(An editor explained last week: when the title of an article is a question, the answer is “no.”)
Just last year two Fields medals were given to nationals of countries outside the OECD and a third to an Indian-Canadian with a deep and active interest in Indian culture. With the ICM traveling from India to Brazil by way of South Korea, is it time to proclaim the end of the division between first-world and other mathematics and the beginning of the era of one-world mathematics?
Without going so far as to examine and compare the material resources available for research in wealthy and less wealthy countries — maybe I will report on the IMU’s efforts in this direction in the future — it suffices to look at the professional affiliations of members of editorial boards of the most prestigious journals to recognize the continued overwhelming dominance of Europe, North America, and Japan in institutional mathematics.
This problem, like the gender question in mathematics that this blog will soon take up, probably as early as next week, is simply too vast to be addressed by a single individual with dubious credentials. Instead, I chose in certain chapters to highlight the existence of traditions in the philosophy of mathematics that arose outside the European continent and whose relation to the Greek tradition is at least not straightforward. My primary objective was to inject some doubt into mainstream philosophical accounts of the nature and goals of mathematics. If mathematics developed and thrived in a variety of cultures with little or no influence from Greek metaphysics (as in India and East Asia) or whose relations Greek metaphysics are complex and contradictory (as in medieval Islam), then perhaps we should have less confidence in the universalizing pretentions of mainstream (European and North American) philosophy to ground mathematics in considerations that derive from (contemporary readings of) the preoccupations of Greek metaphysics.
My credentials for answering these questions are less than dubious, but I suppose I’m entitled to ask them, while waiting for someone more clearly qualified to take over. As I write in the preface,
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies… are occasionally (too rarely) accompanied by no less exciting comparative philosophy…
Here I want to stress the “too rarely” and express my hope that this will soon change.