mathematics
Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.
The formal science of quantity, structure, space and change, which proves results from axioms by logical deduction and is used throughout science and engineering.
What it is for: Reasoning precisely, modelling the world and computing.
It can be prove theorems; model and compute; teach and learn it; verify proofs, including by computer.
Distinguishing features
Truth by proof from axioms
Pure and applied branches
Conventions and notation vary
Results are cumulative and rarely overturned, unlike empirical science
What it looks like
Symbols, equations, proofs, diagrams and code.
How it is recognised
Notation and proofs
Field labels in the Mathematics Subject Classification
Applied fields such as mathematical programming
Related models
has part - objects of study
is used in - applications
is a kind of - discipline
is confused with - a small part
In practice
Families and kinds
algebra
analysis
geometry and topology
number theory
probability and statistics
discrete mathematics
applied mathematics and optimisation
Identifiers
MSC 2020 code two digits, letter, two digits Mathematics Subject Classification
Standards and regulation
ISO 80000-2 mathematical signs and symbols
Failure modes and hazards
Unstated assumptions
Errors in unverified proofs
Misapplied models
Also called
+136
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.mathematics
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Fields Branches.
The field locates a result.
Branch
MSC classification.
Branch
The branch.
- Which branch of mathematics is this? definition
- Which MSC code applies? provenance
Objects
What is studied.
Objects
Mathematical objects.
- Which objects does it concern? definition
- How are they defined? definition
Claims Theorems and conjectures.
Status of a claim is crucial.
Status
Proven or conjectured.
Status
Proof status.
- Is this result proven, and where? provenance
- Is it a conjecture? boundary
Assumptions
Axioms and hypotheses.
Assumptions
Assumptions required.
- Which assumptions does the result need? definition
- What fails without them? boundary
Applications Using mathematics.
Models are only as good as their fit.
Models
Mathematical models.
Model
The model used.
- Which mathematical model is used, and why? definition
- How well does it fit the data? measurement
Computation
Numerics.
Computation
Numerical methods.
- Which numerical methods are used? definition
- What are their error bounds? measurement
Learning Teaching mathematics.
Learning mathematics needs clear explanation.
Explanation
Clear reasoning.
Explanation
How to explain.
- How can this be explained step by step? action
- What misconceptions are common? boundary
Verification
Checking work.
Verification
How to check.
- How can the result be checked? action
- Should a proof assistant be used? definition
What the second pass must settle
- 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?