Forum location: QI.com Forum Index
> U series Talk
View previous topic  View next topic
Unsolved problems 
Page 2 of 2 Goto page Previous 1, 2 
PDR

1414273. Sun Jul 03, 2022 9:56 am 


Surely one of the more famous unsolved problems has to be Maria.
PDR 




ConorOberstIsGo

1414275. Sun Jul 03, 2022 10:14 am 


As for what makes it onto the show; if Godel's Incompleteness Theorem hasn't already been mentioned, then I reckon it's the most explicable and fun one. 




Brock

1414276. Sun Jul 03, 2022 10:17 am 


ConorOberstIsGo wrote:  As for what makes it onto the show; if Godel's Incompleteness Theorem hasn't already been mentioned, then I reckon it's the most explicable and fun one. 
Gödel's Incompleteness Theorem isn't an unsolved problem. It was proved by Kurt Gödel in 1931. 




POLARIS183

1414286. Sun Jul 03, 2022 2:45 pm 


Quote:  Surely one of the more famous unsolved problems has to be Maria. 
See also: how to catch a cloud and pin it down. 




bobwilson

1414293. Sun Jul 03, 2022 5:45 pm 


Quote:  Fermat's Last Theorem, I think you mean. Fermat's theorem (usually known as Fermat's little theorem to distinguish) states that if p is a prime number, then for any integer a, the number a^p − a is an integer multiple of p. The proof isn't too difficult (I remember doing it as an undergraduate). 
Am I missing something here?
Let p=3 (a prime number as required), and a=2 (an integer)
Then a^p = 2^3 = 8
which is not an integer multiple of p (alias 3)
oh  and you're right  the specific theorem of Fermat that is commonly known as his last theorem rather than any of the other theorems with which it could have been misconstrued  apologies 




bobwilson

1414294. Sun Jul 03, 2022 5:52 pm 


Quote:  "Fermat’s unwillingness to provide proofs for his assertions was all too common. Sometimes he really had a proof, other times not."

A statement is not evidence  what evidence do the authors of this statement advance to show that there were occasions when M Fermat claimed a proof while not actually having one to hand? 




bobwilson

1414295. Sun Jul 03, 2022 5:56 pm 


Incidentally  the paradoxical nature of time travel  I've solved that one and you'll hear about it yesterday 




ConorOberstIsGo

1414297. Sun Jul 03, 2022 6:45 pm 


Brock wrote: 
Gödel's Incompleteness Theorem isn't an unsolved problem. It was proved by Kurt Gödel in 1931. 
Apols Brock, I didn't mean it should be listed under 'unsolved problems'; I meant it should be a key thing to mention while talking about unsolved problems more broadly. Not sure what the unsolved problem should be because I'm not hugely enamoured with any mentioned so far.
Which one of the 23 unsolved problems remain of Hilbert's problems? They were pretty influential. 




ali

1414298. Sun Jul 03, 2022 7:48 pm 


bobwilson wrote:  Quote:  Fermat's Last Theorem, I think you mean. Fermat's theorem (usually known as Fermat's little theorem to distinguish) states that if p is a prime number, then for any integer a, the number a^p − a is an integer multiple of p. The proof isn't too difficult (I remember doing it as an undergraduate). 
Am I missing something here?
Let p=3 (a prime number as required), and a=2 (an integer)
Then a^p = 2^3 = 8
which is not an integer multiple of p (alias 3)

The Little Theorem is usually stated as: a^p is congruent to a(mod p)
(In simpler language (a^p) divided by p leaves a remainder of a.)
The version quoted: p divides (a^p  a), is exactly equivalent.
In your example, you forgot to subtract a from a^p.
2^3  2 = 6 




Brock

1414308. Mon Jul 04, 2022 2:40 am 


ConorOberstIsGo wrote: 
Which one of the 23 unsolved problems remain of Hilbert's problems? They were pretty influential. 
There's a list here. I think they're all too advanced for a lay audience though. 




Page 2 of 2
Goto page Previous 1, 2
QI.com Forum Index > U series Talk
All times are GMT  5 Hours
Search Forums
Powered by phpBB © 2001, 2002 phpBB Group