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<p>By applying interpretable machine learning methods such as decision trees, we study how simple models can classify the Galois groups of <i>Galois extensions</i> over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation> of degrees <i>4, 6, 8, 9, and 10</i>, using Dedekind zeta coefficients. Our interpretation of the machine learning results allows us to understand how the distribution of zeta coefficients depends on the Galois group, and to prove new criteria for classifying the Galois groups of these extensions. Combined with previous results, this work provides another example of a new paradigm in mathematical research driven by machine learning.</p>

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Machines learn number fields, but how? The case of Galois groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Kyu-Hwan Lee,
  • Seewoo Lee

摘要

By applying interpretable machine learning methods such as decision trees, we study how simple models can classify the Galois groups of Galois extensions over \(\mathbb {Q}\) Q of degrees 4, 6, 8, 9, and 10, using Dedekind zeta coefficients. Our interpretation of the machine learning results allows us to understand how the distribution of zeta coefficients depends on the Galois group, and to prove new criteria for classifying the Galois groups of these extensions. Combined with previous results, this work provides another example of a new paradigm in mathematical research driven by machine learning.