

 Does it matter if the sum of all integers is -1/12?  - ash
http://blog.rongarret.info/2014/01/does-it-matter-if-sum-of-all-integers.html

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ColinWright
I think this video does matter, but I think it's in a good way. What follows
is a gross over-simplification, and it's more of a rant than a real
explanation. I may not even agree with it tomorrow. Hell, I don't fully agree
with it now. But here's a flavour of how I see it.

Broadly speaking there are four main groups:

A: Those who won't see it or don't care;

B: Those who will use this as an opportunity to diss and dismiss math, to
ridicule and deride those who do math;

C: Those who start asking why and how this can be "true," and why and how it
can be useful;

D: Those who understand that it's really just math geeks having fun.

We can ignore group A, they won't be affected.

We can ignore group B, they will never be converted, and will actively look
for reasons to excuse their disinterest and disengagement. They are the ones
who already seize on things like the usual proofs that 1=2, and so on. No harm
will be done here. In fact, we can use this to identify them, and work with
them to hone the skills they will need. Doing arithmetic and getting hold of a
sense of number will be the best way to help them.

We can ignore group D, they already get it.

But in group C there is an opportunity. These are the ones who we can start to
get engaged in real math, and not the crappy drivel they get exposed to in
school. For them we now have an opportunity to share why math can be fun and
exciting, as well as useful.

The people in group B who rant about how this is overt, obvious nonsense, and
all math is pointless, they are lost already. Sadly some will go on to be
politicians, and we must continue to defend against them, yes. But this sort
of fun video gives us the chance to talk about what real math is like, and
what real math involves, and to capture those who possess the raw skills we
need in the more difficult, technical, abstract, fundamental subjects.

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j2kun
My real issue with the video is not even in the bad proof. It's that
mathematics, which I find to be so great and fun, is being misrepresented.
Mathematics gets so little public exposure as it is, so to have this be the
thing that makes its way through the internet is just sad.

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jackmaney
"Does it matter if the sum of all integers is -1/12?"

Yes. Yes, it does matter, because the series 1 + 2 + 3 + ... diverges. It's
that simple.

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ColinWright
No, it's not that simple. If you go and actually read some of the more
detailed pages you'll find that really, _really_ advanced math allows us to
put a consistent interpretation on it.

