1+2+3+4+... = Is there place for magic in math?

In this new video, I discuss the recent controversy about the infinite sum 1+2+3+4+... as a microcosm of problems with our math education

The cheesiest cellphone in the world would be black magic to anyone who lived a few centuries ago, so yeah, magic definitely has it's place in math.

You are intelligent, humorous, and handsome!  Will you marry me?  I am a bit sapiasexual...and you, sir, are the cats' meow!!  I LOVE your book and I cannot recommend it enough!

Could you do a video explaining how math relates to the real world? For example, can all these weird made up numbers make predictions about real world things? 

The way I see it as a layman to maths, I can understand adding, subtracting, multiplying, all the basic real world stuff. But when you get into using letters, the concept of zero, infinity. patterns in maths ect. It's seems useless and no better than making stuff up. 

At the end of the day math has to be a representation of the real world. basically matter right, atoms, energy. It seems to me most of math is made up. 

I have no education in maths, and most of these videos go over my head from the start. You are talking in another language.  Just pointing out how you might be Preaching to the choir. 

Great videos, much appreciated. Cheers

Never before have I discovered true love until I have discovered true Mathematics. From the bottom of my heart I thank you for sharing your understandings and experience with us all. As never before had woke up being so excited and keen to do Mathematics. I almost feels like I am a kid again and everyday is a new and excitingly fresh new adventure. I feel there is a kind of artistic, longevity, universal, life and purity about Mathematics. I have indeed fallen in love with the art and truth that is Mathematics. I have finally found my reason for living. Thank You for you inspiration Professor Edward Frenkel. I look forward to more of your great videos. Eternally Grateful. Thanks.

А как можно решить 1+1+1... Где лимит в этой задаче?

This makes me want to apply to PhD math at Berkeley and ask if professor Frenkel can be my advisor. Lol!

I am also astounded at mathematicians' cold reception of the -1/12 video.  Goedel's Incompleteness Theorems of 1932 in some sense prove that mystery and "magic" will always be an unavoidable part of math.  Mathematicians who insist otherwise (suggesting math as a complete and consistent axiomatic system) have a lot to learn about their own discipline.  As Musil said, mathematics is an edifice that is "standing in midair."  If mathematicians are uncomfortable with this, maybe they should go into accounting (or "fence painting").

Math made really few sense for me in the high school. I had horrible teachers, but I know, maybe it's not their fault. Anyway, my Data structures professor recommended your book in today's class, some hours ago. When he was talking about you I thought you were contemporary to Tesla, haha. Maybe you are convincing me that math is not a Hydra, and that I can finally deal with it. Thank you!

I remember last summer, I was at the bar and a good friend of mine (who never even went to college) showed up as always, and we were chit-chatting as always do, and I just off-the-cuff asked him "what is the sum 1 + 2 + 3 + 4 + ...", and he replied "-1/12". LOL. I then asked him, "how do you know this" and he replied "what else could it be?". He never explained himself :) I left it at that :)

:)

Thank you very much professor. You are the reason my interest in math got deeper and stronger. I watched your video about riemann hypothesis on numberphile and there this concept infinite sum was introduced to me. When I saw 1+2+3+....=-1/12 I literally couldn't sleep for 2 nights.
Again thank you because of your contribution to numberphile and your book are one of the several major reasons I'm studying math in university.

I'm trying to make sense of this. After watching a video of the proof, -1/12 is only a viable answer if the sum of the series, S1 = "1-1+1-1+1...", is equal to 1/2, i.e. the average of 0 and 1, or the midpoint between 0 and 1. I'm having difficulty making sense of this because I relate it to the "Schrödinger's cat" thought experiment. It's like saying "1/2" is when the cat is both simultaneously alive ("1") and dead ("0"). But I suppose if I thought of 0 and 1 as an oscillation, like a ray of light or sound, I could picture the validity of 1/2 as an answer to S1. Though, it is only an approximation or a perception of what is true... I suppose I can only accept this in the realm of physics (real world), but not in the realm of math (beyond the world).

So many great points here by Edward Frenkel! Ramanujan would be proud.
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