Mathematics for the liberal arts (2013)

Part I. MATHEMATICS IN HISTORY

Chapter 3. MODERN MATHEMATICS

3.5 The Future

This too shall pass.

ANONYMOUS

Mathematics has never been more vibrant than now. There are thousands of research mathematicians the world over, publishing original mathematics in hundreds of journals. A meeting of the main American mathematical societies in 2012 had almost 7200 registered participants. The International Conference of Mathematicians, held every four years, had representatives of more than 100 countries at its 2010 conference in Hyderabad, India. What might the future hold?

Predicting what mathematics will be developed is difficult for lesser mortals than David Hilbert. We can ask ourselves, however, in light of our knowledge of the history of the subject, whether and in what form the current golden age might continue.

First, there are several reasons to believe that it will continue, at least in the coming decades. One is the sheer number of mathematicians. The second is geographical distribution. The Fields Medal, the highest honor bestowed on researchers, has been awarded to 52 mathematicians, representing institutions in 10 countries. This widespread distribution suggests that, if support for mathematics declines in one or two major countries, there will be a haven for scholars in others, much as the United States was a haven for so many scholars fleeing Hitler.

The institutional base for mathematics has never been stronger. In first place among the institutions are the universities. But there are other important homes to mathematical research, including institutions such as the Institute for Advanced Study in Princeton, New Jersey, and corporate research labs such as Bell Labs in New Jersey or IBM Thomas J. Watson Research Center in New York. The largest employer of mathematicians in the United States is the National Security Agency.

The broad institutional support is a reflection of the breadth of mathematical applications in modem society, from traditional applications in the physical sciences, to more recent ones in communications, computing, statistics, biology and elsewhere. As long as mathematics is seen as essential to applications, the support is likely to continue.

Mathematics is healthy, but history has taught us that local conditions can and do often change. The center of research mathematics moved from Europe to America in the 20th century, although Europeans are still very active. Recently, the rise of Asia has been remarkable. The first Fields medalist based in Asia, Shigefumi Mori at the

University of Kyoto, won the award in 1990.¹ There is no reason not to expect that such geographical changes will continue.

Predicting the status of any cultural institution centuries in the future is futile. Physical conditions can change. As Will Durant wrote: “Civilization exists by geological consent, subject to change without notice.” In addition, human societies are always changing, not always for the better. In this time of anti-evolution crusades and professional global warming skeptics, it is natural to reflect on the fragility of society’s support of research. The linguist Nicholas Ostler put it this way. (He was primarily interested in the effect of science on the spread of English.)

Dispassionate enquiry has never been an activity that appeals to a majority, however widely education is made available. Serious research remains a minority activity, which because it is disinterested will always need patronage from others who have accumulated power or wealth. But those political, military, business or religious elites cannot be trusted, especially if it seems that the results of enquiry are telling against their own power, or failing to buttress it: they will then often adjudicate in favor of tradition, or popular ignorance. It is easy to forget how much the ongoing popularity of science depends on its continuing to offer new golden eggs, or new golden bombs. When the flow of goodies slackens, as one day it may, the pursuit of science will be widely seen as an expensive indulgence by its paymasters, in industry and government.

NICHOLAS OSTLER (B. 1952)

¹ “Earth at Night.” C. Mayhew and R. Simmon (NASA/GSFC), NOAA/NGDC, DMSP Digital Archive.

¹ Florian Cajori, A History of Mathematics, fifth edition, Chelsea, New York, 1991.

² David Eugene Smith, History of Mathematics, Volume I, Dover, New York, 1951.

¹ The proposition that the equation xⁿ + yⁿ = zⁿ has no nontrivial solution for n ≥ 3 is Fermat’s Last Theorem (more about that in Chapter 5).

¹ NP stands for “nondeterministic polynomial.”

¹ Mori was not the first Asian-born Fields recipient, however. There have been several others, starting with Kunihiko Kodaira in 1950, who worked at the Institute for Advanced Study. As always, centers of scholarship are magnets for immigrants.