Date: 2011-10-04 10:45 am (UTC)
From: [identity profile] momentsmusicaux.livejournal.com
What you do with or to a proof is more open to debate I think.
But a theorem was true all along, even before anyone knew about it.

Date: 2011-10-04 10:52 am (UTC)
From: [identity profile] momentsmusicaux.livejournal.com
Yes, but the method of the proof itself. Eg, there are tons of proofs of Pythagoras. Each has been invented, I would say. There's only one theorem, which has always been true.

Date: 2011-10-04 12:52 pm (UTC)
From: [identity profile] naath.livejournal.com
Greg Egan wrote a nice short story based on the notion that that is not actually the case :)

Date: 2011-10-04 05:40 pm (UTC)
simont: A picture of me in 2016 (Default)
From: [personal profile] simont
Two short stories! There's a sequel in a more recent collection.

Date: 2011-10-04 12:13 pm (UTC)
From: [identity profile] steer.livejournal.com
Something strictly is only a conjecture until it's proven but this is not always adhered to. Fermat's last theorem was an interesting case because it remained "claimed proven" (but most mathematiciancs now doubt it ever was proven by Fermat) until very recently. Now it is proven. Should it really have been Fermat's last conjecture?

Date: 2011-10-04 12:11 pm (UTC)
From: [identity profile] steer.livejournal.com
I am not sure a "formalist" would agree with "true all along" but instead that a particular theorem is (and always was) a consistent result of manipulation of strings of characters beginning with a set of axioms and rules of inference. However, it is a result of picking the axioms and inference rules. This sits comfortably with, for example, the fact that some statements in mathematics are only "true" for the type of mathematics you choose. For example Zermelo's theorem is "true" in ZF set theory with the axiom of choice but not true in ZF set theory without. In Euclidean geometry Pythagorus is true but not in elliptic geometry.

Given that the mathematician is free to choose the axioms and inference rules he or she works with, is "discovered" the correct word? I'm not wholly sure. Most people would feel uncomfortable saying that Charles Dickens "discovered" the sequence of letters, spaces and punctuation that made The Tale of Two Cities.

June 2025

S M T W T F S
1 2 3 4 5 6 7
8 9 10 11121314
15161718192021
22232425262728
2930     

Most Popular Tags

Style Credit

Expand Cut Tags

No cut tags
Page generated Jun. 12th, 2025 05:03 am
Powered by Dreamwidth Studios