Zhang Yitang asserted that mathematical work is confined to location than many other academic pursuits because a mathematician can think, research, and solve problems, independent of their location. History supports his position. Newton developed calculus while working at the farm in Woolsthorpe. Ramanujan made many remarkable mathematical discoveries while he was working independently in India. And Erdös traveled widely, visiting a large number of mathematicians in their homes, and together in kitchens and home offices, turned out research papers. Most recently, Sir Andrew Wiles proved Fermat’s Last Theorem, working mainly in isolation and Perelman solved the Poincaré Conjecture and merely published his proof on line.
Of course, there are advantages to being located in a university mathematics department when your are surrounded by others working in your field of interest. Seminars, conversations and presentations create a cross pollination of ideas that often spark new inspirations. Also, the psychological stimulation of working in an environment in which everyone is striving to solve problems and publish papers can be a strong incentive. Whether a mathematician prefers to work alone in isolation or together in a structured environment generally depends upon the psychological mindset of that person. By contrast, experimental physicists and chemists are often tied to expensive equipment in a particular location and have no option, but to work on that site.
However, it is important to be affiliated with a university if you wish to have your mathematical discoveries published, because no one wants to read a paper submitted by someone who has no academic credentials. Hundreds of papers proposing solutions to outstanding problems remain unread because they are assumed to come from “crackpots” and no journal editor wants to wade through reams of mathematics to discover an error in a paper submitted by an unknown with no academic credibility. We will never know whether some “crackpot” has proved or disproved the Riemann hypothesis, although it is not likely.
So, Zhang Yitang’s comments are, for the most part, quite valid as long as the isolated mathematician has links to the mathematics community.
