MediMath Science

This blog examines a recurring pattern that has persisted in mathematics since the mid-20th century. A substantial fraction of highly capable researchers devote their efforts to extending or resolving longstanding theoretical problems inherited from earlier generations. This, in itself, is not surprising—mathematics is inherently cumulative, and deep problems often require decades of sustained attention. What is striking, however, is the scale of this concentration. Today, the global population of mathematicians exceeds, by a wide margin, the total number that existed prior to the mid-20th century. At the same time, the set of mathematically grounded problems emerging from modern society—ranging from medical imaging and data-driven modeling to complex systems and engineering constraints—has expanded dramatically. Yet a significant portion of mathematical effort remains focused on classical, internally defined questions rather than on these rapidly growing external demands. At first gla...

 In recent years, many discussions of innovation policy have emphasized the need to “tolerate failure.” While I strongly agree with this principle, I worry that the slogan risks diverting attention from a more fundamental issue: the structure of research evaluation and the design of public R&D investment. Encouraging risk-taking alone does not explain why the descendants of successful entrepreneurs in countries such as Japan and Korea often become effective long-term managers and R&D investors, nor why governments that rely heavily on expert committees frequently struggle to achieve comparable innovation outcomes. The repeated call to “accept failure” can therefore oversimplify the problem. Many researchers are not avoiding risk because they fear failure. Rather, the structure of academic incentives often encourages work that is theoretically elegant and readily publishable rather than work that addresses long-term, system-oriented technological challenges. As a result, res...