Mathematical Ageism
For nearly two decades, I have studied the life cycles of creativity: when in their lives do innovators make their greatest contributions? I have discovered - contrary to the conventional wisdom - that in many intellectual activities, there are two distinct life cycles, each associated with a different kind of innovation. One is that of the conceptual young geniuses who make sudden, dramatic leaps to radical new forms - Einstein, Picasso, Welles, Plath. The other is that of the experimental old masters, who work gradually by trial and error toward profound new results - Darwin, Cézanne, Woolf, Hitchcock.
In empirical, micro-level studies, I have found both conceptual young geniuses and experimental old masters among the very greatest painters, sculptors, poets, novelists, architects, filmmakers, photographers, songwriters, scientists, and entrepreneurs. Occasionally, someone asks me if there is any activity that is inherently experimental or conceptual. My speculation has been that there may be two, mathematics and chess, that are so abstract that innovators must necessarily be conceptual. But according to the mathematician Manil Suri, this is actually not true of mathematics.
Writing in the New York Times, Suri reviews the powerful prevailing notion that important mathematical discoveries are only for the young. And he notes that this idea owes its strength to the belief that mathematical originality requires the absence of established habits of thought - exactly the basis of conceptual creativity. But he then observes that this belief is mistaken. His counterexample is the wise old master Ivo Babuska, whose most-cited paper, published when he was 70, "contains one of those clarifying, deceptively simple-looking ideas that can emerge only with the deep and broad insight of a long career." This is the essence of experimental creativity.
I have previously argued for the rejection of ageism in a wide range of intellectual activities. Manil Suri has now added mathematics to that group, "as a field with diverse goals and needs, where people can expect to make useful contributions regardless of gender or age." Our society has devoted enormous effort to overcoming racism and sexism. It is time for us to give the same condemnation to ageism.