## Grothendieck anagram

Posted by Andreas Holmstrom on January 6, 2013

Looking back on the mathematical year 2012, the most exciting thing happening was probably Mochizuki‘s work on the abc conjecture. Something I had hoped to see during 2012, was the writings of Grothendieck, restored to the Grothendieck circle website. Sadly, this has not happened, as Grothendieck himself apparently is opposed to it. However, it is not clear (to an outsider) if he is opposed to having a website dedicated to his memory and/or publishers making money out of his writings, or if he is actually opposed to his hardcore algebraic geometry texts being made available for free to interested mathematicians. Looking carefully at the name Alexander Grothendieck, one observes that permuting the letters yields the sentence “Hardcore EGA, extend link!”. Although not a decisive argument in the moral/legal debate over Grothendieck’s letter, perhaps it means something ;-)

One a similar note, the sentence “hi’ risk abstract banana hack” is an anagram of “Banach-Tarski”, while “Plain Anarchy Got Us! Shriek! Ahhh!!” is an anagram of “Hartshorne playing shakuhachi”.

Finally, a little anagram puzzle for those of you who need a small recreational break (can also be used as homework for students you for some reason do not like). Let n be a positive integer, and let S be the set of integers between zero and n (inclusive). Let N be the number of anagrams expressing valid arithmetic equalities between elements in the set S. Example: Twelve plus one = eleven plus two. Try to compute N for small values of n. Do you see a pattern? How does N grow with n? What happens if you replace the word “integer” with the word “rational number with bounded height”?

Happy New Year 2013!

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