Docs  /  MathNN mathematical field catalog

MathNN mathematical field catalog

MathNN trains reinforcement-learning tutoring policies over synthetic curriculum environments (category = mathematics in RLCurriculumOrchestrator). Each field is a domain id math_* with a domain-specific action vocabulary mapped into smoke dynamics, plus a kernel backend for hybrid solve (algebra / calculus / ODE / PDE / …).

Master registry: _MathNNMathFields (MathNNMathFields.*) — complete list of fields, families, kernels, MathNN architecture hints, and RL modes.

How fields plug into MathNN

Layer Role
_MathNNMathFields Full catalog, hybrid kernel solve, feature encode, smoke-all / train-all
RLCurriculumOrchestrator DomainSpec Smoke envs under mathematics
MathNNAgentBridge Recommended architecture / RL mode per field
nn math train <id> MathNN DQN on that env (+ EnsureMathAgent)
nn math fields Catalog listing
nn math kernel <id> <problem> Local kernel hybrid solve
ThoughtDecisionTrees domain tree NL → math_* routing features

Safety model for every field: educational / research tutoring only. High-stakes fields (finance, actuarial, crypto math, biology) include non-advice disclaimers.

Field count

Run nn math fields for the live count. The registry targets ~90+ fields across eight families (school core → advanced special topics).

Families

Family Examples
school_core arithmetic … PDE
algebra_discrete linear algebra, abstract algebra, graphs, Lie
analysis_foundations real/complex/functional analysis, logic, set theory
geometry_topology topology, diff geom, algebraic geometry, tensors
probability_info stats, stochastic, information, coding, game theory
applied_computational numerical, optimization, control, FEM, Monte Carlo
cross_disciplinary math physics/finance/biology, actuarial, history
advanced_special HoTT, topos, tropical, p-adic, rough paths, OT, …

Commands

nn math fields
nn math fields analysis
nn math field topology
nn math field math_homological_algebra
nn math kernel linalg demo
nn math kernel pde heat
nn math kernel ode y'=-y
nn math features eigenvalues of a matrix
nn math smoke-all 2 24
nn math train-all 4 24
nn math integrate report

nn math domains
nn math domain pde
nn math smoke mathematics 4 48
nn math train math_optimization 200
nn math train linalg 150

Aliases: pde, linalg, ode, bayes, fem, hott, padic, chaos, …

Kernel backends

Kernel Engines
Algebra / arithmetic Algebra demos, calc probes
Linear algebra _AlgebraKernel sqrt/expm
Calculus / vector calc _CalcKernel derivative/quadrature
ODE _MathODECatalog
PDE _MathPDE heat/wave/poisson
Fourier / numerical / opt / probability demos + curriculum

Architecture hints (MathNNAgentBridge)

Domains Suggested arch Mode
Algebra / college algebra MoE dueling-dqn / dqn
Geometry / projective / fractals vision-CNN dqn
Calculus family / PDE / physics PINN / neural-ODE dqn
Graph theory / GGT GNN dqn
Optimization / OR / OT actor-critic actor-critic
Control world model actor-critic
Logic / analysis / abstract transformer dqn
Stochastic / finance / signals LSTM dqn

Implementation files

  • MathNNMathFields.hpp / .cpp — master field registry + hybrid solve
  • RLCurriculumOrchestrator.cpp — DomainSpec catalog + aliases + smoke envs
  • MathNNFeatures.cpp — nn math … surface
  • MathNNMathExtended.cpp — advanced tutor commands + aliases
  • MathNNAgentBridge.cpp — per-field architecture profiles
  • ThoughtDecisionTrees.cpp — domain routing features
  • docs/MathNN.md — overview

Lua

print(ai_math_fields_status())
print(ai_math_fields_count())
print(ai_math_field("math_topology"))
print(ai_math_hybrid("ode", "decay"))

Quick smoke

  1. nn math fields — full catalog
  2. nn math field pde — details + kernels
  3. nn math kernel pde demo — FD heat/Poisson
  4. nn math train math_algebra 50 — short DQN
  5. nn math smoke mathematics 2 24 — tabular smoke across curriculum math
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