Today, I am going to pick on Vladimir Voevodsky, who is certainly an interesting enough fellow in his own right someone who is trained in mathematics (which is his disciplinary field as a professor) with strong interests in problems relevant to fundamental physics and to population genetics. As I note below, if we ever run into each other, I owe him a few drinks for subjecting him to a somewhat down beat assessment of the individual life accomplishments of this extraordinary man in my post today. But, today, I am more interested in talking about the personal niche he is in, which is shared by a great many others, than is personal accomplishment per se.
Voevodsky in a middle aged guy (he is a few years older than I am, but our years studying at institutions of higher education in the United States overlapped) who did his undergraduate work in Moscow, left to the U.S. to do graduate work at Harvard around the time that the Soviet Union fell, is a math professor at Princeton, and won a Field medal, which is basically the Nobel Prize of mathematics, in 2002. He is by any reasonable account a genius.
Voevodsky, like some many other geniuses, however, is an obscure genius. According to a colleague writing a short biography of him, "he defined and developed
motivic cohomology and the A1-homotopy theory of algebraic varieties; he proved
the Milnor conjectures on the K-theory of fields."
Don't be ashamed that you have no idea what that means. I struggle to understand it, and I skipped to years of undergraduate math in college and instead spent all three of my years in college taking 300 and 400 level math courses. Unless you have taken abstract algebra, topology, and real and complex analysis, which are typically offered as 400 level undergraduate course to mathematics majors or 500 level courses for graduate students, you really have not a prayer of meaningfully understanding even a non-specialist oriented description of what is work involves. Few people who aren't professionals in the relevant field know his name (those who are professional in the relevant field hold him in very high esteem), and not even is they are sophomore or junior math majors at esteemed colleges and universities do (other than Princeton, of course).
Voevodsky's name isn't familiar to politicians and journalists (except a handful of very sharp science journalists with good memories), won't earn him VIP seats at a ballgame or a nice restaurant outside his home town, and probably gets spelled wrong on his junk mail. A decade from now, more people will remember the name of Missy Franklin, a Denver high school student who won a gold medal for swimming in this year's Olympics, than remember today his shining moment in the sun during the year when he was recognized that year as one of the world's premier mathematicians.
None of this is to put him down. If I met him, I'd know his name and I'd certainly look forward to sharing a beer and talking shop in some dark pub (being Russian, he might be a vodka man, and that would be cool too), my treat.
My point is that our very civilization as an advanced complex technological society rests of the collective achievements of thousands of people like him - the creme de la creme of the upper middle class in who excel in a whole panoply of sometimes obscure professional endeavors. They generally live comfortable upper middle class lifestyles, but are usually neither famous nor genuinely rich on the scale of the thousands of people who have net worths of a hundred million dollars or more. Economically, they live the lives of other successful middle managers in big business and professionals who aren't top level employees of law firms and big businesses.
In truth, we could survive without any one of them and wouldn't know the difference. Lots of people wonder what more could have been discovered is Shakespeare had written another play, if Percy Shelly had written another poem, if Feynman had survived another decade, if Mozart had finished another symphony, or if Fermat had been able to work full time on mathematics rather than merely doing it as a hobby. But, were he to be hit by a bus today, nobody but his family, his graduate students, and his fellow department members at Princeton will dwell on what further conjectures in group theory or topology Voevodsky might of proved or proposed beyond his already formidable accomplishments in another decade once he completes his career. Collectively, the impact of obscure geniuses like Voevodsky in a whole range of professions, is enormous. The group effort that is the produce of their endeavors keeps science and the organization of our society moving ever forward.
This situation certainly isn't particular to mathematics. There are six thousand scientists working at the Large Hadron Collider for instance, many of them doing truly intellectually demanding, cutting edge physics every day, on deadline, as a matter of course and these near geniuses have to have enough social skills to be team players as well. Probably at least one or two hundred of them are geniuses who have made contributions to the enterprise that really no one but a genius could manage and are highly esteemed in their field by their colleagues who can understand their accomplishments and talents. But, fewer than a dozen of them will ever be any more famous than Mr. Voevodsky, even to new generations of students within their field.
Mr. Voevodsky is also notably, not just as an individual Russian mathematician, but also as a member of a numerically small mass migration of the creme of the intellectual elite for the former Soviet Union and Eastern Europe that experienced economic collapse before the recovery began again to the West and, in particular, in large numbers to the United States. The world hadn't seen anything like it since the years immediately before and after World War II. This mass migration of this key elite population has had a rise and fall of great powers level of significance in geopolitics and science that several studies of elite performances in the sciences have documented, although it is little known. It had breathed new blood and new ideas into American science, technology and academics, exposing technical scientific knowledge and ideas that had been isolated in the Eastern block and was little known outside it to a much wider audience where the new ideas have cross-pollinated with Western ones.
Maybe one somewhat obscure Field medal class mathematician like Voevodsky will accomplish in his professional life is a tenth or a twentieth of what a mathematical legend known to all math students at the high school level and beyond, like Euler, did. But, there are at least ten or twenty mathematicians of Voevodsky's caliber, probably more, alive today and they are all working hard at their crafts and standing of the shoulders of the giants who came before them. They also have more colleagues who can understand their work and help prod them on to greater achievements with their own insights. And, very few of them are likely to die young and have their potential prematurely cut short, unlike so many of the famous geniuses of earlier times.