Hello! My name is Ryan Maguire, I am a Ph.D. student at Dartmouth college studying mathematics. My current interests are topology, geometry, and set theory. My topological interests include knot theory, manifolds, and continua theory (the study of compact connected metric spaces). In particular I’ve recently developed a fascination with problems in planar topology and the pathologies therein (the pseudo-arc and lakes of Wada are exotic examples). In geometry I study Lorentzian manifolds and their applications to general relativity. Apart from that I have a personal interest in ZFC set theory and attempting to rigorously build mathematics from these foundations.

In the past I studied mathematics and physics at the University of Massachusetts, Lowell, obtaining a B.S. in mathematics and physics and an M.S. in mathematics. I primarily studied analysis, Euclidean geometry, and convex geometry. While there I spent five years working at the center for atmospheric research (CAR), later renamed the Lowell center for science and space technology (LoCSST). Here I worked on DWEL, a botanical experiment involving LIDAR, and HiT&MIS, a spectrograph which was deployed in Kiruna, Sweden to study the aurora. I also participated in the analysis of data from the SPINR sounding rocket mission and performed daily laboratory tasks such as changing out oxygen tanks. My main contribution being HiT&MIS, and both of the instruments we built are quite special to me.

After Lowell I worked at the Whitin observatory at Wellesley College for two years with NASA’s radio science team for the Cassini mission. I studied more analysis, including Fourier analysis, numerical methods, mathematical physics, and iterative methods of solving Fredholm integral equations. These efforts culminated in rss_ringoccs which is a free and open source suite of code written in C and Python for processing the occultation data obtained from Cassini. Here I learned a lot about computer science and the C programming language and also began to obsess over visualizing mathematics.

After departing from Wellesley I entered into a Ph.D. program at Dartmouth, and that’s where I am now. My current goals involve programming projects I’ve been working on. There are two main ones.

libtmpl is an open source library of code for mathematicians and physicists in a variety of situations. It features a (nearly complete) cross-platform implementation of the current standard of libm, the C standard library for mathematical functions, with functions available for 32-bit float, 64-bit double, 80-bit extended precision, 128-bit quadruple, and 128-bit double-double (as mentioned it has cross-platform support). It is very portable, compiling with GCC, LLVM’s Clang, TCC, PCC, and Microsoft’s MSVC, supporting all major operating systems (GNU/Linux, FreeBSD, macOS, Microsoft Windows, Haiku OS, etc.) and architectures (x86, x64, arm64, mips, powerpc, and more). This project started with rss_ringoccs but grew far beyond the scope of astonomy. It contains a cross-platform implementation of complex numbers, 2D and 3D geometry, Fourier transforms, and much more. You’ll find the performance of the algorithms rival other libraries. All functions have tests, when possible, against other implementations (like Boost, glibc, openlibm, etc.).

Mathematics-and-Physics is another library I’ve been working on since around 2017. It is a repository of notes on many areas of mathematics and physics that are ordered in an attempt at being consistent. The aim is to mimic the styling of Euclid’s elements which is theorem, definition, proof, but also add a lot of discussion and images so that one may easily learn from it. This project is very much still in it’s infancy, but already has 1000+ pages and several hundred figures. The codes for these figures are written in C, asymptote, and tikz (though I intend to start phasing out the tikz code for the more powerful asymptote methods). This repository also contains my class notes, presentations, and mini-projects that are usually devoted to raytracing, rendering fractals, and visualizing mathematics. All of it is freely available under the GPLv3.

Here’s me at the top of Mount Mansfield in Vermont.