Increasing Specialization: Why We Need to Make Mathematics More Accessible.

Mathematics is becoming increasingly specialized, divided into a vast and growing number of subfields. While this division of cognitive labor has important benefits, it also has a significant drawback: it can sometimes impede mathematical progress by making it difficult for mathematicians to make connections to subfields other than their own. Mathematicians can address this by making their own subfield more accessible to researchers working in other areas. One way they can do this is by engaging in exposition, as I illustrate with the User's Guide Project in algebraic topology. However, the current reward structure of mathematics does not appropriately credit mathematicians who make their subfields more accessible via exposition. I thus conclude that the reward structure of mathematics should be changed to more highly value such work, with changes being adopted at the level of departments, professional societies and funding agencies. [ABSTRACT FROM AUTHOR]