A Field Guide to Mathematics

Stories about mathematics, students, professors, mathematicians, abstract nonsense, research, papers, publishing, and academia.

Latest Posts

My Favorite Prime Numbers

There is something about prime numbers… An air of mystery surrounds them, that makes them one of the most alluring (and most studied) objects in all of mathematics. In this post, I give a list of my favorite primes, together with some of their fascinating properties.


In each era of the history of mathematics, there have been open problems and conjectures that mathematicians have paid particular attention to, maybe because of the intrinsic beauty of the problem, its perceived importance within an area of study, or simply put, because of the fame that a solution would bestow on the solver.

Clopen Concept

As many other young couples, when my wife and I looked for our first home, we were obsessed with the idea of an “open concept” home. How do I wish now, with 20-20 vision, for a closed concept home or, perhaps, a middle ground: a clopen concept. (A work day at home during a pandemic.)

About Me

I am a Professor in the Department of Mathematics at the University of Connecticut. My research focuses on arithmetic geometry, which is at the cross roads of number theory and algebraic geometry.

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© Álvaro Lozano-Robledo and “A Field Guide to Mathematics”, 2020, 2021. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Álvaro Lozano-Robledo and “A Field Guide to Mathematics” with appropriate and specific direction to the original content.