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In Chapter 2 of Ian Stewart's Another Fine Math You've Got Me Into... (New York: W. H. Freeman & Co., 1992), he mentions a conjecture that "polyominoes of order 3 do not exist" (a polyomino is "a plane figure formed by joining a set of equal-sized squares edge to edge so that the corners match" and the order of a polyomino is "the smallest number of copies that will fit together to fill a rectangle.")

He tells a story involving a certain worm called Albert Wormstein, then claims that Albert has found a proof of the above statement. He continues:

Albert's proof is too complicated to give here. Interestingly, it makes extensive use of symmetry arguments. Albert is currently publishing it as a joint paper with me, since mathematics journals tend to be reluctant to accept contributions from worms---an appalling example of how science is infested by speciesism. (How many articles by worms have you seen in mathematics journals?) This is the first conjecture in mathematics to have been proved by a worm.

I thought it was some private joke until I discovered this paper: "Polyominoes of order 3 do not exist" by I. N. Stewart and A. Wormstein, Journal of Combinatorial Theory, Series A, Volume 61, Issue 1, September 1992, Pages 130–136.

My question is: Does anyone know why Ian Stewart chose to have a fictional (I assume) co-author? Or is Albert Wormstein a real person?

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He's on Facebook - which doesn't seem to make him more real though :) – Hagen von Eitzen Jul 20 '13 at 13:27
Birth date: November 26, 1876. – Mlazhinka Shung Gronzalez LeWy Jul 20 '13 at 13:31
This is the first fictional character I've ever heard of that might have an Erdos number. – Rick Decker Jul 23 '13 at 15:06
up vote 12 down vote accepted

Here is Ian own answer to your question (personal communication with his permission to give it here). His own version of story is nice to hear as ever and it somehow answers the why part of your question.

The link [refering to your question] has the correct story . Albert Wormstein first appeared in one of my articles for Pour La Science / Scientific American, which was used as a chapter in the cited book.

While I was writing that article it suddenly seemed clear that there ought to be a way to prove the conjecture about order 3 polyominoes. It felt as though Albert was tapping me on the shoulder and saying 'come on, we can do this.' It quickly turned out he was right. So I decided to give him credit as a co-author. The journal either spotted the joke and went along with it, or they assumed Albert was a PhD student. At any rate, they published it with him as co-author.

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Wow! This answers my question. Thanks. – Joel Reyes Noche Jul 24 '13 at 0:12

The answer to your amazing question is indeed, Albert Wormstein is a character among others such as Maxdoch Murwell from Ian's mathematical fiction Another Fine Math You've Got Me Into...

It would be the same as asking Lewis whether Alice would be real from Wonderland.

From a mathematical point of view I would say Wormstein is real but from a physical point of veiw no.

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how very platonic of you. +1 – James S. Cook Jul 20 '13 at 14:00

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