On Pythagorean Numbers
E712305
On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
All labels observed (3)
| Label | Occurrences |
|---|---|
| On Pythagorean Numbers canonical | 2 |
| Pythagorean number theory | 2 |
| On Pythagorean Numbers (Speusippus) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8143144 — 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: On Pythagorean Numbers Context triple: [Speusippus, notableWork, On Pythagorean Numbers]
-
A.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
-
B.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
-
C.
Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
-
D.
Legendre's three-square theorem
Legendre's three-square theorem is a result in number theory that characterizes exactly which positive integers can be expressed as the sum of three squares of integers.
-
E.
Pythagorean triples
Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, representing the side lengths of right-angled triangles.
- 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: On Pythagorean Numbers Target entity description: On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
-
A.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
-
B.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
-
C.
Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
-
D.
Legendre's three-square theorem
Legendre's three-square theorem is a result in number theory that characterizes exactly which positive integers can be expressed as the sum of three squares of integers.
-
E.
Pythagorean triples
Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, representing the side lengths of right-angled triangles.
- F. None of above. chosen
Statements (37)
| Predicate | Object |
|---|---|
| instanceOf |
ancient Greek treatise
ⓘ
lost work ⓘ philosophical work ⓘ |
| associatedWith |
Plato's Academy
ⓘ
linked to:
Academy of Athens
|
| author | Speusippus ⓘ |
| connectedTo | Speusippus' interest in mathematical ontology ⓘ |
| culture |
Ancient Greece
ⓘ
linked to:
Greek Antiquity
|
| era | 4th century BCE ⓘ |
| explores |
Pythagorean arithmetic doctrines
ⓘ
Pythagorean number symbolism ⓘ metaphysical significance of numbers ⓘ |
| extantStatus | survives only in fragments or reports ⓘ |
| focusesOn |
Pythagorean views on numerical harmony
ⓘ
doctrines linking numbers and reality ⓘ |
| genre |
doctrinal exposition
ⓘ
philosophical treatise ⓘ |
| hasTitleInEnglish | On Pythagorean Numbers ⓘ |
| hasTitleInGreek | Peri Pythagoreion Arithmon (approximate transliteration) ⓘ |
| historicalContext | early Academy period ⓘ |
| influencedBy |
Pythagoras
ⓘ
Pythagorean school ⓘ
linked to:
Pythagoreanism
|
| knownFrom |
later testimonia
ⓘ
secondary sources ⓘ |
| language | Ancient Greek ⓘ |
| philosophicalDiscipline |
ancient Greek philosophy
ⓘ
metaphysics ⓘ philosophy of number ⓘ |
| philosophicalSchool | Old Academy ⓘ |
| philosophicalTradition | Pythagoreanism ⓘ |
| region | Athens ⓘ |
| relatedTo | Platonic doctrine of forms and numbers ⓘ |
| status | lost ⓘ |
| subject |
Pythagorean numerical doctrines
ⓘ
number theory in Pythagorean philosophy ⓘ philosophy of mathematics ⓘ |
| workOf | Speusippus ⓘ |
| workType | prose ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
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: On Pythagorean Numbers Description of subject: On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: On Pythagorean Numbers
subject linked to:
On Nature
linked to: On Pythagorean Numbers
subject linked to:
On the Soul
linked to: On Pythagorean Numbers