Me and My Research (part 1)

Once upon a time when I was a child I read this book named “Mathematics the art of reasoning” by William P. Berlinghoff. (I am not sure about the author’s name though!) It was a very slim book; hard covered; didn’t take much time to finish. It dealt with the axiomatic approach of reasoning. There I learned this fascinating truth about mathematics;

“You can create your own mathematical system!”

Like there is Euclidian geometry and there is Non-Euclidian geometry, Abelian groups and non-Abelian groups… so, like Euclid and Abel you can also create a mathematical system and play with it. (Of course, it might not be as useful as those by Euclid or Abel, or who knows it might be better!) The trick is to fix up some axioms. Like Euclid’s geometry had 5 axioms and Abel’s groups had this additional axiom of Commutativity.

You create as many axioms as you want, there’s no limit, and then you just do this consistency check to ensure that one of you axiom don’t contradict another! And there you go. You have your own tool for reasoning. Any new reasoning about your system must comply with these initial set of axioms.

And we all know that one have to be very careful about what he teaches to a child, because the psychological effect of that teaching is not 'undoable'. So, here I am; a person who has this huge ‘thing’ for mathematical reasoning! I mean for a reasonable conversation with anyone, before going to any ‘reasoning step’, I have to make sure what the axioms are. I mean first I have to check the consistency of the things taken ‘granted’. No matter how crazy it is, if it doesn’t contradict itself, it’s mathematical! And we can have a fun time working with (maybe, talking about) it.

Actually, by talking about all these things I am trying to create the axiomatic basis of my future discussions. I think we have had enough digression. Let’s start out talk on research:

Richard Hamming one of the greatest minds of our time has given this lecture about 'research'. It actually centered on the idea of what sort or problems to attack, how to know I am doing something important. And he actually described how he himself could end up doing something important! And in the process he pointed out “the difference between those who do and those who might have done.” You should check it out if you missed it up to this point in space-time!

[To be continued]
* I am taking this tea break to read the Hamming lecture again for myself.