Regardless, one cannot help but marvel that the movement of security prices, the motion of molecules, and the diffusion of heat could all be of the s… - Benoit Mandelbrot

My work is more varied than at any other point in my life. I am still carrying out research in pure mathematics. And I am working on an idea that I had several years ago on negative dimensions. … Negative dimensions are a way of measuring how empty something is. In mathematics, only one set is called empty. It contains nothing whatsoever. But I argued that some sets are emptier than others in a certain useful way. It is an idea that almost everyone greets with great suspicion, thinking I've gone soft in the brain in my old age. Then I explain it and people realise it is obvious. Now I'm developing the idea fully with a colleague. I have high hopes that once we write it down properly and give a few lectures about it at suitable places that negative dimensions will become standard in mathematics.

One of my conjectures was solved in six months, a second in five years, a third in ten. But the basic conjecture, despite heroic efforts rewarded by two Fields Medals, remains a conjecture, now called MLC: the Mandelbrot Set is locally connected. The notion that these conjectures might have been reached by pure thought — with no picture — is simply inconceivable.

The thought that one unifying idea should continue forever is simply not realistic and therefore not to be hoped for, but I think that for quite a number of years still, perhaps if I am lucky to the end of my life, because I would hate to see that stop in my lifetime, those questions will become very active and still somewhat separate, as different branches of learning become accustomed to them. I cannot imagine that this idea would vanish, not because I am so proud of what I've been doing all my life, but because this is not an artificial thought coming from nowhere in no time and vanishing again rapidly in no time. It has in every one of its manifestations profound roots in the history of the various sciences and the various manners of human enterprise and those roots will not be broken. The continuity of these thoughts will continue, and if any substitute comes, if any other name comes, which is possible, the ideas will remain.