Equations, LaTeX and Vanishingly Small Probabilities

As we announced yesterday, Equation Editor (with LaTeX support) is the latest feature in Zoho Writer. This one has deep personal relevance to me. My first "programming language", in the sense that I wrote a lot of code, was actually LaTeX. It is a programming langauge for accurate typesetting of documents, that in many ways anticipated developments like HTML/CSS.

As a graduate student at Princeton, I spent countless hours writing and rewriting papers for publication using LaTeX, first with inputs from my advisor, and later from anonymous reviewers at publications like The IEEE Transactions on Information Theory. Of course, my entire PhD thesis was written in LaTeX as well. The most important aspect of LaTeX I loved was its easy facility with equations. You would type in something like (Ampere's Law - thank you Wikipedia!)

\Delta  \times  \mathbf {B} =  \mu_0  \mathbf {J} + \mu_0  \epsilon_0  \frac{\partial  \mathbf {E}}{\partial t}

and the LaTeX compiler would generate

Or the integral form of Ampere's Law:

 \oint_{\partial S}   \mathbf {B} . d \mathbf {l}  =  \mu_0 I_S + \mu_0 \epsilon_0   \frac{d {\Phi}_{E,S}}{dt}

It was pure magic to see the compiler generate such beautiful forms. I spent four years of life with equations like that - pretty much every section, every page in my thesis had them. As a graduate student, I used to wonder if such equations could be generated via a friendly user interface - keep in mind that MS-DOS still ruled the world at that time and graduate students like me had Sun workstations. I myself had little interest in software at that time (I was going to prove theorems, so I looked down on programming as a lowly activity!) so never pursued that thought further. If someone had predicted at that time that I would end up founding a software company one of whose key products is a word processor, and LaTeX would play a role in it, I would have just laughed the idea off as absurd or in technical terms, "of vanishingly small probability", a phrase that sticks in mind after seeing those epsilons and deltas (or \epsilon's  \ and  \ \delta's in LaTeX terminology!). I used to practically dream in epsilons and deltas during that period - so many of the mathematical proofs depended on them being close to but not quite zero. 

I am very happy to see the Equation Editor in Zoho Writer give shape to that user interface idea. There is a lot more potential in typesetting using LaTeX like ideas, and you will see us pursue them in due course.

Thinking back, what is surprising to me now is how little of my PhD I remember. I retrieved my PhD thesis from its long-forgotten closet, dusted it off, and it is all Greek to me. I can scarcely even believe it is my own work I am staring at. I used to be really, really passionate about proving theorems, so it seems even stranger that I would just completely abandon it. The only thing I would have gotten right with all my PhD training was to recognize that vanishingly small probability events can still happen.