Mathematical Tacit Knowledge

A Mathematical Tacit Knowledge is a tacit knowledge that enables mathematical practitioners to sense whether a mathematical approach is promising or implausible through mathematical intuitive judgment.

• AKA: Mathematical Intuition, Mathematical Heuristic Sense, Mathematical Tacit Judgment.
• Context:
  • It can typically guide Mathematical Problem Solving through mathematical intuitive assessments of mathematical proof strategys.
  • It can typically develop through Mathematical Graduate Training and mathematical research experience.
  • It can typically detect Mathematical Implausible Approaches before mathematical formal verification.
  • It can typically distinguish Mathematical Promising Directions from mathematical dead ends in mathematical exploration.
  • It can typically recognize Mathematical Pattern Similarity across mathematical domain boundarys.
  • ...
  • It can often identify Mathematical Circular Reasoning in mathematical argument structures.
  • It can often sense Mathematical Overcomplication in mathematical proof attempts.
  • It can often detect Mathematical Missing Assumptions in mathematical theorem statements.
  • It can often recognize Mathematical Fruitful Analogys between mathematical concepts.
  • It can often anticipate Mathematical Proof Difficulty from mathematical problem structure.
  • ...
  • It can range from being a Weak Mathematical Smell to being a Strong Mathematical Smell, depending on its mathematical practitioner experience.
  • It can range from being a Domain-Specific Mathematical Smell to being a General Mathematical Smell, depending on its mathematical applicability scope.
  • It can range from being a Novice Mathematical Smell to being an Expert Mathematical Smell, depending on its mathematical sophistication level.
  • ...
  • It can inform Mathematical Research Direction through mathematical feasibility assessment.
  • It can influence Mathematical Collaboration Choice via mathematical compatibility recognition.
  • It can shape Mathematical Writing Style through mathematical clarity intuition.
  • It can guide Mathematical Tool Selection based on mathematical problem characteristics.
  • It can affect Mathematical Time Allocation through mathematical difficulty estimation.
  • ...
• Examples:
  • Mathematical Proof Smell Instances, such as:
    • Mathematical Contradiction Smell, detecting when mathematical assumptions lead toward mathematical inconsistency.
    • Mathematical Complexity Smell, sensing when mathematical approaches become unnecessarily convoluted.
    • Mathematical Generalization Smell, recognizing when mathematical specific results suggest mathematical broader principles.
    • ...
  • Mathematical Problem Smell Instances, such as:
    • Mathematical Tractability Smell, assessing whether mathematical problems admit mathematical feasible solutions.
    • Mathematical Structure Smell, identifying hidden mathematical symmetrys or mathematical patterns.
    • Mathematical Connection Smell, sensing relationships to mathematical known results.
    • ...
  • Mathematical Development Contexts, such as:
    • Mathematical PhD Training Smell Development, acquiring mathematical smell through mathematical advisor guidance.
    • Mathematical Seminar Smell Refinement, developing mathematical smell via mathematical peer discussion.
    • Mathematical Review Process Smell Enhancement, strengthening mathematical smell through mathematical manuscript evaluation.
    • ...
  • ...
• Counter-Examples:
  • Mathematical Formal Verification, which uses mathematical rigorous proofs rather than mathematical intuitive assessments.
  • Mathematical Algorithmic Decision, which follows mathematical deterministic rules rather than mathematical tacit heuristics.
  • Mathematical Brute Force Search, which exhaustively tries mathematical approaches rather than using mathematical intuitive guidance.
  • Mathematical Mechanical Calculation, which performs mathematical computations without mathematical conceptual judgment.
  • Mathematical Random Exploration, which selects mathematical directions without mathematical informed intuition.
• See: Tacit Knowledge, Mathematical Heuristic, Mathematical Intuition, Mathematical Experience, Expert Knowledge, Pattern Recognition.

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