Mathematical

To an applied mathematician, an ideal problem is one that is

• important, in the sense that a solution would significantly expand nonmathematical understanding or capability for positive impact in the world,
• mathematically interesting, in the sense that solving it requires more than a routine application of well known methods,
• unsolved, in the sense that its solution is not implied or inferable with high certainty from existing literature, and
• plausibly tractable, in the sense that it appears underserved by mathematically oriented researchers and is not known to be hard.

Up to notions of mechanistic or computational equivalence, problems that satisfy these four criteria are increasingly rare. Of those remaining, many appear to be located in areas that have received limited academic attention, such as heuristic algorithms or tax policy, and areas that span multiple domains, such as electrophysiology or computational linguistics. I work to find these problems and develop solutions for them. 

Organizational

Some problems nearly satisfy the above four criteria - they are important, unsolved, and plausibly tractable, but are organizationally interesting rather than mathematically interesting. Some of these problems are practical. For example, we might seek to outline

• a better organization of academic literature that accurately identifies the most suitable published work for each research question,
• a cross-platform organization of educational resources from which anyone can find the most appropriate materials for their educational needs and background,
• a new model for healthcare that both improves the process of finding relevant physicians and simplifies delivery of care, or
• a taxation model that incorporates the impact of our transactions on systemic risks such as sovereign default and climate change.

Other unsolved organizational problems have a more fundamental or philosophical nature. For instance, we might attempt to construct

• a formal language of conscious experience,
• a formal definition of causality that is suitable for both scientific and philosophical domains, or
• a formal theory of moral judgments.

Practical and theoretical problems of this sort have been considered extensively in literature, but often in a highly incremental, field-specific manner. My research aims to complement this granular work with a broader, more interdisciplinary study of these problems and their possible solutions.