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Rudolf Peierls introduced an argument explaining how a two-dimensional Ising model can sustain magnetic order at low temperature. A reversed island of spins has a boundary whose energy cost grows with its length. The number of possible boundaries also grows, but sufficiently low temperature suppresses their Boltzmann weights strongly enough for order to survive. The Peierls argument makes the competition between energy and the number of fluctuations explicit, helping explain why dimensionality changes collective magnetic behavior.^[ref]

A physicist associated with the Peierls transition and the Peierls argument.

Hans-Joachim Queisser and William Shockley calculated an ideal efficiency limit for a single-junction solar cell using detailed balance. The cell must emit as well as absorb photons, and radiative recombination therefore limits the electrical work extracted from illumination even when other losses are removed. Their 1961 analysis varies the band gap and allows a specified fraction of nonradiative recombination. The familiar limit belongs to stated assumptions about the illumination, cell temperature and device; it is not one universal numerical efficiency for every photovoltaic design.^[ref]

A physicist who coauthored Detailed Balance Limit of Efficiency of p-n Junction Solar Cells by William Shockley and Hans-Joachim Queisser.

Georges Matheron was a mathematician who developed geostatistics from problems of estimating mineral resources using spatially distributed measurements. His work put kriging and spatial variability into a systematic probabilistic framework. He also developed mathematical morphology with Jean Serra, connecting geometric operations on sets with image processing.^[ref] In kriging, nearby measurements are combined using weights determined by a model of spatial dependence. The point is to account for both proximity and redundancy: many closely clustered observations need not contain as much new information as equally many well-separated observations.

A mathematician.^[ref]

Skip Thompson is a mathematician whose work includes the numerical solution of delay differential equations. His authored account explains equations in which the present rate of change depends on earlier values of the solution, with applications including population dynamics and epidemiology.^[ref] For example, $y^{\prime }(t)=-ay(t-\tau )$ with $\tau >0$ requires an initial history on $[-\tau ,0]$, rather than only one initial value. A numerical method must therefore approximate and retrieve past values as integration proceeds. Delayed feedback can also create oscillations that are absent from a corresponding equation without delay.

A mathematician.^[ref]

A mathematician who worked on probability theory.^[ref]

Lloyd Shapley was a mathematician whose work helped shape game theory and the mathematical study of matching markets. His research on stable matching with David Gale supplied an existence theorem and a constructive procedure, while the Shapley value gives a systematic way to allocate the value created by cooperation.^[ref] The Shapley value averages each participant's marginal contribution over all orders in which a group might form. This makes a fairness rule precise through combinatorics, rather than selecting a division solely by bargaining strength or an arbitrary order of arrival.

A mathematician.^[ref]

David Gale was a mathematician whose research connected optimization, game theory and mathematical economics. With Lloyd Shapley, he proved the existence of a stable matching under the classical two-sided preference model and gave an algorithm to construct one.^[ref] Stability means that no unmatched pair would both prefer each other to their assigned partners. This is different from maximizing a single total score: the requirement rules out a mutually beneficial deviation. The Gale-Shapley algorithm became a foundation for applications such as assigning students to schools and doctors to residency programs.

A mathematician.^[ref]

Matjaž Zaveršnik is a mathematician whose work with Vladimir Batagelj includes an efficient algorithm for finding all k-cores of networks. Their paper presents a method whose running time is linear in the number of edges for the networks considered, making the decomposition practical on large inputs.^[ref] The key structural object is a k-core: a maximal induced subgraph whose minimum degree is at least $k$. Assigning each vertex its largest such $k$ provides a compact description of its position within nested connected regions; a high value records local connectivity rather than merely a large original degree.

Mathematician.

Biographical record: www2.arnes.si/~sspmgiac/mirk2003/Zbornik.pdf

Vladimir Batagelj is a mathematician whose work includes graph algorithms and the analysis of large networks. With Matjaž Zaveršnik, he developed an efficient algorithm for finding all k-cores of a network, a way to reveal nested regions of increasing internal connectivity.^[ref] A k-core is a maximal induced subgraph in which every vertex has degree at least $k$. Repeatedly removing vertices of insufficient degree exposes this structure. The decomposition helps distinguish densely connected parts of a network from peripheral vertices without requiring an exhaustive search through all vertex subsets.

Mathematician.

Biographical record: www2.arnes.si/~sspmgiac/mirk2003/Zbornik.pdf

Joseph-Louis Lagrange was a mathematician whose work transformed analysis, number theory and classical mechanics. His correspondence with Leonhard Euler helped develop the calculus of variations, and his later analytical treatment of mechanics organized equations of motion through generalized coordinates.^[ref] In Lagrangian mechanics, a function of position and velocity leads to the Euler-Lagrange equation, giving a systematic way to handle constrained motion. His name also appears in the Lagrange multiplier method and Lagrange's four-square theorem, illustrating the breadth of his contributions across continuous and discrete mathematics.

Mathematician.

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

A mathematician who has worked on orthogonal polynomials.

Institutional biography: dlmf.nist.gov/about/bio/RFSwarttouw

A mathematician who has worked on orthogonal polynomials.

Institutional biography: dlmf.nist.gov/about/bio/RKoekoek

A mathematician who has worked on orthogonal polynomials.

Institutional biography: dlmf.nist.gov/about/bio/THKoornwinder

A mathematician known for work in number theory.

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

A mathematician whose work includes number theory and elliptic integrals.

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

A mathematician and mathematics educator who taught at the Community College of Philadelphia.

Academic memorial: faculty.utrgv.edu/eleftherios.gkioulekas/OGS/santos.html

A mathematician whose research includes harmonic analysis, operator theory and functional analysis.^[ref]

Homepage: heil.math.gatech.edu/

A mathematician known for work in group theory, Galois theory and real analysis, including bounded variation.^[ref]

A mathematician who worked on Fourier series and group theory.^[ref]

Al-Khwarizmi wrote on algebra and treated quadratic equations using both algebraic procedures and geometry.