Defying Logic

For time immemorial, I have believed in the study of Fundamentals. Whenever the study or analysis of any topic of subject is considered, I have always believed that going to the fundamentals will always yield fruits.

After being a student of Mathematics for sometime, I found myself gradually drifting towards areas which can be roughly classified as Mathematical Logic and Scientific Philosophy. These areas of studies, fundamental as they are, held an immediate appeal for me. For sometime, I even thought these were the only areas that would interest me.

I should admit that inspite of my interest, my knowledge in these areas still is extremely limited. But the fascination remained with me for quite some time.

Of late, I have started to drift from that position. I am giving an apology here for my change of stance. There are a few reasons.

Even though, I still believe these fundamental studies are important, I think they are more for the past-masters of Mathematics. These fundamental studies require not just intellectual power, but also a vast experience in Mathematics. Of course, intellectual power also is important for deep fundamental study but they require some level of overall knowledge of what the upper-layer(which is mathematics) looks like. To gain that, considerable amount of time and effort should be spent on atleast a few major areas of Math which can only be done if you are a full-time Mathematician for some period in your life.

Mathematics - whatever form it might take - is always a study of structure and pattern. Infact the concept of "abstraction", which forms the core of higher mathematics, is all about pattern-searching and as a result Generalizing. This is where I find myself in conflict when trying to proceed with Mathematical Logic. Logic forces me to ask questions on my basic assumptions. It tries to break all pattern by trying to reach to the bare fundamentals. So much so that we start doubting our very existence many times.

Anything said in the last paragraph about logic applies for Scientific Philosophy - the art of investigating truth by asking never-ending questions.

After spending some time over such fundamental studies, I have come to the conclusion that - even though these studies are important and have helped historic breakthroughs in the human thought process, they are not suitable for students of mathematics. Students of Mathematics should rather delve into Real Mathematics - which is the study of pattern and structure and the creation of new patterns and structures.

There is a vast ocean of Mathematical knowledge which can be so much fun to experience. Once we have experienced a significant portion of it, we may choose to drift into more fundamental studies of logic and philosophy. However, to start here and go beyond, is like trying to learn the working of a BMW engine rather than taking off on an open highway to explore newer worlds!