John C. Butcher works on numerical methods for ordinary differential equations, particularly Runge-Kutta methods and general linear methods. His research connects the algebraic structure of a numerical method with its approximation and numerical stability properties. The Butcher tableau records the stages and weights of a Runge-Kutta method compactly.^[ref]

Homepage: www.math.auckland.ac.nz/~butcher/biography.html

A German mathematician who studied linear differential equations and later held a chair in technical mechanics at Karlsruhe. His work on second-order equations with four singular points led to the Heun equation, extending the family associated with the hypergeometric differential equation.

His name is also attached to Heun's method, a predictor-corrector Runge-Kutta method for numerical integration. The predictor estimates an endpoint slope and the correction averages it with the initial slope. The special-function equation and the numerical method are distinct contributions linked by the study of differential equations, rather than two names for the same construction. ^[ref]

Homepage: mathshistory.st-andrews.ac.uk/Biographies/Heun/

A German mathematician whose work combined numerical analysis with spectroscopy. He studied numerical solution of equations and the measured wavelengths of elemental spectral lines, rather than treating mathematical computation as separate from experimental questions.

His name is attached to the Runge-Kutta method for approximating ordinary differential equations, alongside Martin Kutta. Such methods replace a continuous evolution by a succession of computed time steps. His work on spectral regularities similarly sought structure in numerical measurements. These two interests make him an example of the exchange between practical calculation and mathematical models of physical observations. ^[ref]

Homepage: mathshistory.st-andrews.ac.uk/Biographies/Runge/

Rodolfo Ruben Rosales works in applied mathematics, including nonlinear waves, fluid mechanics, materials science and numerical partial differential equations. His research connects differential equations with physical wave propagation and the numerical methods for approximating those dynamics.^[ref]

Homepage: math.mit.edu/directory/profile.html?pid=228

Steven G. Krantz works in complex analysis, including several complex variables and their connections to harmonic analysis. His research includes boundary behavior and estimates for holomorphic functions, integral operators and the geometry of complex domains. His books develop these analytic and geometric viewpoints as well as introductory real analysis.^[ref]

Homepage: www.math.wustl.edu/~sk/

Daniel Dadush studies mathematical optimization, including linear programming, integer programming, geometry of numbers and discrepancy theory. His work connects the geometry of high-dimensional convex sets with algorithms for mathematical optimization.^[ref]

Homepage: homepages.cwi.nl/~dadush/

Albert W. Tucker worked in topology, game theory and nonlinear optimization. With Harold W. Kuhn he helped formulate the conditions now called the Karush-Kuhn-Tucker conditions, which extend the use of Lagrange multipliers to inequality constraints. He also supplied the familiar name and narrative for the prisoner's dilemma.^[ref] That example makes a mathematical distinction memorable: individually advantageous choices can lead to an outcome both players prefer less than a coordinated alternative. The payoff inequalities, rather than the story alone, define the strategic conflict.

Biography: mathshistory.st-andrews.ac.uk/Biographies/Tucker_Albert/

Harold W. Kuhn connected game theory with continuous and discrete optimization. His work with Albert W. Tucker supplied the1951 nonlinear-programming formulation behind the Karush-Kuhn-Tucker conditions, while his1955 Hungarian algorithm addressed the assignment problem. He also developed extensive-form games and the relation between mixed strategies and behavioral strategies.^[ref] These contributions distinguish three mathematical questions: local constrained optimality, a discrete cost-minimizing assignment, and which randomized decisions can represent a player's information-dependent plan.

Biography: www.princeton.edu/news/2014/07/05/harold-kuhn-princeton-mathematician-who-advanced-game-theory-dies-88

William Karush obtained necessary conditions for inequality-constrained optimization in his1939 master's thesis. The result was independently rediscovered and published by Harold W. Kuhn and Albert W. Tucker, producing the name Karush-Kuhn-Tucker conditions.^[ref] Their distinguishing idea is that an inequality constraint can be active or inactive: a nonnegative Lagrange multiplier pairs with its constraint through complementary slackness. A constraint qualification is needed for the usual necessary-condition theorem; a stationary Lagrangian equation alone is insufficient.

Biography: www.math.u-szeged.hu/~hajnal/courses/MSc_Optimalizalas/2014/Cottle%20-%20William%20Karush%20and%20the%20KKT%20theorem.pdf

A French mathematician who studied linear differential equations, particularly equations with periodic coefficients. His 1883 memoir developed the structure now called Floquet theory: periodic changes can be separated from exponential evolution in a fundamental solution matrix. This reduces a periodically driven linear problem to information accumulated over one period.^[ref]

The Floquet multipliers then determine whether repeated periods amplify or suppress perturbations. The idea is useful in the stability analysis of periodic motions, where a coefficient matrix need not be constant for its long-term growth to be tractable. Floquet's teaching and research career was closely associated with Nancy. ^[ref]

Biography: mathshistory.st-andrews.ac.uk/Biographies/Floquet/

Marco Gualtieri works in differential geometry and mathematical physics, with a focus on generalized geometry. His own research page identifies that focus rather than presenting him only as an instructor.^[ref] The geometric viewpoint concerns structures carried by a smooth manifold, where tangent directions and covectors can be studied together. It connects the study of complex geometry and symplectic geometry with mathematical descriptions of physical fields.

Homepage: www.math.toronto.edu/mgualt/

Instructor for the 2012 Topology I: smooth manifolds (MAT1300HF) course; the course information explicitly identifies his role as instructor.

John M. Lee is a mathematician working in geometry and topology, and the author of textbooks on topological manifolds, smooth manifolds, Riemannian manifolds and complex manifolds. His expository work develops the different structures that can be placed on a manifold, from local coordinates on topological manifolds to differentiability and Riemannian geometry.^[ref]

Homepage: sites.math.washington.edu/~lee/

A mathematician whose research includes probability theory, stochastic processes and statistics.^[ref]

Homepage: www.randomservices.org/Siegrist.html

A mathematics educator and senior contributing author of Prealgebra 2e.^[ref]

A mathematics educator and senior contributing author of Prealgebra 2e.^[ref]

A mathematics educator and senior contributing author of Prealgebra 2e.^[ref]

An electrical engineer working in signal processing. ^[ref]

He authored lecture notes and transparencies. ^[ref]

Michael R. Clarkson is a computer scientist whose teaching connects practical computer programming with reasoning about correctness. His work includes OCaml Programming: Correct + Efficient + Beautiful by Michael R. Clarkson and others, which develops functional programming, data structures and methods for specifying and checking program behaviour.^[ref]

One characteristic example separates an abstraction function from a representation invariant. A list can represent a mathematical set, but an implementation that assumes no duplicate entries must maintain that condition after every operation. The explanation shows how an abstract interface is justified by concrete representation rules.^[ref]

Marijn Heule is a computer scientist whose work connects Boolean satisfiability solving with machine-checkable mathematical proofs. With Emre Yolcu and Xinyu Wu, he studied proofs of the colouring requirements of Mycielski graphs.^[ref]

Their study separates two questions: does a short proof exist in a specified proof system, and can an automated solver find it efficiently? Constructing and checking a proof answers the first without automatically answering the second. The distinction helps explain why stronger proof rules alone do not settle the practical difficulty of proof search.^[ref]

Xinyu Wu is a computer scientist whose research has included the theoretical foundations of quantum computing, pseudorandomness in quantum states and quantum channels. A 2021 Carnegie Mellon research profile describes this combination of tools from mathematics, physics and computer science.^[ref]

With Emre Yolcu and Marijn Heule, Wu also studied the complexity of proving colouring properties of Mycielski graphs. Their work connects short formal proofs with experiments on automated proof search.^[ref]