You say your intent is to teach and to inform. I don't doubt that this is the case. The reason why I found your response triggering is that you did not come of

You say your intent is to teach and to inform. I don't doubt that this is the case. The reason why I found your response triggering is that you did not come off, in this exchange, as genuinely having that intention, from the very beginning. To be completely frank it just looked as though you were looking for a fight. I recognized your username among the responses. I knew you had that kind of background and wanted to hear from you. I am not an expert nor I claim to be, mine are just fade memories, but as far as I know using "proof" to mean "derivation" is not uncommon, see for instance[1][2][3]. I was very particular about separating the "formal" and "informal" kind in any case. I don't think I can be accused of playing fast and loose with definitions. If you are trying to correct me on something else, I don't understand what it is. Since you brought up that point yet again, by "proofs just are", an unfortunate choice of words, I do not mean anything mystical or platonic. I never had any intention of making such claims and I certainly don't stand by anything like it. I wanted to say that derivations (I used the "proof-in-the-formal-sense" language to which you object, I am amending it here) are mathematical objects, proofs (meant as you do, informally) are social processes. I do not understand your response as saying anything different. As far as I understand, all you're objecting to is my use of language. This is perhaps fair, but not terribly interesting. If there's something else, I'm afraid I failed to understand what it is. In any case, thank you for this exchange. I would like to encourage you to keep sharing your knowledge if you can make the time. I am sure this common space would benefit from it. --- [1] https://www.ams.org/notices/200811/tx081101395p.pdf https://www.ams.org/notices/200811/tx081101395p.pdf [2] https://link.springer.com/referenceworkentry/10.1007/978-3-030-19071-2_35-1 https://link.springer.com/referenceworkentry/10.1007/978-3-0... [3] https://monks.scranton.edu/files/courses/Math299/math-299-lecture.pdf https://monks.scranton.edu/files/courses/Math299/math-299-le...