Theorems are often named after who proved it.
The ones who conjectured it are often forgotten.

Mordell's conjecture was solved by Falting.
It is now called
Faltings' Theorem.

Vazsonyi's conjecture was solved by Joseph Kruskal.
It is now called
The Kruskal Tree Theorem.

Baudet's conjecture was solved by van der Waerden.
It is now called
van der Waerden's theorem .
Even though van der Waerden's original paper has as its title
(roughly translated) On a conjecture of Baudet, Baudet is
not well known.

Fermat's last theorem was solved by Wiles.
If you type Wiles into Wikipedia you get as options
Wiles Theorem which goes to a page whose web address is
http://en.wikipedia.org/wiki/Wiles_theorem
but whose title on the page is
Fermat's Last Theorem.
This one may still be in transition from being someones conjecture
to someones theorem. It may be for a while. This one is so
tied to Fermat that it might always have his name on it somehow.
If you know of other examples please comment.
Is it unfair that the original conjecturers are forgotten?
Alexander Soifer thinks so.
In his book
The Mathematical Coloring Book: Mathematics of Coloring and the Colorful
Life of its Creators
(reviewed in my latest
SIGACT NEWS
Book Review Column) he
suggests that we should name a theorem after
both
who conjectures it
and who solves it.
So what I call
Van der Waerden's Theorem
Soifer calls
The BaudetSchurVan der Waerden Theorem.
(Baudet is known to have conjectured it.
Soifer argues convincingly that Schur also conjectured it.)
Reading over van der Waerden's own account of how
the theorem was discovered
(included in Soifer's book) it seems to me that Artin contributed
some to the solution of Baudet's conjecture. If standards for coauthorship
were weaker then
he may have been a coauthor.
In this alternative universe
what I would call
The ArtinVan der Waerden Theorem
Soifer would call
The ArtinBaudetSchurVan der Waerden Theorem.
This is odd since you have proverconjecturerconjecturerprover
in the ordering. Perhaps another convention would arise.
Perhaps it would be called the ABSVtheorem or ABSWtheorem.
Perhaps we are better off, just for the sake of simplicity,
using just the prover's name. There have been some fierce
battles over who PROVED what. Do we really want to have
fierce battles over who CONJECTURED what? I conjecture
that we do not.
Too late, there already have been fierce battles over who conjectured what when. For example how a Weil conjecture became the TaniyamaWeil conjecture and then either the TaniyamaShimura or the TaniyamaShimuraWeil conjecture depending on who is writing.
ReplyDeleteSerge Lang tells the story (from an antiWeil position) here
Wow, Serge Lang comes off as a complete nutjob.
ReplyDeleteI wouldn't say that the conjectures were solved, I'd say they were proven.
ReplyDeleteIt seems like naming the conjecturer is even worse, because it's quite likely that some obscure paper conjectures a given result. It seems the name should be awarded not only for stating the conjecture, but also realizing its importance (e.g. Riemann).
ReplyDeleteAlso, in some situations, the conjecturer's name does stay attached to the theorem. Mordell's conjecture is still referred to by name, as are the Bieberbach conjecture and the Weil conjectures. Mertens conjecture is false and is still usually referred to by that name. Other things, like the Kepler and Poincare conjectures, may be too recent to have name changes yet.
I conjecture that being famous for other results, as well as having your conjecture open for a long time, will help your name stay. As such, I think the Riemann Hypothesis will keep its name.
The Poincare Conjecture might not be too recent to provide evidence. The Poincare Conjecture for higher dimensions was proven decades ago (dimension 4 in the 80's, 5 and higher in the 60's), and those results are still called the Poincare Conjecture.
ReplyDeleteFor example, people just as often say "the Poincare Conjecture for dimensions 5 and higher," etc. rather than Smale's theorem, Freedman's theorem, etc.
On a related note, sometimes conjecturers get too much credit by getting conjectures named after them that they didn't even conjecture. These can be extensions or generalizations of the original. The Poincare conjecture in higher dimensions is one example, as is the smooth Poincare conjecture, etc.
Main Conjecture of Iwasawa Theory
ReplyDeleteRegarding Serge Lang coming off as a nutcase, the linked article is actually a mild example. He wrote extensively on his disbelief that HIV causes AIDS.
ReplyDeleteHere's a more slippery slope. What credit to give to a theorem's Announcer? What I mean is this: someone announces in public "X is true". He/she may even have given a talk outlining his/her proof. It may get referenced in a paper or two. But the proof never appears (e.g. the announcement was made 10 years ago, nothing happened since).
ReplyDeleteNow you find your own proof. It is a significant piece of work. Where does the credit go?