Marjorie Rice - The Most Remarkable Housewife You've Never Heard Of

17th September 2015

In the news last month was the announcement that someone had discovered a new type of pentagonal tiling – we didn’t know a huge amount about the subject but we knew it was one of the numerous ongoing unsolved maths puzzles.

Basically if you can cover a flat surface using only identical copies of the same shape leaving neither gaps nor overlaps, then that shape is said to tile the plane. Loads of shapes do this easily, but regular pentagons do not – however, some non-regular pentagons do, and the search to find these exact shapes has driven mathematicians for nearly a hundred years since German mathematician Karl Reinhardt, discovered five in 1918.

Karl Reinhardt

Reading up on the history of the problem we discovered a fascinating story centred around a seemingly normal 1970’s housewife from suburban California. A story about a wife and mother with no formal mathematical training who was nevertheless able to make significant contributions to the field, pipping plenty of professional mathematicians to the post as she did so.

Marjorie Rice enjoyed arithmetic at school but it wasn’t until her final year of high school she realised how much she enjoyed the challenge of further maths. In a documentary she explained "It wasn’t until my senior year at high school when I took a general mathematics course that I really found out how much I had been missing and how much that I liked it, but I only had that one year… and then I graduated."

We noticed this was said with a resigned wistfulness, as if perhaps she still can’t help but wonder what might have been. Certainly with her intuitive intellect if she had had formal higher mathematical training think what she could have achieved!

Still from an interview with Rice on the TV series "The Nature of Things" 1996

Rice graduated high school and took a clerical job but her intellectual curiosity led her to read voraciously on the subjects of science and psychology. She soon married Gilbert and they went on to have five children, which obviously left little time to indulge her intellectual curiosity.

However, when her son showed an interest in science she purchased him a subscription to ‘Scientific American’. But while the kids were at school and she’d finished her housework she would read puzzles master Martin Gardner’s maths puzzle column.

It was here she encountered the problem of pentagon tiling explaining later that she thought, "My, that must be wonderful that somebody could discover these things that no one had seen before, these beautiful patterns. So I started figuring out some way to work on the problem…. I became fascinated by the subject and wanted to understand what made each type unique. Lacking a mathematical background I developed my own notation system and in a few months discovered a new type"

"I was so delighted when I found it, I couldn’t believe it. I didn’t really think I would find anything and I was just so thrilled and I sent it to Martin Gardner, and he sent it to Doris Schattschneider"

Doris Schattschneider was a respected mathematician and despite having no clue who this housewife was, confirmed she had indeed found a new type of pentagonal tile. At first she was confused, as since Rice had no formal training whatsoever she was unable to produce a formal proof. Rice said "The diagram that was my key to finding different tilings is a small five sided shape like the little houses children draw" with annotations all around like chicken scratchings – but it worked! Her work was pictorial and crude but correct.

As Schattschneider commented in the essay "In praise of amateurs" Rice provided "a very striking illustration of an amateur’s intuition and observation using elementary tools leading to a correct conclusion but the necessity of more sophisticated mathematical means and a trained mathematical mind to provide irrefutable proof"

Meaning Rice’s intuition was correct although a ‘real’ mathematician was needed to verify her remarkable discoveries to the mathematical community.

This ordinary housewife had made mathematical history, all from her kitchen table! Encouraged by Doris Schattschneider who published her findings she continued her work and over the next two years she discovered three other types of pentagon tiles named 11, 12 and 13. No more were discovered until 1985 and 2015 respectively.

Rice recounted that at one point she resolved to stop her investigations because of family commitments but found she was unable to. Apparently they were "not so easy to lay aside" and that is the crux of it – she did it for the sheer love of the puzzle, the excitement of the maths.

Rice also had a keen interest in art and has also, in the manner similar to Escher, used her tilings to represent the beauty in her findings with tessellating works of art like this.

Rice was encouraged by the praise of her mathematical supporters but she didn’t become famous or rich. She just loved making her discoveries for their own sake, for their beauty and perfection and that, we think, is wonderful. Among mathematicians she is respected and always will be - one of her tilings decorates the foyer floor of the Mathematical Association of America too, an honour indeed – and she is now respected by us at ConquerMaths Towers too. 

The Foyer Of The Mathematical Association Of America

And the best part? She’s still alive! 90 years old and living with her daughter in California.