As a key medium for transferring knowledge across disciplines, mathematical symbols do not undergo a direct formal transfer when applied in computer science and physics. Rather than simple reuse, this process involves a structured transformation that includes adjustment of logical rules, extension of symbolic meaning, and alignment with disciplinary environments. Using two representative cases—formal verification in computer science and quantum modeling in theoretical physics—this study applies case analysis and comparative methods to identify three central challenges in the cross-disciplinary adaptation of mathematical symbols: logical conflicts, excessive semantic load, and context-related deviations. Based on these issues, a three-layer adaptation framework of “logical mapping - semantic layering - contextual anchoring” is established. The analysis shows that the limits of symbol adaptation are jointly influenced by the expressive capacity of symbols and the cognitive requirements of the target discipline. The findings indicate that set theory symbols must be integrated with temporal logic operators in concurrent program verification, while linear algebra symbols need to express probability amplitude in quantum state representation. These adaptation processes are restricted by the threshold of semantic density and the value-cost balance of disciplinary needs. The proposed framework is supported by step-by-step comparative analysis and quantitative heuristic boundaries rather than descriptive summarization, which enhances analytical rigor and reusability. The proposed mechanism offers methodological support for the appropriate use of mathematical symbols in interdisciplinary research and contributes to the development of mathematical semiotics and interdisciplinary integration theory.
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