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PDR
1414273.  Sun Jul 03, 2022 9:56 am Reply with quote

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

PDR

 
ConorOberstIsGo
1414275.  Sun Jul 03, 2022 10:14 am Reply with quote

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 Reply with quote

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 Reply with quote

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 Reply with quote

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 Reply with quote

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 Reply with quote

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 Reply with quote

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 Reply with quote

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 Reply with quote

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.

 

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