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Science and InventionMarjorie Rice and her discovery of new pentagon tilings
Marjorie Rice was a housewife and mathematician interested in art who discovered new pentagon tilings of the plane.
She was inspired to work on tilings after reading in Martin Gardener's column that the list of pentagonal tilings was "complete", contradicted a short time later by another reader submitting a single new pentagonal tiling.
She took that as a challenge and then, over two or three years, discovered over a 100 new pentagonal tilings. She created her own notation which helped her categorize the tilings into several types. Her work was verified by another female mathematician, Doris Schattschneider.
Here's a five minute video by a girl giving an introduction to tilings and Rice's contributions. The video's very well done and inspired me to post this here.
Here's a recent magazine article talking about how her discoveries fit alongside other mathematical discoveries. It references journal articles and her own essays discussing her work, as well as including many quotations by her daughter talking about her mother's process.
Of the 15 tiling types known today, she discovered 4 of them. There's a 2017 proof that claims that these are the only 15 tiling pattern types which use a single convex pentagon repeating, although it does not appear that this proof has appeared in any journal.
Note: Marjorie Rice was not a mathematician; she had only a high school math education. Though she took an interest in other tiling problems, it doesn't sound like she ever learned more mathematics than can be found in Martin Gardner's column in Scientific American.
Is being a mathematician defined by having formal education in higher mathematics or by making mathematical discoveries that are accepted and respected by the professional mathematical community? I think the latter is a better definition. Most sources describe her as an amateur mathematician, which is probably the most accurate.
Being a mathematician is defined by doing formal mathematics, regardless of the formality of your education. Discovering a tiling (but proving nothing about the general case of such tilings) is a sort of corner case. A mathematician could have done it but would at least have attempted the formal categorization of such tilings that was eventually made. An amateur could (evidently) also do it as a puzzle, but that doesn't turn the amateur into a mathematician.
I'm not sure what's motivating your responses here, but you're making several blatant misassumptions about Rice. She didn't have a formal mathematical training, but she did independently categorize tilings, as I stated in my original post. Doris Schattschneider goes into great deal of detail about her collaboration with Rice in the 1981 magazine article "In Praise of Amateurs" where she describes sending preprints for Rice to look at, talks about sending Rice conjectures which Rice found counterexamples for, and explains the how the numbers of the categorization that Rice found correspond exactly to the numbers of the categorization that professional mathematicians used. She does acknowledge that Rice's lack of formal training meant that many of her explanations did not qualify as complete proofs, giving at least two examples, but she calls Rice a mathematician, and looking at the full body of her contributions, I would agree. It's up to you if you disagree, but do try to justify your position in a way that's grounded in facts.
My responses are motivated by an intimate knowledge of formal mathematics. Doris Schattschneider may disagree, but I think the majority of mathematicians would not call Marjorie Rice (or a man with similar achievements) a mathematician. This is not to denigrate her; it’s just not how the term is used by mathematicians.
What would she be called, if not an "amateur mathematician"?
There's no obligation to make up terms for unique or unusual people, any more than it is to use the wrong terms for them for lack of something better. Most people don't feel it necessary to call M. C. Escher or Martin Gardner amateur mathematicians, or to categorize them at all.
We can label both of those people without much difficulty—Gardner was a popularizer of mathematics, and Escher was a modern artist, mostly a printmaker.
"Popularizer" is not very flattering, and your description of Escher omits all mention of mathematics.