This page is mostly bookmarking for me. When I come across freely available essays and writing that I like, I'll put them here (if I remember to!). #### Am I allowed to still have a [blogroll](https://en.wikipedia.org/wiki/Glossary_of_blogging)? [Keith Conrad](https://kconrad.math.uconn.edu/) has a fantastic collection of mathematical ["blurbs"](https://kconrad.math.uconn.edu/blurbs/). - Ever wondered when exactly you can [differentiate under the integral sign](https://kconrad.math.uconn.edu/blurbs/analysis/diffunderint.pdf)? (Also see this wonderful and careful development of the problem in the multi-dimensional setting: [Flanders, MAA, 1973](https://www.tandfonline.com/doi/abs/10.1080/00029890.1973.11993339).) - Would you like to see eleven proofs of the [Gaussian integral](https://kconrad.math.uconn.edu/blurbs/analysis/gaussianintegral.pdf) formula? [Statistical Modeling, Causal Inference, and Social Science](https://statmodeling.stat.columbia.edu/) by Andrew Gelman [Gowers's Weblog](https://gowers.wordpress.com/) by Timothy Gowers - "[What sort of maths are LLMs good at?](https://gowers.wordpress.com/2026/08/12/what-sort-of-maths-are-llms-good-at/)" by Tim Gowers (Aug 12, 2026) A snapshot in time on the abilities of AI systems in solving math problems. He finds himself asking the interesting question: what is a counterexample, really? [Almost Sure](https://almostsuremath.com/about/) by Gregory Lowther #### Is there a right way to learn linear algebra? Actually I think both of these guys enjoy each other's perspective. - [Linear Algebra Done Right](https://linear.axler.net/), by Sheldon Axler ( [pdf](https://linear.axler.net/LADR4e.pdf) ) - [Linear Algebra Done Wrong](https://sites.google.com/a/brown.edu/sergei-treil-homepage/linear-algebra-done-wrong), by Sergei Treil ( [pdf](https://www.math.brown.edu/streil/papers/LADW/LADW_2026_04-30.pdf) ) #### Notes on computation A must read in every first-year applied math course: "[Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later](https://scott-a-mckinley.net/s/moler-van-loan-2006-nineteen-dubious-ways-to-compute-the-exponential-of-a-matrix-twenty-five-years-l.pdf)" by Cleve Moler and Charles Van Loan ([journal link](https://epubs.siam.org/doi/10.1137/S00361445024180)). "[An Introduction to the Conjugate Gradient Method Without the Agonizing Pain](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)" by [Jonathan Shewchuk](http://people.eecs.berkeley.edu/~jrs/), who has [written several nice introductions](https://people.eecs.berkeley.edu/~jrs/jrspapers.html). #### Random probability essays "[The unexpected sensitivity of rare events](https://research.phys.cmu.edu/biophysics/2020/12/29/on-the-unexpected-sensitivity-of-rare-events/)" by Markus Deserno (Dec 29, 2020) #### Financial math essays "[An Intuitive Explanation of Black–Scholes](https://gregorygundersen.com/blog/2024/09/28/black-scholes/)" by Gregory Gunderson (Sep 28, 2024) "[The Black-Scholes equation](https://terrytao.wordpress.com/2008/07/01/the-black-scholes-equation/)" by Terry Tao (July 1, 2008)