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Cantor's theorem, Woodin Cardinal, Sacks Forcing and Martin's Axiom are just some of well-known theorems and concepts of mathematics which have the name of those mathematicians who introduced these theorems and concepts for the first time. I think no reasonable mathematician calls his or her discovered theorem and concept using his or her own name at the first time. In fact after a while the mathematics community gives such names to theorems and concepts. Also there are many other new theorems and concepts which remain without any particular name.

Question: What are the main parameters which attach the name of a mathematician to his or her discovered theorem and concept? Any references in sociology of mathematics community about this phenomena is welcome.

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    This is only speculation, but I believe that a theorem gets the name of the discoverer (or rediscoverer) when a person cites them in their paper and chooses to do the honor of calling it "The theorem of Cantor" or "Cantor's Theorem". Then subsequent papers would refer to it in the same fashion until it has caught on enough that it falls into general knowledge. – Joel Jun 06 '14 at 13:55
  • @Alex: I can understand not hearing about the rest; but Cantor's theorem is fairly fundamental. It states that every set has a cardinality strictly less than its power set. – Asaf Karagila Jun 06 '14 at 13:57
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    The practice varies widely from field to field. At one extreme, some fields of mathematics attach proper names to concepts with abandon. At the other extreme, some fields of mathematics are very parsimonious with proper names, instead naming theorems with dry mathematical phrases. – Lee Mosher Jun 06 '14 at 13:57
  • @AsafKaragila: my background is mostly Statistics and Computer science and a lot of self-learning. I don't know that many people who are well-familiar with it. – Alex Jun 06 '14 at 13:59
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    "Well-known"?? But for Cantor's Theorem, which is known even to non-mathematicians, the other three seem to be rather very specialized , particular things in advanced set theory and logic – DonAntonio Jun 06 '14 at 13:59
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    @Alex, don't worry: they really are not, not even among professional mathematicians who don't work within those fields. – DonAntonio Jun 06 '14 at 14:00
  • @DonAntonio: The last comment of Alex was referring to Cantor's theorem (at least it replies to a comment referring only to Cantor's theorem). If you think that no one except set theorists know about Cantor's theorem then you're contradicting your previous comment. Or as we call it in the branch of logic and set theory, you "prove a Reinhardt cardinal" or "you're inconsistent" or so on. :-) – Asaf Karagila Jun 06 '14 at 14:03
  • @AsafKaragila, you surely missed the "But for Cantor's Theorem..." part of my message...a rather long and important part of it, if may I add. :) – DonAntonio Jun 06 '14 at 14:06
  • @DonAntonio: I was referring to your second comment in my reply. – Asaf Karagila Jun 06 '14 at 14:07
  • @AsafKaragila: I have no doubt it's a famous theorem, but I don't have a formal math education and I'm sure people in my area are only vaguely familiar with it at best. – Alex Jun 06 '14 at 14:08
  • Someone should probably edit the question because it seems to deal with more than just theorems. – Brad Jun 06 '14 at 14:12
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    @whoever edited the question to change "his" to "his or her": why not "his or her or its"? Why do you hate theorem-proving machines? You must be some kind of an -ist. – bof Jun 06 '14 at 14:14
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    See "Eponymy in Mathematical Nomenclature: What's in a Name and What Should Be" by Merwyn R. Henwood and Ivan Rival, for a forceful argument against the naming of mathematical concepts after persons, and in favor of descriptive names. – bof Jun 06 '14 at 14:22
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    Related: http://math.stackexchange.com/questions/671534/mathematicians-names-in-structures. – Martín-Blas Pérez Pinilla Jun 06 '14 at 14:29
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    In this talk V.I. Arnold affirms in French with Russian accent that mathematical theorems almost never get names of their inventors: http://www.irem.univ-paris-diderot.fr/videos/la_mathematique_experimentale/ – Alexey Jun 06 '14 at 14:34
  • It reminds me the Arnold's theorem, loosely translated as "Every theorem in mathematics that bears the name of a mathematician was neither formulated nor proven by that mathematician". – TZakrevskiy Jun 06 '14 at 14:35
  • @Alexey beat me 3 seconds to it! – TZakrevskiy Jun 06 '14 at 14:36

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