Why has the MPE2103 movement been popular with mathematicians? The traditional view of mathematicians is that they like to work in solitude and that there is a great divide between pure and applied mathematicians. So how has MPE2013, a massive collaborative effort on the part of pure and applied mathematical scientists, managed to bridge this chasm? It seems to me that there has never before been such a unified effort on the part of the mathematical sciences community, nor has the level and scale of collaboration been so apparent. To give you an idea of the scope, this year in MPE there will be more than 10 long-term programs, 60 workshops, dozens of special sessions at society meetings, two big lecture series, summer and winter schools for graduate students, research experiences for undergraduates, an art competition and traveling exhibition, and the promise that high-quality curriculum materials for all ages and grades will be developed this year—all of this coordinated by the more than 120 partner organizations. I’m pretty sure this level of effort and cooperation is unprecedented in the annals of mathematics.
I think there are two explanations for the success of this initiative. One is that mathematical scientists have become far more collaborative than they used to be. Fifty years ago the average number of co-authors was 1.3 researchers per paper. Now it is more than 2. While it is common in the experimental sciences to have dozens of or even a hundred co-authors on a single publication, the record in pure mathematics until a few years ago was surely fewer than 10. There were 28 co-authors on the paper recently posted to the arxiv, which is now believed to be the record. This new degree of collaboration is undoubtedly due to the internet, the computer age, the ease of collaboration, and the fact that more and more workshops are devoted to creating and promoting collaborations.
The second explanation is that it is becoming clearer to mathematicians that they have something tangible, something important to offer to the consideration of the problems of the planet. Many of the issues such as weather, climate, climate change, spread of disease, natural hazards and financial distortions lead to the creation of seriously complex mathematical models. Computers can quickly give us far more data than before, which leads to feedback and refinements of the models. Importantly, this process has also opened the door to new mathematical ideas that can enhance the modeling process. I am amazed by the way that pure mathematics can help with problems which were previously considered the sole domain of applied mathematics with its stock set of tools and methods. G. H. Hardy, the British
number theorist, used to pride himself on his subject being so pure that there was virtually no chance for applications. But the fact that finding large prime numbers is easy, whereas factoring large composite numbers is hard, paved the way for the current ubiquity of internet security algorithms based on number theory. Large data sets can now be analyzed using algebraic topology to model the clusters. Statistics has been invaded by algebraic geometry. The high-brow theory of percolation within statistical mechanics is used to study ice. Modeling phase transitions is a seriously complicated endeavor that uses some of the most sophisticated mathematics around. Uncertainty quantification is a new field that can give new information about the likelihood of rare events occurring. Data assimilation is another important new tool. Perhaps it is becoming clearer that there is the opportunity for pure mathematicians to apply their know-how in ingenious ways to weigh in on some of the big problems that we face. Having a role for all mathematical scientists, I think, is the second factor that accounts for the apparent success of the MPE2013 initiative.
A word of warning: mathematics moves slowly. We can’t expect great results from just one year of work. But we are off to a great start!
Brian Conrey, Director
American Institute of Mathematics