Haynes Miller works in algebraic topology, homotopy theory and homological algebra. His early research helped develop chromatic homotopy theory, and his solution of the Sullivan conjecture connected questions about maps of spaces with the structure of Lie groups. His lecture notes and expository writing develop the algebraic topology used to turn geometric questions into calculations with algebraic invariants.^[ref]

Identity source: math.mit.edu/directory/profile.html?pid=186

Dan Romik works in number theory, combinatorics and probability theory.^[ref] His Complex Analysis Lecture Notes by Dan Romik also develops holomorphic functions, contour integrals and the geometry of the Riemann sphere, providing an expository connection between complex analysis and geometry.

Identity source: www.math.ucdavis.edu/people/general-profile?fac_id=romik

Daniel Reem is a mathematician whose research includes functional equations. His work on the Cauchy functional equation examines existence, regularity and stability on subsets of Euclidean spaces and tori. It also studies variants such as the Jensen functional equation and multiplicative forms of the Cauchy functional equation.^[ref] The central issue is that the algebraic identity $f(x+y)=f(x)+f(y)$ alone permits pathological solutions on the real numbers. A suitable regularity assumption forces the familiar form $f(x)=cx$, so this subject clarifies how analytic hypotheses constrain algebraic identities.

Identity source: arxiv.org/pdf/1002.3721v7

Alwin Korselt is associated with Korselt criterion for Carmichael numbers. The criterion characterizes a composite positive integer $n$ by squarefreeness and the divisibilities $p-1\mid n-1$ for every prime divisor $p$ of $n$.

It turns a universal modular-exponent condition into a finite collection of arithmetic tests on prime factors. For example, $561=3\cdot 11\cdot 17$ is squarefree, and $2,10,16$ all divide $560$, giving the standard example of a Carmichael number.^[ref]

A mathematician associated with Carmichael numbers and the Carmichael function.^[ref]

A mathematician whose 1885 numerical list is discussed in Carmichael number.^[ref]

A mathematics educator and lead author of Precalculus 2e by Jay Abramson.^[ref]

Institutional profile: search.asu.edu/profile/230861

A Swiss mathematician and teacher remembered for finding an empirical pattern in the hydrogen emission spectrum. In 1885 he expressed the wavelengths of its visible spectral lines through a simple formula in integer parameters. The resulting Balmer series connected measured wavelengths that had previously looked like separate experimental numbers.

Balmer's result was a numerical regularity, rather than a physical explanation of atomic structure. Its success included a further predicted line consistent with observation. The later Bohr model explained why transitions between discrete energy levels produce such a series. The episode shows how a mathematical pattern can become evidence guiding a later physical theory. ^[ref]

A mathematician.^[ref]

A mathematician researching general relativity, including singularity theorems.^[ref]

A mathematician associated with the Frobenius method and representation theory.

A mathematician associated with Laplace expansion, the Laplace transform and Laplace's equation.

A mathematician associated with Laguerre polynomials and the Laguerre differential equation.

A mathematician associated with Rodrigues' formula and the Rodrigues rotation formula.

A mathematician associated with the Dirichlet problem.

A mathematician associated with Green functions and Green's identities.

A historian of science.^[ref]

A historian of science.^[ref]

A historian of science.^[ref]

A historian of science.^[ref]

A historian of science.^[ref]