I'm getting old and forgetful.

Everyone here knows the difference between theorem, corollary, lemma, proposition, conjecture, axiom, and postulate.

I once heard another one, a Latin term, that IIRC meant something like "illustrative example." The only example I ever found of it being used was from Euler.

It may be rare, but I like having a complete list. Can someone help me out and remind me what this mathematical term is?

  • $\begingroup$ "Everyone here knows the difference between theorem, corollary, lemma and proposition" - I certainly don't, except in a very vague touchy-feely way. "Conjecture" is quite clear. I have never understood the ancient Greek distinction between axiom and postulate. And pace you and GEdgar a scholium is a comment not an example. $\endgroup$
    – Rob Arthan
    Mar 12 at 0:27
  • $\begingroup$ In legal and other settings, it can be a comment. I don’t believe that is how Newton and Euler used it. $\endgroup$ Mar 12 at 23:05
  • $\begingroup$ And the fact that you recognize that it is difficult to distinguish, from the entire list, postulate vs axiom tells me that you understand what the words mean. I don’t understand how it would be touchy-feely. $\endgroup$ Mar 12 at 23:13
  • $\begingroup$ I know what postulate and axiom mean, but I have never understood what the ancient Greek distinction between (the words that we translate as) postulate and axiom was (this could well be due to lack of diligence on my part). The differences between theorem, lemma and proposition as currently used are undoubtedly touchy-feely - how do some excellent authors get away without ever calling a result a proposition, for example? So you really can't claim that "everyone here knows the distinction between ...". $\endgroup$
    – Rob Arthan
    Mar 12 at 23:21
  • $\begingroup$ I can, because the statement was not made as a formal predicate. Although I can also understand why there would be many people here who view it that way... $\endgroup$ Mar 12 at 23:50

Here is one, which I like:

scholium NOUN (pl. scholia)
Pronunciation /ˈskəʊlɪəm/
A marginal note or explanatory comment made by a scholiast.
‘They fall into two categories: the first, a group of ten plays which have been transmitted to us in our medieval manuscripts complete with the accumulation of ancient notes and comments that we call scholia.’
Mid 16th century modern Latin, from Greek skholion, from skholē ‘learned discussion’.

  • $\begingroup$ That's it! Thanks! It seems Newton used them too... $\endgroup$ Mar 11 at 16:11
  • 2
    $\begingroup$ I had a very old prof, of some renown, whose every second word seemed to be an expletive, some of which were sadly unknown to me. So naturally, when he used 'scholium,' my hopes had been high... $\endgroup$
    – peter a g
    Mar 11 at 16:15
  • $\begingroup$ @peterag: how does "scholium" qualify as an expletive? Can you please tell us more of your old professor's expletives? $\endgroup$
    – Rob Arthan
    Mar 12 at 0:22
  • $\begingroup$ @RobArthan it does not qualify as an expletive, of course..., but he exclaimed the word, before writing it down on the board, so it could have been. And, no, I will NOT share any of his characteristic idioms - for, old as I thought he was at the time [he did look old], he seems still to be v. much among the living. $\endgroup$
    – peter a g
    Mar 12 at 1:43
  • $\begingroup$ @RobArthan and I did say 'some' expletives were unknown to me. My grasp of Anglo-Saxon was sufficient for most... e.g., as in, "let's prove this f-er." $\endgroup$
    – peter a g
    Mar 12 at 1:47

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