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| # app.py – Now includes DuckDuckGo, arXiv, and Semantic Scholar crawling | |
| from sentence_transformers import SentenceTransformer | |
| from sklearn.metrics.pairwise import cosine_similarity | |
| import gradio as gr | |
| import arxiv | |
| from semanticscholar import SemanticScholar | |
| from duckduckgo_search import DDGS | |
| # Load sentence transformer | |
| model = SentenceTransformer('all-MiniLM-L6-v2') | |
| # Math domain definitions (trimmed for brevity) | |
| DOMAINS = { | |
| "Real Analysis": "Studies properties of real-valued functions, sequences, limits, continuity, differentiation, Riemann/ Lebesgue integration, and convergence in the real number system.", | |
| "Complex Analysis": "Explores analytic functions of complex variables, contour integration, conformal mappings, and singularity theory.", | |
| "Functional Analysis": "Deals with infinite-dimensional vector spaces, Banach and Hilbert spaces, linear operators, duality, and spectral theory in the context of functional spaces.", | |
| "Measure Theory": "Studies sigma-algebras, measures, measurable functions, and integrals, forming the foundation for modern probability and real analysis.", | |
| "Fourier and Harmonic Analysis": "Analyzes functions via decompositions into sines, cosines, or general orthogonal bases, often involving Fourier series, Fourier transforms, and convolution techniques.", | |
| "Calculus of Variations": "Optimizes functionals over infinite-dimensional spaces, leading to Euler-Lagrange equations and applications in physics and control theory.", | |
| "Metric Geometry": "Explores geometric properties of metric spaces and the behavior of functions and sequences under various notions of distance.", | |
| "Ordinary Differential Equations (ODEs)": "Involves differential equations with functions of a single variable, their qualitative behavior, existence, uniqueness, and methods of solving them.", | |
| "Partial Differential Equations (PDEs)": "Deals with multivariable functions involving partial derivatives, including wave, heat, and Laplace equations.", | |
| "Dynamical Systems": "Studies evolution of systems over time using discrete or continuous-time equations, stability theory, phase portraits, and attractors.", | |
| "Linear Algebra": "Focuses on vector spaces, linear transformations, eigenvalues, diagonalization, and matrices.", | |
| "Abstract Algebra": "General study of algebraic structures such as groups, rings, fields, and modules.", | |
| "Group Theory": "Investigates algebraic structures with a single binary operation satisfying group axioms, including symmetry groups and applications.", | |
| "Ring and Module Theory": "Extends group theory to rings (two operations) and modules (generalized vector spaces).", | |
| "Field Theory": "Studies field extensions, algebraic and transcendental elements, and classical constructions.", | |
| "Galois Theory": "Connects field theory and group theory to solve polynomial equations and understand solvability.", | |
| "Algebraic Number Theory": "Applies tools from abstract algebra to study integers, Diophantine equations, and number fields.", | |
| "Representation Theory": "Studies abstract algebraic structures by representing their elements as linear transformations of vector spaces.", | |
| "Algebraic Geometry": "Examines solutions to polynomial equations using geometric and algebraic techniques like varieties, schemes, and morphisms.", | |
| "Differential Geometry": "Studies geometric structures on smooth manifolds, curvature, geodesics, and applications in general relativity.", | |
| "Topology": "Analyzes qualitative spatial properties preserved under continuous deformations, including homeomorphism, compactness, and connectedness.", | |
| "Geometric Topology": "Explores topological manifolds and their classification, knot theory, and low-dimensional topology.", | |
| "Symplectic Geometry": "Studies geometry arising from Hamiltonian systems and phase space, central to classical mechanics.", | |
| "Combinatorics": "Covers enumeration, existence, construction, and optimization of discrete structures.", | |
| "Graph Theory": "Deals with the study of graphs, networks, trees, connectivity, and coloring problems.", | |
| "Discrete Geometry": "Focuses on geometric objects and combinatorial properties in finite settings, such as polytopes and tilings.", | |
| "Set Theory": "Studies sets, cardinality, ordinals, ZFC axioms, and independence results.", | |
| "Mathematical Logic": "Includes propositional logic, predicate logic, proof theory, model theory, and recursion theory.", | |
| "Category Theory": "Provides a high-level, structural framework to relate different mathematical systems through morphisms and objects.", | |
| "Probability Theory": "Mathematical foundation for randomness, including random variables, distributions, expectation, and stochastic processes.", | |
| "Mathematical Statistics": "Theory behind estimation, hypothesis testing, confidence intervals, and likelihood inference.", | |
| "Stochastic Processes": "Studies processes that evolve with randomness over time, like Markov chains and Brownian motion.", | |
| "Information Theory": "Analyzes data transmission, entropy, coding theory, and information content in probabilistic settings.", | |
| "Numerical Analysis": "Designs and analyzes algorithms to approximate solutions of mathematical problems including root-finding, integration, and differential equations.", | |
| "Optimization": "Studies finding best outcomes under constraints, including convex optimization, linear programming, and integer programming.", | |
| "Operations Research": "Applies optimization, simulation, and probabilistic modeling to decision-making problems in logistics, finance, and industry.", | |
| "Control Theory": "Mathematically models and regulates dynamic systems through feedback and optimal control strategies.", | |
| "Computational Mathematics": "Applies algorithmic and numerical techniques to solve mathematical problems on computers.", | |
| "Game Theory": "Analyzes strategic interaction among rational agents using payoff matrices and equilibrium concepts.", | |
| "Machine Learning Theory": "Explores the mathematical foundation of algorithms that learn from data, covering generalization, VC dimension, and convergence.", | |
| "Spectral Theory": "Studies the spectrum (eigenvalues) of linear operators, primarily in Hilbert/Banach spaces, relevant to quantum mechanics and PDEs.", | |
| "Operator Theory": "Focuses on properties of linear operators on function spaces and their classification.", | |
| "Mathematical Physics": "Uses advanced mathematical tools to solve and model problems in physics, often involving differential geometry and functional analysis.", | |
| "Financial Mathematics": "Applies stochastic calculus and optimization to problems in pricing, risk, and investment.", | |
| "Mathematics Education": "Focuses on teaching methods, learning theories, and curriculum design in mathematics.", | |
| "History of Mathematics": "Studies the historical development of mathematical concepts, theorems, and personalities.", | |
| "Others / Multidisciplinary": "Covers problems that span multiple mathematical areas or do not fall neatly into a traditional domain." | |
| } | |
| domain_names = list(DOMAINS.keys()) | |
| domain_texts = list(DOMAINS.values()) | |
| domain_embeddings = model.encode(domain_texts) | |
| def fetch_arxiv_refs(query, max_results=3): | |
| refs = [] | |
| try: | |
| search = arxiv.Search(query=query, max_results=max_results) | |
| for r in search.results(): | |
| refs.append({ | |
| "title": r.title, | |
| "authors": ", ".join(a.name for a in r.authors[:3]), | |
| "year": r.published.year, | |
| "url": r.entry_id, | |
| "source": "arXiv" | |
| }) | |
| except: | |
| pass | |
| return refs | |
| def fetch_duckduckgo_links(query, max_results=3): | |
| links = [] | |
| try: | |
| with DDGS() as ddgs: | |
| results = ddgs.text(query, max_results=max_results) | |
| for res in results: | |
| links.append({ | |
| "title": res['title'], | |
| "url": res['href'], | |
| "snippet": res['body'], | |
| "source": "DuckDuckGo" | |
| }) | |
| except: | |
| pass | |
| return links | |
| def classify_math_question(question): | |
| q_embed = model.encode([question]) | |
| scores = cosine_similarity(q_embed, domain_embeddings)[0] | |
| sorted_indices = scores.argsort()[::-1] | |
| major = domain_names[sorted_indices[0]] | |
| minor = domain_names[sorted_indices[1]] | |
| major_reason = DOMAINS[major] | |
| minor_reason = DOMAINS[minor] | |
| out = f"<b>Major Domain:</b> {major}<br><i>Reason:</i> {major_reason}<br><br>" | |
| out += f"<b>Minor Domain:</b> {minor}<br><i>Reason:</i> {minor_reason}<br><br>" | |
| refs = fetch_arxiv_refs(question, max_results=3) | |
| links = fetch_duckduckgo_links(question, max_results=3) | |
| if refs: | |
| out += "<b>Top Academic References (arXiv):</b><ul>" | |
| for p in refs: | |
| out += f"<li><b>{p['title']}</b> ({p['year']}) - <i>{p['authors']}</i><br><a href='{p['url']}' target='_blank'>{p['url']}</a></li>" | |
| out += "</ul>" | |
| else: | |
| out += "<i>No academic references found.</i><br>" | |
| if links: | |
| out += "<b>Top Web Resources (DuckDuckGo):</b><ul>" | |
| for link in links: | |
| out += f"<li><b>{link['title']}</b><br>{link['snippet']}<br><a href='{link['url']}' target='_blank'>{link['url']}</a></li>" | |
| out += "</ul>" | |
| else: | |
| out += "<i>No web links found.</i>" | |
| return out | |
| iface = gr.Interface( | |
| fn=classify_math_question, | |
| inputs=gr.Textbox(lines=5, label="Enter Math Question (LaTeX supported)"), | |
| outputs=gr.HTML(label="Predicted Domains + References"), | |
| title="⚡ Fast Math Domain Classifier with arXiv + DuckDuckGo", | |
| description="Classifies math problems into major/minor domains and fetches fast references from arXiv + DuckDuckGo." | |
| ) | |
| iface.launch() |