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<p>This article argues that the development from the Pythagorean theorem through the Chomsky hierarchy to modern artificial intelligence–-assisted programming follows a&#xa0;common principle: the persistent navigation along the boundary between formal decidability and human expressive power. Drawing on Fermat’s Last Theorem and the impossibility of integer solutions to aⁿ + bⁿ = cⁿ for <i>n</i> &gt; 2, the article examines the analogous impossibility of combining the full semantic flexibility of natural language with the provable correctness of formal systems. It traces how computer science has not overcome this boundary but has pragmatically circumnavigated it through a&#xa0;paradigm shift—from formal specification to statistical prompting—and discusses the resulting consequences for reliability and developer productivity.</p>

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Vom Pythagoras zum Prompt

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Burhan Dinler

摘要

This article argues that the development from the Pythagorean theorem through the Chomsky hierarchy to modern artificial intelligence–-assisted programming follows a common principle: the persistent navigation along the boundary between formal decidability and human expressive power. Drawing on Fermat’s Last Theorem and the impossibility of integer solutions to aⁿ + bⁿ = cⁿ for n > 2, the article examines the analogous impossibility of combining the full semantic flexibility of natural language with the provable correctness of formal systems. It traces how computer science has not overcome this boundary but has pragmatically circumnavigated it through a paradigm shift—from formal specification to statistical prompting—and discusses the resulting consequences for reliability and developer productivity.