The Mathematician’s Shiva by Stuart Rojstaczer Read Free Book Online

anyone who could show that the Navier-Stokes equation was indeed appropriate for all conditions, even turbulent ones. You can do a lot with $1 million, of course. But the money associated with a Millennium Prize isn’t really an incentive. It’s used as a symbol of importance, to show that a community views the solution of a problem to be so enormously difficult that it is willing to offer a ridiculous amount of money to anyone who can solve it.
    Even before this million-dollar prize was offered it was recognized just how near impossible this problem was. Hilbert knew it. Kolmogorov, who had studied turbulence, knew it. My mother, who studied turbulence with Kolmogorov and unlike him continued her research in this field, of course knew it as well.
    It is one thing to derive this equation and another to truly understand it. When I see the Navier-Stokes equation, it comes to life for me. It’s not just an abstract combination of symbols that will eventually produce numbers. It is a living and breathing description of fluids dancing in space to whatever may be whipping them around. I can see the fluids. I can imagine clearly the forces upon them as they move in a way that is semi-ordered but ultimately unpredictable.
    Actually, it’s more than this. The big
D
in the Navier-Stokes equation is called the material derivative, and it refers to watching velocities of fluid change not from a fixed reference frame but from one in which you are riding with the storm. When I think of Navier-Stokes, sometimes I imagine myself as a Lilliputian in a tiny canoe that has been lifted up and tossed high into the hurricane. The wind is so strong that it lifts my cheeks, distorting them as if the storm were a real-life version of a fun-house mirror. I watch as the fluids careen against and flow around me.
    As well as I can visualize these fluids dancing, I know that my mother could see them even better. She couldn’t describe what she saw to me in any concrete way, but I know from her work just how much more ornate, nuanced, and ultimately more accurate her vision was than mine. That’s why she was a mathematician, the best of her generation. That’s, obviously, why I am not.
    The problem of the universal appropriateness of the use of the Navier-Stokes equation was the problem that my mother was rumored to have cheated death to solve. Where does such a crazy idea come from? I submit to you the following evidence: my mother, a seventy-year-old woman, ill, taking medications several times a day that made her throw up, weak, unable to realistically command anywhere near the concentration required to solve such a problem, and far too old, even if healthy, to have the freshness of mind to make any headway on such a task. Who could possibly think my mother could somehow capture the magic necessary to answer a question that had baffled mathematicians, the greatest and brightest minds, for more than a century? Here is one simple answer. Mathematicians can think like this. Impossible problems perhaps require impossible scenarios. Since no one young and healthy had solved this problem, perhaps someone old and sick, by sheer will, could.
    Here is another answer. Only crazy people can think like this. And mathematicians are, as my uncle would say,
szalency
, inherently crazy dreamers. They have no real sense of what can and can’t be done. They work on impossible problems because they are impossible people. As I’ve noted, there are likely no reasonable geniuses in this world. While there are, I know from personal experience, some reasonable mathematicians, they are not at the forefront of their profession but mere worker bees. Even most worker bees in mathematics are hopeless as fully functioning human beings.
    For better or worse, I’m stuck with them. They are all I’ve ever known. I grew up around them. They are my family. I love them wholeheartedly. After a brief and unsuccessful effort at trying to pull away from this intensely dysfunctional