This novella is what I would call a "feel good fantasy" about the mathematician Benoit Mandelbrot who coined the term fractal.
It takes the form of a memoir written by an elderly Mandelbrot recalling his childhood in Nazi occupied France. The story includes historical elements, such as the role of his uncle in encouraging his mathematical interests and his parents' occupations. It also contains some realistic but entirely fictional aspects. (As far as I can tell, the part about his competitor at school who told the Nazis about the Mandelbrot family's Jewish heritage is a creation of the author.) The main focus, however, is on the fantastical scenes in which young Mandelbrot combines Jewish mysticism with mathematics to save his family, hiding them behind a fractal boundary which prevents the Nazi soldiers from finding them.
I am sure there are many people who would love this book. The prose is beautifully written, the story is uplifting, and it is filled with fascinating imagery. However, it has retained too little of the actual idea and feeling of the mathematics of fractal geometry for me. The book does introduce some of the early fractals, like the Koch Snowflake and the Sierpinski Gasket, which it describes as the "monsters" that have fascinated little Benoit. And, it uses a recurring theme of cauliflower as an example of selfsimilarity in nature. Those form a good start. But, it all went downhill from there from my perspective. The connection between the formula "z=z^{2}+c" (which is mentioned a few times) and the Mandelbrot set is not explained at all. The idea that there is something dynamic (that points are moving under this rule and either staying near the origin or flying away) or that it is being used to select some points (those that stay near the origin forever) and reject others is not even hinted at. And, although the term "Hausdorff Dimension" is tossed around, it is completely misused. (No, it is not a dimension one can go to where things are bigger on the inside than the outside. That's a TARDIS. It is a way to measure how many dimensions a geometric object takes up. If you apply it to a curve like a parabola you get the number 1, that is its Hausdorff dimension, and if you apply it to a disk you get 2 because it is 2dimensional. The thing that makes something a fractal is if its Hausdorff Dimension is not a whole number, if it has a fractional Hausdorff dimension.)
Undoubtedly, I will receive email from readers who disagree with my review. (Please do feel free to do so. If your disagreement is polite and wellwritten, I will even post it here.) But, I would like to point out that there are many works of mathematical fiction in which the math is used magically, metaphorically, and poetically but in a way that still feels and sounds like math. I really love many of them because they can sometimes convey the numinous quality of mathematics to people who may only have previously encountered math as part of a dry classroom experience. Although Mandelbrot the Magnificent seems to be trying to achieve the same thing, it instead trivializes both the mathematics of fractal geometry and the horrors of the Holocaust in a fairy tale that is a bit too simplistic.
