Why -1/12 is a gold nugget

Featuring Professor Edward Frenkel. More links & stuff in full description below ↓↓↓

Okay, the links...

Animation by Pete McPartlan

NUMBERPHILE

Videos by Brady Haran

[karlmadsen]

"Does the square root of negative one exist? Come on, Brady." He taunts Brady with a glint in his eye and an evil grin.

[sunofslavia]

"Euler was a mathematical gangster."
- Prof. E. Frenkel

[maxhedges]

Imagine being in an infinite job where you're paid 1 more dollar every day then at the end get a paycheck with - 1/12 dollars.

[toddgoul]

"There is magic, but we always want to explain it." What a perfect encapsulation of scientific endeavor.

[FrankenSteinsGate]

Russian Jaime Lannister makes some compelling points.

[hunszaszist]

"One thing which is important in mathematics is that we just can never leave [...] loose ends. [...] Mathematics is rigorous, and at the end of the day we are looking for a rigorous justification of everything. In other words, we are not content with just saying that there is some magic over there. There is magic, but we always want to explain it."
Edward Frenkel, Professor of Mathematics

I just... this... wow...

[jeck]

Euler did some painstaking work and lost his vision.
After the loss of vision he said "Now I will have fewer distractions"
Now thats gangster lol

[kingbane]

man this professor must be an amazing educator. he makes things so clear and easy to understand.

[mattbritzius]

He looks like a guy that would be taunting Bruce Willis over the phone in a diehard movie.

[numberphile]

Watched the whole video? Seen the links? Watched the other videos?

Then why not leave a comment! :)

[amazen]

This man is BRILLIANT. The way he clearly explains complex topics in a language that is not his mother tongue is astounding.

[OldSchoolCancer]

his accent just make everything better

[splitzerjoke]

"Euler was a kind of mathematical outlaw... a kind of a mathematical gangster..."

Euler: don't worry dear Riemann, i`ll make 'em a proof they can't refuse... LOL

[michaelzimmermann]

I am a physicist and I deal with quantum-electro-dynamics (QED). I want to share with you (or show you ) the existance of a finite value for divergent sums.
In QED we calculate vertices (meaning something like electron interacts with another electron via one photon). And we can calculate the magnitude of this interaction. But if one includes fluctuations (which are known to be omnipresent) we always get infinity. The vertex "electron interacts with itself via a photon" is for instance always infinite and can be added to any interaction. And now the above video comes into the game. We can renormalize the infinte sums just the way described above. and the outcome of the theory is absolutly impressive. QED has given values of physical constants up to the 14 spot behind 0 correctly, compared with experiments (which is unreached in any other physical theory). Therefore the existance of finite values for divergent sums is not a mathmatical fantacy, it is the TRUE reality.

[russellthorburn]

6:52 "Does the square root of -1 exist". I laughed so hard (in delight) when he said that because his point was made blindingly obvious by asking such a simple question. Elegance at it's best. I'd sit through one of his lectures any time any where.

[expensivetechnology]

I respect this professor’s mastery of my language (English), his second language, in addition to his mastery of mathematics.

[alexanderlindblad]

Numberphile has managed to take the subject I disliked the most in school and turned it into one of my favourite and inspiring subjects on YouTube! Bravo!

[opmike]

The best explanation of this -1/12 business I've ever seen. There IS a lot more going on here than some of the other professors did a poor job of articulating.

[LostAlienOnEarth]

I just watched Srinivasa Ramanujan movie, "The man who mew infinity"

[Crustyislooking]

We used to “throw away” negatives, I wonder if someday looking back we’ll understand those series better