Riemann Hypothesis ...

[ColinJ]

Like Morecambe and Wise, "I understand most of the words, though not necessarily in that order" ... Be interested to see what other people think (who actually know what they're talking about).

I looked up what the hypothesis is and didn't even understand that, so I won't be bothering with the proposed proof!

In another life, I would have loved to study maths beyond what I did for my electronic engineering degree but I think my brain is probably too addled for it now.

PS I have just been looking at OpenLearn and there are some interesting-looking modules available there. Perhaps I'll give one or two a go...?

 

[marinyork]

PS I have just been looking at OpenLearn and there are some interesting-looking modules available there. Perhaps I'll give one or two a go...?

Keith Devlin who wrote the millenium problems popular science book (the riemann hypothesis is one of the seven, poincaré another and B S-D a third) used to have a popular MOOC on the foundations of mathematics.

 

[marinyork]

Like Morecambe and Wise, "I understand most of the words, though not necessarily in that order" ... Be interested to see what other people think (who actually know what they're talking about).

So apparently some people thought the new auditorium, third floor was a prank .

I see now that it is related to an attempt at deriving the fine structure constant earlier this year and as he said out popped the Riemann Hypothesis. Many doubt that the fine structure constant is a constant. Seems a very bold claim that a function is complex analytical and matches all of the required bits AND is unique.

Read Baez and seen that MA has had a few others the last few years. Although reading some of the comments earlier suddenly reminded me that J-P Serre much later in life made a contribution to how Fermat's Last Theorem might be proven (epsilon conjecture).

 

[C R]

So apparently some people thought the new auditorium, third floor was a prank .

I see now that it is related to an attempt at deriving the fine structure constant earlier this year and as he said out popped the Riemann Hypothesis. Many doubt that the fine structure constant is a constant. Seems a very bold claim that a function is complex analytical and matches all of the required bits AND is unique.

Read Baez and seen that MA has had a few others the last few years. Although reading some of the comments earlier suddenly reminded me that J-P Serre much later in life made a contribution to how Fermat's Last Theorem might be proven (epsilon conjecture).

Is that fine structure constant Sommerfeld's constant or a different one?

If a proof of a mathematical theorem would also implied that the fine structure constant is indeed constant the set of possible unification theories would suddenly become much smaller. That would be as groundbreaking as the proof itself.

 

[marinyork]

Is that fine structure constant Sommerfeld's constant or a different one?

If a proof of a mathematical theorem would also implied that the fine structure constant is indeed constant the set of possible unification theories would suddenly become much smaller. That would be as groundbreaking as the proof itself.

It is and yes it would be.

 

[swansonj]

The fine structure constant is indeed constant. Bech, Bethe and Reizler derived it in 1931. Basically they noted that an electron has 1/alpha degrees of freedom. So, for an electrically neutral crystal with an equal number of protons, you have to remove 2/alpha degrees of freedom, less one remaining for the orbital motion of the electron, to reduce it to absolute zero (all degrees of freedom frozen). Absolute zero is -273, so 2/alpha -1 = 273, giving alpha=1/137.

It must be true because (a) Hans Bethe went on the get a Nobel prize and (b) it was published in Die Naturwissenschaften.

 

[marinyork]

The fine structure constant is indeed constant. Bech, Bethe and Reizler derived it in 1931. Basically they noted that an electron has 1/alpha degrees of freedom. So, for an electrically neutral crystal with an equal number of protons, you have to remove 2/alpha degrees of freedom, less one remaining for the orbital motion of the electron, to reduce it to absolute zero (all degrees of freedom frozen). Absolute zero is -273, so 2/alpha -1 = 273, giving alpha=1/137.

It must be true because (a) Hans Bethe went on the get a Nobel prize and (b) it was published in Die Naturwissenschaften.

That's what a physicist calls a constant or these days a fundamental constant, of which it is. The question is a fine tuning problem and why does it have the value it does? Is there some reason or does it just have that value (and the separate question investigated the last twenty odd years is it actually constant in the sense you mean)? Uncle Leonard et al think there's 10^500 false vacua, other bunch of people think there's a lot but a lot smaller than that. Doesn't get us anywhere of working out where it comes from (well it does actually as stuff like electroweak tells you, but then you still get the problem of where the smeg does it come from).

 

[marinyork]

Wow. I probably learned about that at uni. But like 90% of my degree I wiped it from my brain the instant my last exam finished.

And what has this got to do with number theory?

Atiyah thinks it's related to other constants such as e and π. He thinks it is a (mathematical not a physicist's) constant.

For a physicsy motivation to do with number theory there is the Hilbert-Po'lya conjecture which is a major approach to the Riemann Hypothesis. And yeap e appears there too (infact similar scalings to Atiyah's first paper).

 

[C R]

That's what a physicist calls a constant or these days a fundamental constant, of which it is. The question is a fine tuning problem and why does it have the value it does? Is there some reason or does it just have that value (and the separate question investigated the last twenty odd years is it actually constant in the sense you mean)? Uncle Leonard et al think there's 10^500 false vacua, other bunch of people think there's a lot but a lot smaller than that. Doesn't get us anywhere of working out where it comes from (well it does actually as stuff like electroweak tells you, but then you still get the problem of where the smeg does it come from).

That's anthropic principle territory now.

 

[marinyork]

That's anthropic principle territory now.

Yeah, but our resident scientist didn't understand where that was going so a necessary clarification. A difference in naming, clear to one person, not clear to another.

Or swamplands and all that.

 

[Rezillo]

That's what a physicist calls a constant or these days a fundamental constant, of which it is. The question is a fine tuning problem and why does it have the value it does? Is there some reason or does it just have that value (and the separate question investigated the last twenty odd years is it actually constant in the sense you mean)? Uncle Leonard et al think there's 10^500 false vacua, other bunch of people think there's a lot but a lot smaller than that. Doesn't get us anywhere of working out where it comes from (well it does actually as stuff like electroweak tells you, but then you still get the problem of where the smeg does it come from).

That would be an ecumenical matter.

 

[swansonj]

Yeah, but our resident scientist didn't understand where that was going so a necessary clarification. A difference in naming, clear to one person, not clear to another.

Or swamplands and all that.

Am I, perchance, said resident scientist? (There are layers upon layers here and I confess i’m quite enjoying it...)