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mathematics

vr.tr.mathematics · thing-q395

Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.

Thing Registry Information and virtual systems INF.KNW
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Fields Branches.

Branch

MSC classification.

Branch

The branch.

  1. Which branch of mathematics is this? definition
  2. Which MSC code applies? provenance

Objects

What is studied.

Objects

Mathematical objects.

  1. Which objects does it concern? definition
  2. How are they defined? definition
Claims Theorems and conjectures.

Status

Proven or conjectured.

Status

Proof status.

  1. Is this result proven, and where? provenance
  2. Is it a conjecture? boundary

Assumptions

Axioms and hypotheses.

Assumptions

Assumptions required.

  1. Which assumptions does the result need? definition
  2. What fails without them? boundary
Applications Using mathematics.

Models

Mathematical models.

Model

The model used.

  1. Which mathematical model is used, and why? definition
  2. How well does it fit the data? measurement

Computation

Numerics.

Computation

Numerical methods.

  1. Which numerical methods are used? definition
  2. What are their error bounds? measurement
Learning Teaching mathematics.

Explanation

Clear reasoning.

Explanation

How to explain.

  1. How can this be explained step by step? action
  2. What misconceptions are common? boundary

Verification

Checking work.

Verification

How to check.

  1. How can the result be checked? action
  2. Should a proof assistant be used? definition

Classifiers Filled

Family
Thing Registry
Category
Information and virtual systems
Entry kind
thing
Plane
INF
Domain
INF.KNW
Other names and narrower kinds
systems science, informal mathematics, mathematical geography, ecosystemology, gnomonics, combinatorial topology, mathematical programming, Māori mathematics, computational mathematics, calendrical mathematics, number theory, Mathematics-Economics

What it is Filled

The formal science of quantity, structure, space and change, which proves results from axioms by logical deduction and is used throughout science and engineering.

Why it exists Filled

Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.

Distinguishing features Filled

  • Truth by proof from axioms
  • Pure and applied branches
  • Conventions and notation vary
  • Results are cumulative and rarely overturned, unlike empirical science

What robots and AI may and may not do Filled

Must not

  • Present an unverified proof as established.
  • Hide assumptions behind results.
  • Apply a model outside its valid range without saying so.

Only with a human decision

  • Relying on a mathematical model in decisions about people's safety or rights.

May

  • Prove results or cite proofs, stating assumptions.
  • Check calculations and flag unverified steps.

Moral aspects Filled

  • Mathematical models used in decisions can encode bias behind a show of objectivity.

Who is affected

  • Users of models
  • Students

Owners Filled

Steward

Nobody owns mathematics; it is held in common.

Links to other meta-models Filled

parent

  • Q7991 - registry parent class

contains

  • integer, sequence, series - objects of study

related

  • science and engineering - applications
  • formal science - discipline
  • arithmetic - a small part

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.mathematics
  • Wikidata: Q395 (https://www.wikidata.org/wiki/Q395)
  • MSC 2020 code: two digits, letter, two digits Mathematics Subject Classification

Direct properties not applicable Not applicable

Not applicable

Plane INF: no invented physical properties.

Recognition optional Filled

  • Notation and proofs
  • Field labels in the Mathematics Subject Classification
  • Applied fields such as mathematical programming
  • Symbols, equations, proofs, diagrams and code.

Capabilities and actions required Filled

  • prove theorems
  • model and compute
  • teach and learn it
  • verify proofs, including by computer

Hazards and failure modes required Filled

  • Unstated assumptions
  • Errors in unverified proofs
  • Misapplied models

Standards and interfaces required Filled

  • ISO 80000-2 mathematical signs and symbols

Context of use required Filled

  • Reasoning precisely, modelling the world and computing.
  • algebra
  • analysis
  • geometry and topology
  • number theory
  • probability and statistics
  • discrete mathematics
  • applied mathematics and optimisation

Sources Filled

  1. Wikidata item Q395: mathematics - identity and sense of the item
  2. Wikipedia: Mathematics - general description of the item

Open questions

  • Should fields be separate entries by MSC?
  • How should agents distinguish proven results from conjectures?
  • The registry entry has merged aliases such as ecosystemology; should they be split off?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q395/spec.json