arXiv subjects

Ron Buckmire

Publications and source records attributed to Ron Buckmire.

5 recordsLinked to original sources

arXiv2026

A Discrete-Time Model of the Academic Pipeline in Mathematical Sciences with Constrained Hiring in the United States

The field of the mathematical sciences relies on a continuous academic pipeline in which individuals progress from undergraduate study through graduate training and postdoctoral program to long term faculty employment. National statistics report trends in bachelor's, master's, and doctoral degree awards, but these data alone do not explain how individuals move through the academic system or how structural constraints shape downstream career outcomes. Persistent growth in postdoctoral appointments alongside relatively stable faculty employment indicates that degree production alone is insufficient to characterize workforce dynamics. In this study, we develop a discrete time compartmental model of the academic pipeline in the field of the mathematical sciences that links observed degree flows to latent population stocks. Undergraduate and graduate populations are reconstructed directly from nationally reported degree data, allowing postdoctoral and faculty dynamics to be examined under completion, exit, and hiring processes. Advancement to faculty positions is modeled as vacancy limited, with competition for permanent positions depending on downstream population size. Numerical simulations show that increases in degree inflow do not translate into proportional faculty growth when hiring is constrained by limited turnover. Instead, excess supply accumulates primarily at the postdoctoral stage, leading to sustained congestion and elevated competition. Sensitivity analyses indicate that long run workforce outcomes are governed mainly by faculty exit rates and hiring capacity rather than by degree production alone. These results demonstrate the central role of vacancy limited hiring in shaping academic career trajectories within the field of the mathematical sciences.

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arXiv2026

A dynamical model of the U.S. mathematics graduate degree pipeline

We present a latent-stock compartmental framework for modeling degree production systems when only completion flows, rather than enrollments, are observed. Applied to U.S.\ mathematics degrees from 1969 to 2017, the model treats master's and PhD populations as latent compartments -- unobserved state variables that are inferred indirectly because they generate the observed completion flows -- with time-varying routing fractions and completion hazards. Using information-criterion model comparison across a grid of specifications, we find strong support for smooth nonlinear time variation in routing fractions and hazards, while models with explicit international forcing are disfavored. The preferred model achieves a log-scale root mean squared error of approximately 0.036, corresponding to a typical multiplicative error of about 4\% in fitted degree counts, and highlights key structural shifts in the graduate pipeline: the master's pathway became increasingly central to PhD production through the late twentieth century before weakening, while direct bachelor's-to-PhD entry remained small but persistent. Estimated completion hazards for both degrees rise over time, indicating faster effective turnover in the graduate compartments. Methodologically, our main contribution is a latent stock dynamical approach that recasts linked degreecompletion time series as a coherent stock-flow system when intermediate enrollments are unobserved, making explicit both what features of pipeline dynamics are identifiable from completion data alone and what limitations such data impose.

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arXiv2023

Quantifying and Documenting Inequity in PhD-granting Mathematical Sciences Departments in the United States

We provide an example of the application of quantitative techniques, tools, and topics from mathematics and data science to analyze the mathematics community itself in order to quantify and document inequity in our discipline. This work is a contribution to the new and growing interdisciplinary field recently termed "mathematics of Mathematics," or "MetaMath." Using data about PhD-granting institutions in the United States and publicly available funding data from the National Science Foundation, we highlight inequalities in departments at U.S. institutions of higher education that produce PhDs in the mathematical sciences. Specifically, we determine that a small fraction of mathematical sciences departments receive a large majority of federal funding awarded to support mathematics in the United States. Additionally, we identify the extent to which women faculty members are underrepresented in mathematical sciences PhD-granting institutions in the United States. We also show that this underrepresentation of women faculty is even more pronounced in departments that received more federal grant funding.

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arXiv2023

The Mathematics of Mathematics: Using Mathematics and Data Science to Analyze the Mathematical Sciences Community and Enhance Social Justice

We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community. We engage in this project with a focus on including research that highlights, documents, or quantifies (in)equities that exist in the mathematical sciences, specifically, and STEM (science, technology, engineering, and mathematics) more broadly. We seek to enhance social justice in the mathematics and data science communities by providing numerous examples of the ways in which the mathematical sciences fails to meet standards of equity, equal opportunity and inclusion. We introduce the term ``mathematics of Mathematics" for this project, explicitly building upon the growing, interdisciplinary field known as ``Science of Science" to interrogate, investigate, and identify the nature of the mathematical sciences itself. We aim to promote, provide, and posit sources of productive collaborations and we invite interested researchers to contribute to this developing body of work.

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arXiv2023

On definitions of "mathematician"

The definition of who is or what makes a ``mathematician" is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline -- both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to examine and challenge systemic barriers that exist in certain spaces of the community. This paper explores and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, we present a framework of definitions based on identity, function, and qualification and exploring several different meanings of ``mathematician". By interrogating various definitions, we highlight their risks and opportunities, with an emphasis on implications for broadening and/or narrowing participation of underrepresented groups.

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