It is hard to state this bluntly but i came out of that meeting convinced that a programmer who doesn't know math is somehow crippled(so is a mathematician who can't program, but that is another story). The power of those equations ,drawing down a whole set of tremendously complex abstractions into clean lines of force that thrummed with power , and seized even our bumbling thoughts and flung them unceremoniously into a world of bewildering possiblities, seemed to have affected Mridul too.The first thing he said after the meeting was "Damn ! we should learn math.If we could wield it the way these scientists do, we could create so many fantastic programs ". We had a long discussion over lunch on what we had perceived and distilled it down to these basic points.
- the combination of deep mathematical skill and expert level programming ability would be the ultimate "level up"
- the first step in mastering math is be to learn to read the notation. just like learning the syntax of a new programming language
- the second is to grasp the reality expressed by the notation at a gut level , like understanding the paradigm and patterns lying underneath a programming language , like ,say ,beginning to grok "oo"
- the third is to use that understanding to create new possibilities
- the fourth is to use a programming language to embody and refine those possibilities , thus creating programs that do what has never been done before.