Adam Kirsch in Tablet Magazine [h/t:Tunku Varadarajan]:
Mandelbrot’s life work was to develop mathematical tools able to measure that kind of fiendishly difficult, real-world complexity. The challenge facing The Fractalist is that it is almost impossible for a non-mathematician to advance beyond these generalities and understand what precisely it is that Mandelbrot accomplished. Knowing this, he allows no mathematical formulas or notation in the book—the formula for the Mandelbrot set is the sole exception. It is clear enough, however, that the mathematics Mandelbrot worked with has nothing to do with the kind most of us learned in school; it is infinitely more creative and exciting. His own gift, he writes, was an intuitive ability to “see” complex shapes. As a student, he could solve difficult problems much faster than the rest of the class by turning equations into mental geometry: “In no time, searching for and studying symmetry became central to my work … hopelessly complicated problems of integral calculus could be ‘reduced’ to familiar shapes that made them easy to resolve.”
For this reviewer, reading The Fractalist is rather like reading about a poet who wrote in a foreign language for which no adequate translation is available. You know Mandelbrot is up to exciting things, but you have to take them mostly on faith. What he can share, and does copiously, are the steps of his worldly career: the professorial appointments, the job as a researcher at IBM, the papers published and colleagues courted and impressed. There is so much of this kind of thing in the second half of The Fractalist that it comes to read like an annotated CV, and it has the effect of making Mandelbrot seem very vain. But then, this is a man who decided early in life that he wanted to be a second Kepler, founding a new field of study and revolutionizing humanity’s picture of the world. (In his own view, he accomplished this: “In my Keplerian quest I faced many challenges. The good news is that I succeeded.”) All of this sits oddly with his later declaration that “a memoir is a lesson in humility.”