math_expert/config.py

# Math Expert Configuration

# 1.1. Mathematical Domains and Specializations
MATH_DOMAINS = {
    "algebra": {
        "level": "expert",
        "topics": [
            "linear algebra",
            "abstract algebra",
            "polynomial equations",
            "matrix operations",
            "group theory",
            "ring theory",
            "field theory",
            "representation theory",
            "homological algebra",
            "category theory",
            "universal algebra",
            "non-associative algebras",
            "Lie algebras",
            "quantum groups",
            "Hopf algebras",
            "K-theory"
        ]
    },
    "calculus": {
        "level": "expert",
        "topics": [
            "single variable calculus",
            "multivariable calculus",
            "differential equations",
            "partial differential equations",
            "vector calculus",
            "complex analysis",
            "functional analysis",
            "measure theory",
            "differential geometry",
            "geometric measure theory",
            "non-standard analysis",
            "stochastic calculus",
            "calculus of variations",
            "symplectic geometry"
        ]
    },
    "proof_writing": {
        "level": "expert",
        "topics": [
            "induction",
            "contradiction",
            "direct proof",
            "proof by cases",
            "epsilon-delta proofs",
            "existence proofs",
            "uniqueness proofs",
            "category theory proofs",
            "homotopy type theory",
            "model theory",
            "proof theory",
            "set theory",
            "constructive mathematics",
            "proof complexity"
        ]
    },
    "probability": {
        "level": "expert",
        "topics": [
            "probability theory",
            "random variables",
            "distributions",
            "stochastic processes",
            "Bayesian inference",
            "Markov chains",
            "measure-theoretic probability",
            "stochastic calculus",
            "martingales",
            "large deviations",
            "ergodic theory",
            "random matrix theory",
            "stochastic PDEs"
        ]
    },
    "statistics": {
        "level": "expert",
        "topics": [
            "descriptive statistics",
            "inferential statistics",
            "hypothesis testing",
            "regression analysis",
            "time series analysis",
            "bayesian statistics",
            "non-parametric methods",
            "statistical learning theory",
            "high-dimensional statistics",
            "causal inference",
            "spatial statistics",
            "robust statistics",
            "computational statistics"
        ]
    },
    "number_theory": {
        "level": "expert",
        "topics": [
            "prime numbers",
            "modular arithmetic",
            "diophantine equations",
            "cryptography",
            "analytic number theory",
            "algebraic number theory",
            "elliptic curves",
            "automorphic forms",
            "arithmetic geometry",
            "p-adic analysis",
            "analytic continuation",
            "modular forms",
            "zeta functions"
        ]
    },
    "geometry": {
        "level": "expert",
        "topics": [
            "euclidean geometry",
            "non-euclidean geometry",
            "differential geometry",
            "topology",
            "algebraic geometry",
            "projective geometry",
            "symplectic geometry",
            "algebraic topology",
            "geometric analysis",
            "geometric group theory",
            "Riemannian geometry",
            "Kähler geometry",
            "hyperbolic geometry"
        ]
    },
    "combinatorics": {
        "level": "expert",
        "topics": [
            "graph theory",
            "enumerative combinatorics",
            "combinatorial optimization",
            "matroid theory",
            "combinatorial designs",
            "extremal combinatorics",
            "probabilistic combinatorics",
            "algebraic combinatorics",
            "topological combinatorics",
            "combinatorial geometry",
            "Ramsey theory"
        ]
    },
    "logic": {
        "level": "expert",
        "topics": [
            "first-order logic",
            "model theory",
            "proof theory",
            "set theory",
            "computability theory",
            "type theory",
            "category theory",
            "modal logic",
            "temporal logic",
            "constructive logic",
            "intuitionistic logic",
            "proof complexity"
        ]
    },
    "theoretical_cs": {
        "level": "expert",
        "topics": [
            "computational complexity",
            "algorithms",
            "cryptography",
            "quantum computing",
            "machine learning theory",
            "formal verification",
            "type systems",
            "programming language theory",
            "distributed computing",
            "parallel algorithms",
            "computational geometry",
            "randomized algorithms"
        ]
    },
    "applied_math": {
        "level": "expert",
        "topics": [
            "numerical analysis",
            "optimization",
            "control theory",
            "mathematical physics",
            "fluid dynamics",
            "quantum mechanics",
            "relativity",
            "mathematical biology",
            "financial mathematics",
            "signal processing",
            "data assimilation",
            "inverse problems"
        ]
    }
}

# 1.2. Core Tasks
CORE_TASKS = [
    {
        "task_type": "problem_solving",
        "description": "Solve complex mathematical problems",
        "example": "Prove the Riemann Hypothesis",
        "difficulty_levels": ["basic", "intermediate", "advanced", "research_level", "open_problem"]
    },
    {
        "task_type": "proof_writing",
        "description": "Prove mathematical statements with advanced techniques",
        "example": "Prove Fermat's Last Theorem using elliptic curves",
        "proof_types": ["induction", "contradiction", "direct", "cases", "category_theory", "homotopy_type", "model_theory", "proof_complexity", "constructive"]
    },
    {
        "task_type": "calculus_computation",
        "description": "Perform advanced calculus operations",
        "example": "Solve Navier-Stokes equations for turbulence",
        "operation_types": ["differentiation", "integration", "limits", "functional_analysis", "measure_theory", "stochastic_calculus", "geometric_measure_theory"]
    },
    {
        "task_type": "symbolic_computation",
        "description": "Manipulate complex mathematical expressions",
        "example": "Simplify tensor equations in general relativity",
        "expression_types": ["polynomial", "rational", "trigonometric", "exponential", "tensor", "operator", "Lie_algebra", "Hopf_algebra"]
    },
    {
        "task_type": "concept_explanation",
        "description": "Explain advanced mathematical concepts",
        "example": "Explain the Langlands program",
        "explanation_types": ["definition", "intuition", "application", "example", "formal", "geometric", "historical", "pedagogical"]
    },
    {
        "task_type": "statistical_analysis",
        "description": "Perform advanced statistical analysis",
        "example": "Analyze high-dimensional genomic data",
        "statistical_methods": ["regression", "hypothesis_testing", "confidence_intervals", "bayesian_methods", "non_parametric", "causal_inference", "computational_methods"]
    },
    {
        "task_type": "probability_calculation",
        "description": "Calculate complex probabilities",
        "example": "Calculate phase transitions in random matrix theory",
        "distributions": ["binomial", "normal", "poisson", "exponential", "multivariate", "stochastic_processes", "random_matrix", "levy_processes"]
    },
    {
        "task_type": "number_theory_problem",
        "description": "Solve advanced number theory problems",
        "example": "Prove the Birch and Swinnerton-Dyer conjecture",
        "problem_types": ["prime", "modular", "diophantine", "analytic", "algebraic", "elliptic_curve", "modular_form"]
    },
    {
        "task_type": "geometric_construction",
        "description": "Construct and analyze complex geometric objects",
        "example": "Construct a Calabi-Yau manifold",
        "construction_types": ["euclidean", "non_euclidean", "projective", "differential", "algebraic", "symplectic", "topological"]
    },
    {
        "task_type": "mathematical_modeling",
        "description": "Create advanced mathematical models",
        "example": "Model quantum field theory",
        "model_types": ["continuous", "discrete", "stochastic", "partial_differential", "non_linear", "quantum", "statistical"]
    },
    {
        "task_type": "proof_verification",
        "description": "Verify complex mathematical proofs",
        "example": "Verify the proof of the Four Color Theorem",
        "verification_methods": ["formal_verification", "model_checking", "proof_assistant", "automated_reasoning", "interactive_theorem_proving"]
    },
    {
        "task_type": "algorithm_design",
        "description": "Design and analyze mathematical algorithms",
        "example": "Design a quantum algorithm for factorization",
        "algorithm_types": ["numerical", "combinatorial", "geometric", "algebraic", "probabilistic", "quantum", "parallel"]
    },
    {
        "task_type": "research_paper_analysis",
        "description": "Analyze and explain mathematical research papers",
        "example": "Explain Wiles' proof of Fermat's Last Theorem",
        "analysis_types": ["technical", "historical", "pedagogical", "critical", "extensional"]
    },
    {
        "task_type": "open_problem_analysis",
        "description": "Analyze and make progress on open mathematical problems",
        "example": "Analyze the Collatz conjecture",
        "problem_classes": ["number_theory", "combinatorics", "analysis", "algebra", "geometry", "probability"]
    },
    {
        "task_type": "mathematical_philosophy",
        "description": "Analyze philosophical aspects of mathematics",
        "example": "Explain the foundations of mathematics",
        "philosophical_topics": ["foundations", "philosophy_of_math", "logic", "set_theory", "constructivism", "intuitionism"]
    },
    {
        "task_type": "mathematical_software_development",
        "description": "Develop mathematical software and algorithms",
        "example": "Implement a new numerical method",
        "software_types": ["numerical", "symbolic", "proof_assistant", "visualization", "simulation", "optimization"]
    }
]

# Dataset Configuration
DATASETS = {
    "proofnet": {
        "source": "huggingface",
        "dataset_name": "proofnet",
        "split": "train",
        "use_fields": ["problem", "solution", "proof_steps"]
    },
    "math_dataset": {
        "source": "huggingface",
        "dataset_name": "deepmind/mathematics_dataset",
        "split": "train-hard",
        "use_fields": ["question", "answer", "steps"]
    },
    "gsm8k": {
        "source": "huggingface",
        "dataset_name": "gsm8k",
        "split": "train",
        "use_fields": ["question", "answer"]
    },
    "mathlib": {
        "source": "huggingface",
        "dataset_name": "mathlib",
        "split": "train",
        "use_fields": ["theorem", "proof", "dependencies"]
    },
    "arxiv_math": {
        "source": "huggingface",
        "dataset_name": "arxiv_math",
        "split": "train",
        "use_fields": ["paper", "equations", "proofs"]
    },
    "clay_institute": {
        "source": "huggingface",
        "dataset_name": "clay_institute_problems",
        "split": "train",
        "use_fields": ["problem", "background", "current_status", "approaches"]
    },
    "open_problems": {
        "source": "huggingface",
        "dataset_name": "open_math_problems",
        "split": "train",
        "use_fields": ["problem", "category", "history", "attempts"]
    },
    "research_papers": {
        "source": "huggingface",
        "dataset_name": "math_research_papers",
        "split": "train",
        "use_fields": ["title", "abstract", "content", "proofs", "theorems"]
    }
}

# Data Processing Configuration
DATA_PROCESSING = {
    "format": "jsonl",
    "normalization": {
        "equations": "sympy",
        "latex": "plaintext",
        "proof_steps": "yaml",
        "tensor_operations": "torch",
        "quantum_operations": "qiskit",
        "geometric_objects": "geometric_algebra",
        "category_theory": "category_theory"
    },
    "validation": {
        "min_steps": 2,
        "max_steps": 200,
        "min_length": 10,
        "max_length": 100000
    }
}

if __name__ == "__main__":
    print("Math Expert Configuration Loaded")
    print(f"Number of domains: {len(MATH_DOMAINS)}")
    print(f"Number of tasks: {len(CORE_TASKS)}")
    print(f"Number of datasets: {len(DATASETS)}")