With fast development of AI, it is becoming increasingly interested to learn how to use AI tools effective for research. The following is the response generated by DeepSeek to the question “How to Use AI to Effectively Read Articles and Books for Math Research”. Do you have any comments or suggestions on how to use AI for research? Please feel free to share.
How to Use AI to Effectively Read Articles and Books for Math Research
Clarify Definitions and Theorems
Request Explanations: Input complex definitions or theorems and ask for step-by-step breakdowns. Example:
“Explain the proof of Theorem X in simpler terms.”Contextualize Concepts: Ask for historical background or significance of theorems to understand their role in broader frameworks.
Deconstruct Proofs and Arguments
Step-by-Step Analysis: Copy-paste proofs (preferably in LaTeX) and request elaboration on unclear steps. Example:
“Why does Step 3 in this proof require Lemma Y?”Error Checking: Use AI to identify potential gaps or alternative approaches, but always verify conclusions manually.
Notation and Symbol Clarification
Symbol Interpretation: Input equations and ask for explanations of uncommon symbols. Example:
“What does the operator ⊗ denote in this context?”Cross-Notation Translation: Request conversions between notations (e.g., matrix vs. component form).
Summarization and Note-Taking
Section Summaries: Generate concise summaries of dense sections. Example:
“Summarize the key results of Section 2.3.”Highlight Key Points: Extract main theorems, definitions, and examples for quick reference.
Problem Solving and Exercises
Exercise Guidance: Input textbook problems and request hints or
“How would I approach Problem 5 in Chapter 4?”Example Generation: Ask for illustrative examples of abstract concepts. Example:
“Provide an example of a non-Euclidean metric.”Literature Review and Connections
Related Work Suggestions: Identify seminal papers or recent advancements. Example:
“What are key papers citing Theorem Z?”Interdisciplinary Links: Explore connections to other fields. Example:
“How is this algebraic structure used in topology?”LaTeX and Technical Inputs
Direct LaTeX Parsing: Input LaTeX equations for analysis, ensuring proper symbol interpretation.
Image-to-Text (if supported): Use image analysis for equations/text, though typed LaTeX is more reliable.
Workflow Integration
Structured Queries: Frame specific, focused questions to avoid vague responses. Example:
“Explain the intuition behind cohomology groups in this proof.”Time Management: Set session objectives (e.g., “Understand Section 3.2 today”) to maintain focus.
Verification and Critical Engagement
Cross-Reference Sources: Validate AI outputs against trusted textbooks or papers.
Active Engagement: Treat AI as a supplement, not a replacement, for deep reading and problem-solving.
Language and Translation
- Translate Explanatory Text: Use translation features (if available) for non-native language texts while preserving mathematical notation.
Example Workflow
Input Text: Copy a theorem and its proof from a paper into the tool.
Request Breakdown: “Explain the proof of Theorem A, focusing on how Lemma B is applied.”
Explore Connections: “How does this theorem relate to optimization algorithms?”
Summarize: “Provide a bullet-point summary of this section.”
Verify: Cross-check explanations with textbooks or peer-reviewed sources.