How the infinite term in mathematics gets thrown away

I introduce you to two videos that seem to support the following quotation

Quote:

“In modern terms, Dr. Frenkel explained, the gist of the calculations can be interpreted as saying that the infinite sum has three separate parts: one of which blows up when you go to infinity, one of which goes to zero, and minus 1/12. The infinite term, he said, just gets thrown away.”

Introductory short version

Extended version of the same presentation

Also see the related New York Times article