리서치·학습 스킬

Approach abstract algebra problems involving groups, sets with an operation satisfying specific rules. Follow checks for group axioms, subgroups, structure-preserving maps, and element counts or orders, supported by proof and symbolic calculation commands.

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• Checking whether a set and operation form a group
• Proving that a subset is a subgroup
• Checking whether a map preserves group operations

Choose a mathematical approach for a problem you do not yet know how to model. Guided questions clarify change, uncertainty, optimization goals, and required precision, leading to a recommended framework, starting equations, tools, and related skills.

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• Choosing a mathematical approach for a real-world problem
• Deciding how to model discrete or continuous change
• Selecting methods for uncertainty or optimization

Review progress while solving a math problem by organizing previous attempts, checking intermediate results, and assessing growing complexity. The skill recommends whether to continue, adjust the approach, switch strategies, or tackle a smaller problem first.

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• Review an approach when stuck on a math problem
• Assess calculations that keep getting more complicated
• Check intermediate results

Work through operator theory problems in functional analysis with structured steps for boundedness, adjoints, spectra, and compactness. Includes example commands for symbolic calculations and proof checks using SymPy and Z3.

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• Check whether an operator is bounded
• Work out an adjoint operator
• Study the spectrum of a self-adjoint operator

Work through first-order ordinary differential equations by classifying their form and choosing a solution method. The skill also covers numerical initial-value problems, checking solutions against the equation and conditions, and examining equilibrium stability.

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• Choosing a method for a first-order differential equation
• Computing a numerical solution with initial values
• Checking a solution against the equation and conditions

Work through continuity problems in real analysis by checking function values and limits. The skill outlines separate checks for piecewise functions and provides commands for limit calculations with SymPy and proof checks with Z3.

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• Checking whether a function is continuous at a point
• Comparing left and right limits of piecewise functions
• Comparing a computed limit with the function value

Choose approaches for prime number problems, including primality testing, factorization, and prime distribution. The skill outlines relevant algorithms and theorems, with commands for symbolic calculation and checking mathematical claims.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Choosing a primality testing method
• Selecting a factorization approach
• Studying prime distribution and gaps

Work through information theory problems involving entropy, a measure of uncertainty. Provides formulas, properties, and calculation examples for discrete and continuous distributions, joint and conditional entropy, and choosing distributions through the maximum entropy principle.

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• Calculating Shannon entropy from a probability distribution
• Working through joint and conditional entropy problems
• Calculating differential entropy for continuous distributions

Choose numerical methods for approximating integrals based on the interval, function behavior, and number of dimensions. The skill guides SciPy calculations, error tolerance settings, and accuracy checks against known solutions or repeated calculations with tighter tolerances.

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• Choosing a method for a definite or improper integral
• Computing two- or three-dimensional integrals
• Checking accuracy by tightening error tolerances

Researches library documentation, implementation practices, and specific web pages using Nia, Perplexity, and Firecrawl through MCP tools. Produces a handoff document with findings, available code examples, recommendations, pitfalls, and source links for another agent.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Research library APIs before planning a feature
• Compare recommended implementation practices
• Collect content from a specific documentation page

Turn mathematical claims into Lean4 proofs, checked by a theorem prover. A five-phase workflow researches existing results, designs the proof, tests candidate lemmas, implements it, and reports remaining proof gaps and any custom axioms.

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• Formalizing a mathematical claim in Lean4
• Finding reusable results in Mathlib
• Testing candidate lemmas for counterexamples

Research library usage, recommended approaches, and general topics using external documentation and web sources. Choose a brief or thorough investigation, then organize examples, pitfalls, comparisons, and source links into a research document or implementation handoff.

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• Researching library APIs and usage examples
• Comparing tools and implementation approaches
• Compiling a topic report with source links

Use Perplexity to find web sources, get cited research summaries, explore complex decisions, or investigate a topic in depth. Separate modes support quick questions, ranked search results, combined answers, and comprehensive research.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Find recent sources on a topic
• Combine multiple sources into a cited answer
• Compare options for a complex decision

Use Pint to convert measurements, calculate with units, and check whether units describe compatible physical quantities. It also breaks quantities into values and units, simplifies compound units, and returns calculation results as JSON.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Converting measurements between unit systems
• Calculating with mixed units
• Checking the dimensional consistency of formulas

Turn math requests into specific command-line instructions using pattern-based routing. It covers calculus, equations, unit conversion, geometry, logical proofs, and plotting, returning a command for the agent to execute with the corresponding math script.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Turning integration or differentiation requests into commands
• Finding commands for unit conversion or compatibility checks
• Routing geometry calculations and plotting requests

Handle equations, calculus, matrices, unit conversions, and mathematical explanations through one entry point. The skill selects a suitable calculation tool or topic guide, including symbolic math tools that work directly with expressions.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Solve equations and calculate integrals
• Find matrix eigenvalues
• Convert between units

Retrieve web page content from a URL or search query through Firecrawl MCP. Export it as Markdown, HTML, or plain text, with support for extracting structured data from pages.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Collecting content from a specific web page
• Searching the web and retrieving page content
• Extracting structured data from web pages

Find the right tool for equations, calculus, numerical calculations, proof checks, or math practice. The guide connects tasks to commands for computing results, verifying steps, requesting hints, and plotting functions.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Solving equations and checking the answers
• Learning with practice problems and progressive hints
• Choosing tools for proofs and constraint problems

Investigate where or when a photo was taken using visible clues, metadata, reverse image search, maps, and image comparisons. Results include coordinates, an error radius, evidence images, and confidence levels that distinguish verified findings from uncertain candidates.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Investigating where a photo was taken
• Estimating capture time from sunlight and shadows
• Comparing location candidates against maps and street views

Search Wayback Machine archives for deleted GitHub files, issues, pull requests, and wiki pages. Recover available text and repository details from saved web pages to investigate a project's past state.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Recovering a deleted README or documentation
• Checking deleted issue and pull request discussions
• Reviewing a repository's past state

Prepares Claude Code or OpenAI Codex for in-depth research with hyperresearch, then hands the request to a structured workflow for research reports, literature reviews, and analysis using multiple sources with verified citations.

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• Preparing a research report with verified citations
• Reviewing literature on a specific topic
• Comparing evidence from multiple sources

Investigate firsthand sources before making a judgment or recommendation. Separate verified facts, reasoned inferences, and unknowns, document their sources, and produce a conclusion that explains the current situation, constraints, and remaining uncertainty.

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• Understand an unfamiliar codebase or system
• Gather evidence before making a decision
• Check when a proposed approach actually applies

Retrieve pages blocked by web access filters, read Chinese and social platforms through dedicated tools, and inspect archived copies with their dates. Escalate to browser interaction when simpler extraction methods cannot provide the needed content.

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• Read a page that returns a 403 error
• Retrieve posts from Chinese platforms
• Check dated archives of unavailable pages

Investigate a topic with cooperating agents assigned to distinct questions. Track sources, conflicting evidence, and unresolved claims, then assemble a cited deliverable with verification records and quality checks suited to the requested format.

한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.

• Investigating a topic from several perspectives
• Checking conflicting claims against their sources
• Comparing a specification with observed behavior