2005 : WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?

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Sterling Professor of Mathematical Sciences, Yale University; IBM Fellow Emeritus (Physics) at the IBM; author, The Fractalist; Memoir of a Scientific Maverick
Mathematician, Yale University; Author, The Fractal Geometry of Nature

Wandering through the frontiers of the sciences, and the arts, I have always trusted the eye while leaving aside the issues that elude it. It can mislead—of course—therefore I check endlessly and never rush to print. 

Meanwhile, for over fifty years, I have watched as some disciplines exhaust the "top down" problems they know how to tackle. So they wander around seeking totally new patterns in a dark and deep mess, where an unlit lamp is of little help.

But the eye can continually be trained and, long ago, I have vowed to follow it, therefore work "from the bottom up." Like the Antaeus of Greek myth, I gather strength and persist by often touching the earth.

A few of the truths the eye told me have been disproven. Let it be. Others have been confirmed by enormous and fruitful effort, and then blossomed, one being the four thirds conjecture in Brownian motion. Many others remain, one being the MLC conjecture about the Mandelbrot set, in which I believe for no other reason than trust in the eye.