This is one of those blog posts written so I don't have to answer lots of people individually.
If you're angry, I doubt it will make you less angry. It 's just a collection of links and other stuff you should check out.
You're probably here after watching this video about the sum of all the integers. It shows how some physicists deal with the problem of the diverging sum 1+2+3+4, etc:
Here is an accompanying video we uploaded at the same time. You may have missed it:
Here is an article written by Tony Padilla after the video was published. I really recommend reading it if this topic interests you. For me, it is the most important link on this page. Tony directly explains what he does in the video.
Here's a video I later made with Ed Frenkel, where he discussed the result:
The New York Times wrote about it. Here is their take.
NEW ADDITION: Physicist Leonard Susskind discusses it here in this Stanford University video around 1:13:50. He also wheels out -1/12 for the sum of the integers - curious how often such a precise and arbitrary number is associated with that sum and all the different ways people get to it.
Here's a Wikipedia article about it (this was already famous, or infamous, well before the Numberphile video).
This video about the Riemann Hypothesis contains a section which also neatly shows where -1/12 fits into all this:
If the notion of 1+1-1+1-1 brought you here, here's something else:
If you are still angry, that's okay.
I warned you this blog probably would not help!
I'll give the last word to Ramanujan - a pretty handy mathematician: