ABSTRACT We report the results of a study in which we asked 94 mathematicians to evaluate whether five arguments qualified as proofs. We found that mathematicians disagreed as to whether a visual argument and a computer-assisted argument qualified as proofs, but they viewed these proofs as atypical. The mathematicians were also aware that many other mathematicians might not share their judgment and viewed their own judgment as contextual. For typical proofs using standard inferential methods, there was a strong consensus amongst the mathematicians that these proofs were valid. An instructional consequence is that for the standard inferential methods covered in introductory proof courses, we should have the instructional goal that students appreciate why these inferential methods are valid. However, for controversial inferential methods such as visual inferences, students should understand why mathematicians have not reached a consensus on their validity.

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关于数学家对什么构成证明的分歧

摘要 我们报告了一项研究的结果，在该研究中，我们要求 94 位数学家评估五个论证是否有资格作为证明。我们发现数学家对于视觉论证和计算机辅助论证是否有资格作为证明存在分歧，但他们认为这些证明是非典型的。数学家们也意识到许多其他数学家可能不会分享他们的判断，并将他们自己的判断视为上下文。对于使用标准推理方法的典型证明，数学家们一致认为这些证明是有效的。一个教学结果是，对于介绍性证明课程中涵盖的标准推理方法，我们的教学目标应该是让学生理解为什么这些推理方法是有效的。然而，