Finding Gemstones: on the quest for mathematical beauty and truth

About this blog

Welcome! The purpose of this blog is to record some of the particularly beautiful mathematical ideas I have seen or invented, and share them with you.

The process of doing mathematics is much like a quest to uncover mathematical truths. Sometimes, such a truth may be valid but uninteresting, just another pebble or grain of sand along the beach. But other times, you will uncover a gemstone — a particularly aesthetic, beautiful, or useful truth hiding in the vast sandpiles of information.

This blog is devoted to the gemstones of my mathematical investigations. I hope you enjoy it!

Ratings: The posts are rated in difficulty according to five categories: Amber, Pearl, Opal, Sapphire, and Diamond. (Notice that they are ordered by the hardness of the gemstones.)

  • Amber: This category contains posts that anyone with very basic elementary or middle school mathematics background can appreciate.
  • Pearl: For Pearl posts, some high school courses or early college courses may be helpful in understanding the content.
  • Opal: These posts are aimed at undergraduates with some basic first-course background knowledge in algebra, analysis, discrete math, or topology.
  • Sapphire: These gemstones would be appreciated by mathematics graduate students or professors, or those with at least an undergraduate degree in mathematics.
  • Diamond: The hardest type of gemstone. These posts are highly specialized, containing content that only mathematicians who have studied the topic in depth will have the background to understand.

About the Author

Dr. Maria Monks Gillespie is a mathematician at Colorado State University in Fort Collins, Colorado. She got her start in mathematics through success in math competitions in high school, and went on to get a bachelors’ in mathematics at MIT and a Ph.D. at the University of California, Berkeley. Dr. Gillespie’s specific research interests lie in algebraic combinatorics, but she loves diving into any area of math, discovering its secrets, and sharing them with others.


Thank you to Daniel Matriccino for helping me get this off the ground by hosting the first version of this website on his servers.

Thank you also to Ken G. Monks helping me set up MathJax rendering in the first version of this blog, and for setting up the server that hosted the second version for nearly ten years.

Thanks to my husband Bryan Gillespie for his good eye and helpful feedback on the banner design, and my brother Keenan Monks for suggesting some of the gemstones to represent various levels of difficulty.

Special thanks to Bryan Gillespie for helping me redo this entire blog in markdown and move it to an independent server in 2024.

Finally, thanks to readers like you for making my writing worthwhile!