory ⓘ q-series ⓘ |
| hasPublication |
Ramanujan’s lost notebook
self-linksurface differs
ⓘ
surface form:
Ramanujan’s Lost Notebook, Part I
Ramanujan’s lost notebook self-linksurface differs ⓘ
surface form:
Ramanujan’s Lost Notebook, Part II
Ramanujan’s lost notebook self-linksurface differs ⓘ
surface form:
Ramanujan’s Lost Notebook, Part III
Ramanujan’s lost notebook self-linksurface differs ⓘ
surface form:
Ramanujan’s Lost Notebook, Part IV
|
| influenced |
modern number theory
ⓘ
partition theory ⓘ research on q-series ⓘ theory of mock modular forms ⓘ |
| language | English ⓘ |
| notableFor |
advanced results decades ahead of their time
ⓘ
large number of unproved but correct formulas ⓘ systematic treatment of mock theta functions ⓘ |
| pageCountApproximate | over 100 pages ⓘ |
| physicalLocation |
Trinity College Library, Cambridge
ⓘ
surface form:
Wren Library, Trinity College, Cambridge
|
| posthumous | true ⓘ |
| relatedTo |
mock theta functions
ⓘ
surface form:
mock theta conjectures
|
| relatedWork |
Ramanujan’s lost notebook
self-linksurface differs
ⓘ
surface form:
Notebooks of Srinivasa Ramanujan
|
| timeGapBetweenCreationAndDiscovery | about 55 years ⓘ |
How these facts were elicited
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Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Ramanujan’s lost notebook Description of subject: Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Ramanujan’s notebooks
this entity surface form:
Ramanujan’s Lost Notebook, Part I
this entity surface form:
Ramanujan’s Lost Notebook, Part II
this entity surface form:
Ramanujan’s Lost Notebook, Part III
this entity surface form:
Ramanujan’s Lost Notebook, Part IV
this entity surface form:
Notebooks of Srinivasa Ramanujan