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  • $\begingroup$ The key point is that Computer Algebra Systems are not typically equipped with machinery to produce proofs. For example, mathematica can tell me that the sum of the first n integers is n*(n+1)/2, but it will not produce a proof of why this is the case. $\endgroup$
    – Agnishom Chattopadhyay
    Commented Feb 8, 2022 at 20:27
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    $\begingroup$ @AgnishomChattopadhyay Well, what is a proof? If the answer is "anything mathematicians accept as a proof" then CASs do form proofs. If the answer is "anything accepted by the trusted kernel" than they don't. $\endgroup$
    – Will Sawin
    Commented Feb 8, 2022 at 20:31
  • $\begingroup$ @WillSawin I wouldn't count a CAS doing a computation using an algorithm that is justified by a separate proof external to the CAS as the CAS "producing a proof". Is there some other sense in which you would say that they do? $\endgroup$
    – Mike Shulman
    Commented Feb 9, 2022 at 18:11
  • $\begingroup$ @MikeShulman I mean when someone writes in a paper Lemma 3.7 and in the proof it says "This was checked in Magma", that's a (informal) proof produced by a CAS. $\endgroup$
    – Will Sawin
    Commented Feb 9, 2022 at 18:19
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    $\begingroup$ @MikeShulman Sure - my point is just that saying "machinery to produce proofs" admits multiple interpretation depending on your view of what a proof is. I thought what I said in the body of my answer, talking about formal proofs, the formal system they're written in, the kernel that verifies them, and the rest of the proof assistant that helps you produce them, was more precise. $\endgroup$
    – Will Sawin
    Commented Feb 9, 2022 at 18:51