mathematical reputations based on erroneous work

As an undergraduate math student I once overheard a conversation relating to someone whose mathematical reputation was ruined due to an erroneous published theorem. I am writing a book in which I wish to make the assertion that mathematics is a social endeavor and cannot reliably be done in isolation.

Example:

"Russell wrote to Gottlob Frege with news of his paradox on June 16, 1902. The paradox was of significance to Frege's logical work since, in effect, it showed that the axioms Frege was using to formalize his logic were inconsistent."

Russell's Paradox (Stanford Encyclopedia of Philosophy)

Re: mathematical reputations based on erroneous work

I don't know if your hypothesis will be valid in the future. Mathematicians and computer scientists are now working on computer-assisted proof systems (e.g. automated proof verification or proof construction), so in the future, it would be theoretically possible to work in isolation. (For references, see Computer-assisted proof - Wikipedia, the free encyclopedia and Mizar system - Wikipedia, the free encyclopedia.)

There are some other issues, as well. I think that there are some areas where releasing a paper to the community does not help either. For example, I've been told by a few professors that the massive proof of Fermat's Last Theorem is understood by a very small handful of people in the world. In some sense, it isn't all that reliable or satisfactory that almost nobody can understand it. (And this may be some motivation to get computers to do the checking.)

These things aside, I don't think that your claim is specific to mathematics, so I can't really see a point to your book. You can probably name any field in the arts or sciences where people exchange ideas in order to advance the field. It seems more fruitful to look for an activity that is done in complete isolation (which looks like a very hard-press). What specific ideas did you have in mind?

Re: mathematical reputations based on erroneous work

Quote:

Originally Posted by

**roninpro** ... What specific ideas did you have in mind?

I had a lucid dream/astral dream experience many years ago in which I encountered an individual, a mathematician, who appears to be a fixture in the afterlife astral realm.

You can read about the encounter here (note: "prepositional calculus" should be "propositional calculus"):

Looking for a Mathematician

In my book, I wish to contend that even though the mathematician of this experience seems to be content and lost in a world that consists only of herself and her ideas, sooner or later she will make mistakes that will not likely be rectified because she interacts with no one who would be able to verify her work. She has eternity to ponder her work. Perhaps she'll find her errors and correct them—perhaps not.

Thanks for the reference to the Mizar system. It may be useful for my book. Perhaps this thread will be used as a reference.

Re: mathematical reputations based on erroneous work

it is conceivable, that even in isolation, one could discover errors by repeated checks for consistency. how one would learn mathematics in isolation seems unclear, but having learned it (or at least enough of it) i see no reason why one might not practice it alone.

the story about your dream was interesting. one wonders (at least i do) if the mathematician in your dream was a metaphor for god.

Re: mathematical reputations based on erroneous work

Quote:

Originally Posted by

**Deveno** it is conceivable, that even in isolation, one could discover errors by repeated checks for consistency. how one would learn mathematics in isolation seems unclear, but having learned it (or at least enough of it) i see no reason why one might not practice it alone.

the story about your dream was interesting. one wonders (at least i do) if the mathematician in your dream was a metaphor for god.

A metaphor for a metaphor?

CB

Re: mathematical reputations based on erroneous work

would that be, then, a meta-metaphor?

Re: mathematical reputations based on erroneous work

Quote:

Originally Posted by

**Deveno** would that be, then, a meta-metaphor?

meta^2phor (Devil) (Mooning)

CB

Re: mathematical reputations based on erroneous work

Quote:

Originally Posted by

**Deveno** it is conceivable, that even in isolation, one could discover errors by repeated checks for consistency. how one would learn mathematics in isolation seems unclear, but having learned it (or at least enough of it) i see no reason why one might not practice it alone.

I hear Ramanujan learned maths without any guidance.

Re: mathematical reputations based on erroneous work

Quote:

Originally Posted by

**ymar** I hear Ramanujan learned maths without any guidance.

but...he had books, no?