kottke.org posts about Leonard Euler

The sum of all positive integersJan 16 2014

What do you think you get if you add 1+2+3+4+5+... all the way on up to infinity? Probably a massively huge number, right? Nope. You get a small negative number:

This is, by a wide margin, the most noodle-bending counterintuitive thing I have ever seen. Mathematician Leonard Euler actually proved this result in 1735, but the result was only made rigorous later and now physicists have been seeing this result actually show up in nature. Amazing. (thx, chris)

Update: Of course (of course!) the actual truth seems more complicated, hinging on what "sum" means mathematically, etc. (via @cenedella)

Update: As usual, Phil Plait sorts things out on this complicated situation. (via @theory)

kottke.org

Front page
About + contact
Site archives

Subscribe

Follow kottke.org on Twitter

Follow kottke.org on Tumblr

Like kottke.org on Facebook

Subscribe to the RSS feed

Advertisement

Ads by The Deck

Support kottke.org shop at Amazon

And more at Amazon.com

Looking for work?

More at We Work Remotely

Kottke @ Quarterly

Subscribe to Quarterly and get a real-life mailing from Jason every three months.

 

Enginehosting

Hosting provided EngineHosting