Favourite Numberphile vidoes?

A couple of months back I started watching videos by Numberphile on YouTube.
I was just curious as to what people's favourite videos are so I could go and check them out!
If you've never seen any and you like maths then they are definitely for you! Go check them out! :smile:

Personally my favourite is the proof that the sum of all the natural numbers is -1/12 because it got me interested in the Riemann hypothesis.

Reply 1

TeeEm

19

Original post by nickk_harrisonn

Personally my favourite is the proof that the sum of all the natural numbers is -1/12 .

how?

Reply 2

nickk_harrisonn

OP

1

Original post by TeeEm

how?

Take a look, it's quite long though

Reply 3

TeeEm

19

Original post by nickk_harrisonn

Take a look, it's quite long though

Do you mean that 1+2+3+4 + ....= -1/12?

This is what your post says.

I do not know how to break these news to you but this is not likely to be -1/12...
is this a "mock proof"?

(edited 9 years ago)

Reply 4

Noble.

17

Original post by nickk_harrisonn

A couple of months back I started watching videos by Numberphile on YouTube.
I was just curious as to what people's favourite videos are so I could go and check them out!
If you've never seen any and you like maths then they are definitely for you! Go check them out! :smile:

Personally my favourite is the proof that the sum of all the natural numbers is -1/12 because it got me interested in the Riemann hypothesis.

It's a bit of a stretch to call it a proof - it isn't mathematically rigorous (which is fairly obvious as you're summing a load of positive numbers and getting a negative answer).

See my post here when this was bought up before - http://www.thestudentroom.co.uk/showthread.php?t=2563118&p=45933012#post45933012

Reply 5

nickk_harrisonn

OP

1

Original post by TeeEm

Do you mean that 1+2+3+4 + ....= -1/12?

This is what your post says.

I do not know how to break these news to you but this is not likely to be -1/12...
is this a "mock proof"?

The maths is sound when you look at it from an analysis point of view, summing infinite sequences etc... And it makes sense when you consider it as a Dirichlet series which converges as opposed to the Zeta function of -1 which diverges. There are ways to get it to converge though otherwise the Zeta function wouldn't have any zeroes whatsoever in the negative real part of the complex plane.

Reply 6

TeeEm

19

Original post by nickk_harrisonn

The maths is sound when you look at it from an analysis point of view, summing infinite sequences etc... And it makes sense when you consider it as a Dirichlet series which converges as opposed to the Zeta function of -1 which diverges. There are ways to get it to converge though otherwise the Zeta function wouldn't have any zeroes whatsoever in the negative real part of the complex plane.