Mandelbrot was able to take the lessons he learned in financial prices and other wide ranging fields of interest and tie it back to his core area of strength – mathematics. The Mandelbrot set is named. By thinking of fractal math as dimensions defined by fractions, rather than whole numbers, he further extended humanity’s ability to name and study this field.

Best Quote(s)

“And I understood from readings and course material that a field might simply die for lack of manageable and interesting unsolved questions.” 3848

Benoit Mandelbrot, Chapter 25, Location 3848

Mandelbrot thought about fields of study as a social construct, which required the intrigue, interest and commitment of individual scientists to grow and prosper.

“Stephen Jay Gould (1941–2002), a lively paleontologist with multiple appointments at Harvard. Quite independently, we had become two very visible champions of discontinuity—he in paleontology and I in the variation of financial prices.” 3825

Benoit Mandelbrot, Chapter 25, Location 3825

Good products have competitors. Products that don’t have a competitor warrant skepticism in their review. Gould’s framing of discontinuity in the fossil record – known as punctuated equilibrium, explained the fractured lineages of the fossil record by explaining them as bursts of fast moving periods of evolution.

Page by Page, Screen by Screen, Swipe by Swipe

3794

“These pictures were intriguing objects I then called lambda and mu-ma—alternative ways of representing a fundamental new mathematical structure that became known as the Mandelbrot set. It has been called the most complex object in mathematics, has become a topic of folklore, and remains my best and most widely known contribution to knowledge.”

3809

A Luncheon That Changed a Life

“Stephen Jay Gould (1941–2002), a lively paleontologist with multiple appointments at Harvard. Quite independently, we had become two very visible champions of discontinuity—he in paleontology and I in the variation of financial prices.”

3825

Physics in Broken Dimension

3831

“Most of our papers concerned spaces where dimension is not 1, 2, 3, or higher but a fraction, and brought fractals toward the mainstream of statistical physics.”

Amnon Aharony, a physicist from Tel Aviv University

“This led me to put forward a bold conjecture: that solving the usual partial differential equations of physics can yield either familiar and expected smoothness, or fractality.”

3842

“Early in life, I learned that for a scholar, nirvana is to take an unsolved problem that had been stated long before and solve it.”

3848

“And I understood from readings and course material that a field might simply die for lack of manageable and interesting unsolved questions.”

3864

A Turning Point in Mathematics

3887

“Thought wanders to Napoleon’s saying that a good sketch, in all its complexity, is worth a thousand words, or even to the biblical Let there be light.”

3915

“My answer distilled—once again—the already told story of my scientific life: when I seek, I look, look, look, and play with pictures. One look at a picture is like one reading on a scientific instrument. One is never enough.”

3931

Zigzagging Through the First Course Ever on Fractals

“The personal computer had not yet hit the world,…”

3937

“I was expected to pursue and teach my style of using computers, but computers and their use were not welcome at Harvard. Hence, there was a near-total absence of both equipment and skills among the students and faculty.”

Wide Wonder, Complexity, and Mystery

3961

“…for the Mandelbrot set, many view it as extremely—miraculously!—complex. I feel exceptionally privileged that my wanderer’s life led me to be the agent of this discovery.”

3966

Never before described, “The title is “Fractal Aspects of the Iteration of [Quadratic Maps] for Complex [Parameter and Variable].” It appeared in late 1980 in Annals of the New York Academy of Sciences.”

3982

Annual mirabilis? “… was a year of a single miracle that developed slowly over time, while the 1979–80 miracle came on like lightning—as miracles should.”