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<p>Algorithms play increasingly important roles in mathematics as they facilitate solving complex problems both in teaching and research contexts. Moreover, algorithms, proofs, and definitions all play important roles in mathematics as products of research and objects worthy of study in the classroom. Nevertheless, limited research has examined mathematicians’ views of algorithms, the broader goals of the mathematical community that relate to algorithms, or mathematicians’ views across algorithms, proofs, and definitions and the&#xa0;related activities. Based on interviews with nine mathematicians who work with algorithms, we highlight three values upheld by a variety of norms related to algorithms as well as similarities and differences between the values associated with these mathematical activities and relative importance placed on the varied activities. Notably, values centered on mathematical objects tended to be in tension with values centered on activities. Moreover, the relative importance of different activities, especially algorithmatizing and proving, appeared to be in tension based on participants’ conceptual emphasis on different aspects of mathematics.</p>

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Mathematicians’ values and norms related to algorithms, definitions, and proofs: How do they interrelate?

  • 期刊论文

  • 发表日期：

    2026年3月21日

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  • Rachel Rupnow,
  • Peter Sassman,
  • Alastair Fletcher

摘要

Algorithms play increasingly important roles in mathematics as they facilitate solving complex problems both in teaching and research contexts. Moreover, algorithms, proofs, and definitions all play important roles in mathematics as products of research and objects worthy of study in the classroom. Nevertheless, limited research has examined mathematicians’ views of algorithms, the broader goals of the mathematical community that relate to algorithms, or mathematicians’ views across algorithms, proofs, and definitions and the related activities. Based on interviews with nine mathematicians who work with algorithms, we highlight three values upheld by a variety of norms related to algorithms as well as similarities and differences between the values associated with these mathematical activities and relative importance placed on the varied activities. Notably, values centered on mathematical objects tended to be in tension with values centered on activities. Moreover, the relative importance of different activities, especially algorithmatizing and proving, appeared to be in tension based on participants’ conceptual emphasis on different aspects of mathematics.