Rota’s Indiscrete Thoughts

I am a huge fan of Gian-Carlo Rota, who has been said to be the founding father of modern algebraic combinatorics. (He is also my mathematical grandfather-to-be.)

Rota was a philosopher as well as a mathematician, and wrote an entire book primarily concerning the philosophy of mathematics. His book is called Indiscrete Thoughts.

I’ve been reading this recently, and I highly recommend it. It reads like a novel; he motivates everything with enticing examples regarding mathematicians that he has known or familiar mathematical theorems and proofs. He brings up a lot of interesting points and questions, including:

  • Is mathematics “created” or “discovered”? This is a common point of debate among mathematicians, and Rota addresses it beautifully. He gives clear and precise examples of mathematical work that is obviously one or the other, and then goes on to show how the two notions can, and do, naturally coexist.
  • How can we make rigorous some of the notions that mathematicians use all the time, but can never formally write about? There are plenty of processes that go on in our mind, leaps of faith and intuition, that we cannot easily talk about and use in a formal mathematical setting, because they are not part of established formal logic.
  • What is mathematical beauty, and why does it seem to depend on context and historical era?

Even if you don’t agree with Rota’s conclusions, his examples are so vivid and revealing that it’s impossible not to get something out of this book. I personally am coming away with a clearer perspective on mathematics and what it actually is.


First post in several weeks; term has hit. But in the midst of the hustle and bustle of the start of the semester, I’ve discovered a gemstone within the mathematical software world that was too good not to share: TeXStudio.

I discovered it while preparing for the “LaTeX Tricks” seminar this week, which I am organizing as part of the UC Berkeley Toolbox Seminar. (The seminar is looking to be quite exciting if you’re in the area – we will have a variety of speakers give 10-minute talks on their favorite LaTeX tool or package. It will be this Wednesday from 2:30-4PM in room 891 Evans Hall.)

Since I will be giving the introductory talk, I was looking around at LaTeX front-ends today to see which ones to recommend. My first conclusion was that Wikipedia is awesome. They have a nice comparison chart of TeX editors here:

I then went through and tried out a few of the more “green” editors on that chart. A long-time Gedit user myself, I first tried the LaTeX Gedit plugin. It looked nice, but after about 10 minutes it mysteriously stopped working. It turns out it isn’t compatible with the new version of Gedit, and you can’t go back to the old version of Gedit sicne it doesn’t run on the new version of Ubuntu (12.04). Sigh.

So I tried a few of the others. One was LyX, which has a nice GUI that automatically renders your math mode code inline. But I find it to be slower to type in, since there are odd cursor placings after the automatic rendering. (Perhaps one just needs to get used to it.) Other highly-rated editors on the comparison chart were AUCTEX, a plugin for Emacs, and TeXlipse, a plugin for Eclipse. However, I haven’t yet gotten past the Emacs learning curve, and I don’t need the full power of Eclipse.

Finally, I tried out TeXStudio. It’s great! It has:

  • Nice auto-complete features based on your most-used commands. So, you’ll begin typing \begin{it… and it will ask you if you want a \begin{itemize}...\end{itemize} block with an \item command in the middle. Yes, I do, thanks.
  • It aligns your code nicely. The next line is automatically tabbed like the last one. Particularly useful in a series of \item lines.
  • It has a collapsible toolbar on the left that can display a number of things, the most important being an outline of your entire document by sections and subsections. You can click on the outline to jump to a section of your document.
  • A nice pdf previewer that you can search, and you can jump to that point in your code by clicking on the pdf! A wonderful feature.
  • Helpful menus for things like Asymptote, PStricks, TikZ, and all the really weird symbols that you always forget the commands for, like $\wp$ (\wp).
  • Last but not least, it is highly customizable. You can make your own macros for strings that you commonly type, you can change the font and size of the code, and the side and bottom toolbars can be easily collapsed (and then brought back) if you don’t feel like looking at them.

Here is a screenshot that demonstrates many of the above features:

Well, I’m sold. I will be switching to TeXStudio.


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.  Enjoy!