May

29

# think you’re smart? really?

(Originally posted 9/19/2012)

Sometimes I think it’s important we remind ourselves just how stupid we are. I think we get carried away feeling like we’re really contributing something to humanity when in fact we’re riding on the coattails of really smart people. They’re off sitting somewhere being brilliant and you’re here reading this.

Case closed.

For example, Shinichi Mochizuki, a professor at the Research Institute for Mathematical Sciences at Kyoto University, recently proved the ABC conjecture in number theory. For the sake of proving my point without a shadow of a doubt I will give you the definition of ABC conjecture as stated by the Mathematical Institute of Leiden University:

The ABC conjecture involves abc-triples: positive integers a,b,c such that a+b=c, a < b < c, a,b,c have no common divisors and c > rad(abc), the so-called radical of abc.* The ABC conjecture says that there are only finitely many a,b,c such that log(c)/log(rad(abc)) > h for any real h > 1. The ABC conjecture is currently one of the greatest open problems in mathematics. If it is proven to be true, a lot of other open problems can be answered directly from it.

(*The rad(abc) is the “product of the unique prime factors of a,b, and c”)

It’s important that you don’t skip ahead here. I want you to bask in just how much you don’t understand what ABC conjecture is. You walk around using computers and cell phones thinking to yourself how wonderful it is that humanity is so bright and has invented so many things to make our lives easier and much less chimp-like when the truth is that the “humanity” you speak of is about .000001% of the population and without them you’d be walking around in animal skins thinking that fire was a pretty nifty breakthrough.

I hope you understand that the above quote was just the definition of ABC conjecture. The actual proof is 500 pages of this: The present paper is the first in a series of four papers, the goal of which is to establish an arithmetic version of Teichm¨uller theory for number fields equipped with an elliptic curve — which we refer to as “inter-universal Teichm¨uller theory” — by applying the theory of semi-graphs of anabelioids, Frobenioids, the ´etale theta function, and log-shells developed in earlier papers by the author. We begin by fixing what we call “initial Θ-data,” which consists of an elliptic curve EF over a number field F, and a prime number l ≥ 5, as well as some other technical data satisfying certain technical properties. This data determines various hyperbolic orbicurves that are related via finite ´etale coverings to the once-punctured elliptic curve XF determined by EF. These finite ´etale coverings admit various symmetry properties arising from the additive and multiplicative structures on the ring Fl = Z/lZ acting on the l-torsion points of the elliptic curve. We then construct “Θ±ellNF-Hodge theaters” associated to the given Θ-data. These Θ±ellNF-Hodge theaters may be thought of as miniature models of conventional scheme theory in which the two underlying combinatorial dimensions of a number field — which may be thought of as corresponding to the additive and multiplicative structures of a ring or, alternatively, to the group of units and value group of a local field associated to the number field — are, in some sense, “dismantled” or “disentangled” from one another. All Θ±ellNF-Hodge theaters are isomorphic to one another, but may also be related to one another by means of a “Θ-link”, which relates certain Frobenioid-theoretic portions of one Θ±ellNF-Hodge theater to another is a fashion that is not compatible with the respective conventional ring/scheme theory structures. In particular, it is a highly nontrivial problem to relate the ring structures on either side of the Θ-link to one another. This will be achieved, up to certain “relatively mild indeterminacies,” in future papers in the series by applying the absolute anabelian geometry developed in earlier papers by the author. The resulting description of an “alien ring structure” [associated, say, to the domain of the Θ-link] in terms of a given ring structure [associated, say, to the codomain of the Θ-link] will be applied in the final paper of the series to obtain results in diophantine geometry. Finally, we discuss certain technical results concerning profinite conjugates of decomposition and inertia groups in the tempered fundamental group of a p-adic hyperbolic curve that will be of use in the development of the theory of the present series of papers, but are also of independent interest.

First of all, go back and read that you lazy bastard! Read it all.

Second, that was only the first page of 500 pages of the most ass-puckering math you’ve ever imagined. The kind of math that would have futuristic robots wriggling their metallic arms around and having white smoke belch forth from their shiny robot heads.

Now my goal here isn’t to bring you down and have you slumped over in anguish for the rest of the day but I need you to realize what a dumbfuck you are. And I am. Don’t misunderstand, I can copy and paste away all day but that doesn’t make me any brighter than you. Every time I feel all full of myself because I figure out how replace the little plunger thing in the toilet I’m suddenly brought crashing back to earth by the realization that quantum mechanics is being debated not an hour’s drive from my now-functioning lavatory while I sit beaming and damp.

I was going to call it a shitter but I already feel like a Neanderthal, do I really need embarrass myself further?

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