# Luboš Motl

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bio website motls.blogspot.com location Czech Republic age 40 member for 2 years, 10 months seen Mar 6 at 19:34 profile views 2,409

Hi, I am a string theorist and a publicist.

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 Mar6 comment Why does $1+2+3+\dots = {-1\over 12}$? Sure, it's a completely analogous sum. Just like $1+2+3+\dots$ quantifies the ground state energy in 1+1 dimensions (of a string), $1+1+1+\dots$ quantifies the ground state's charge (of a system of free fermions, for example). It's really the reason why the two degenerate states $|0\rangle$ and $c_0|0\rangle$ have ghost numbers $\pm 1/2$, for example. Feb10 comment Why does $1+2+3+\dots = {-1\over 12}$? It might be but it is a wrong conclusion. The key property of this $\infty$, which may be subtracted by a counterterm, is that it is independent of all independent variables, so it is formally a scale-invariant constant, and $0$ is the number to be associated with it. The fact that the sum of integers equals $-1/12$ is perhaps the most important fact about mathematics among the laymen - and among mathematicians without breadth and depth. Feb8 answered Equivalence of Two Lorentz Groups Jan24 comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$ Dear @Pedro, I am saying that $\zeta(2k+1)$ are transcendental numbers because I am ready to bet all my wealth on the validity of the claim. After all, even $\pi^n$ are transcendental numbers for rational nonzero values of $n$ so even zeta of even positive integers are (provably) transcendental. But the zetas of odd positive integers are (I claim without a rigorous proof) much more transcendental than the powers of $\pi$. I never claimed that I had a rigorous proof of the transcendentality but if you want to claim that I said something incorrect, you should have a proof which you don't have. Jan24 comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$ Nope, it's just believed by me and almost everyone that they're transcendental. The much "easier" proof that zeta(3) is irrational came just recently, in 1978, see en.wikipedia.org/wiki/Ap%C3%A9ry's_theorem Jan23 comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$ Nice, +1. An alternative calculation of $\zeta(0)=-1/2$ appears early in this article: motls.blogspot.com/2014/01/… - See my comment under the OP's question for 4 more articles about the topic if you wish... Jan23 comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$ Five more articles with 8 different ways to compute the sum of integers (most of the methods extend to the "sum of ones", too) etc.: motls.blogspot.com/2007/09/… motls.blogspot.com/2011/07/… motls.blogspot.com/2014/01/… motls.blogspot.com/2014/01/… motls.blogspot.com/2014/01/… Jan11 comment Why does $1+2+3+\dots = {-1\over 12}$? "Incorrect", "not right", and "opposite of right" are the same thing, also known as "synonyma". Sep20 comment Showing Dirac Delta Behavior Well, I think you would also have to discuss that the negative regions of $(\sin x)/x$ don't combine to other distributions like $\delta'$ etc. But otherwise OK, I upvote it. Jun25 comment Fourier transform of a signal sequence? I would be sort of surprised if there is an analytic formula for the Fourier transform of this contrived function. Jun18 awarded Good Answer May29 revised How find the number of $z$,such that$|a^2-b^2-b+1|\le 10$ added 365 characters in body May29 answered How find the number of $z$,such that$|a^2-b^2-b+1|\le 10$ May28 answered Evaluate integral in terms of Gamma function May24 revised Grover Algorithm Orthogonal vectors added 15 characters in body May24 comment Grover Algorithm Orthogonal vectors Sorry, I made a mistake. I meant that $\omega$ and $s'$ are orthogonal. My answer is hopefully fixed. I don't understand the question "how I will be able to define $\sqrt{N}|\omega\rangle$". It's just multiplication, right? One should know how to multiply vectors by numbers. May24 answered Grover Algorithm Orthogonal vectors May7 awarded Yearling Feb3 awarded Enlightened Feb3 awarded Nice Answer