DIALECTICS of MODELING
Based on a talk given by Al Vilcius at York University, November 1996.
This discussion gives my personal view of mathematics in industry, from the perspective of a person in industry, and keeping it not too technical. I have worked in the Finance Industry for over 20 years now, but still think of myself as a retread algebraist.
So what can a mathematician do in industry?
Indeed the landscape has change quite dramatically over the last 20 years. At first, being a mathematician in industry was a liability; it was a fact that needed to be played, even concealed at times, and certainly required justification and "selling" at all times. However, it was possible to sell this situation, and slowly it started to become a real asset.
Rather than just reviewing a list of job opportunities, or a list of formulas required, I will try to present a little more philosophical view.
I regard mathematics as an extension of the natural language that increases our power to make inference. This may be taken almost at the level of a slogan that should trigger an enormous amount of concepts in support of the process of solving problems.
We generally accomplish this through modeling: I'll explain with a picture:
I consider this picture to represent a framework for applying math to "real world" problems
of course we can iterate this through several steps
example: pricing a derivative security
..................... some discussion of derivatives: options, first option, ....
see "Optional Math is not optional" Notices AMS for a start
So where is the math?
and where is the philosophy?
thesis, antithesis, synthesis
What sort of math might be useful in industry?
statistics - but do we actually understand variation?
i.e. reasoning with uncertainty to draw conclusions
not just computational, but creative e.g. risk neutral measures
so real analysis and measure theory are important prerequisites
Economists are finding good applications for dynamical systems and game theory also
Even though I tend to have a non-standard view, I still believe in the basics
logic - ability to make inference in different "worlds" e.g. quantum worlds
number theory - cryptography
category theory - computer science, or maybe to really understand variation
The gateway to mathematical applications in industry for me has been through risk management
however, I have recently made another change, from Investment Banking to electronic commerce: "Smart Card" IC Technology
new challenges of quantifying risk are leading me into simulation modeling, including AI concepts - also "data mining" is a hot topic!
the essence is pattern recognition
I suppose I have always been prone to hero worship
but my heroes have not been entertainers or sports stars
rather they have been mathematicians, like John von Neumann
Another one of my heroes was a math professor I had as an undergraduate who greatly influenced my life
I once asked him: what do I really need to know to be a good mathematician ?
I expected a list of topics or even theorems
but rather he said: two things you must know
- how to count
- how to recognize patterns
That gave me the connection of mathematics to life within the framework of the dialectic
and the motivation to study the structural side
at least to me, that is what mathematics is all about.
and that is what I wanted to leave you with today.
thank you very much ................ Al Vilcius
Talk given Nov. 5, 1996 Vari Hall Lecture Theatre "A", 5:30 pm
Ref: Prof. Norm Purzitsky, Organizer