Dear Neeraj or Amartya (or whoever you are),
You say
>One of the chief reasons why most
> of us are drawn to the notion of rigor today however, is not religious
> but simply because of the elegant, sublime, almost surreal nature of
> rigorous mathematical proofs.
First, I established in my previous mail/post, that the notion of “rigor” to which you refer is a culturally-specific notion of “rigor” according to Christian metaphysics, and that it is non-rigorous, and contrary to the notion of “rigor” in various other systems of philosophy. Certainly, the church aims to dominate and become “universal”, by eliminating all others, and it uses various tricks to suggest that its notions are already “universal”, but that has not yet happened. So please don’t pretend like the church that that the notion of “rigor” is already universal, by using it without qualifying adjectives as your Western indoctrination taught you to do. Try to be honest and at least call it “rigor according to Christian theology”, or “rigor according to Christian mathematics”. The moment you apply those adjectives it becomes clear that this “rigor” is a matter of culturally-specific belief; that itself is enough to justify why I call it religious. (There are other reasons, but I won’t go into them here. My forthcoming book Euclid and Jesus explains this in more detail.)
I have no objection if you want to do math because you find it beautiful. (But why so many adjectives? (“elegant, sublime, surreal”) That suggests lack of confidence in what you are saying, for most people do not see that beauty; so maybe you are afraid that you are just deluding yourself, as so many people do about so many things.)
My first objection to formal math is this: why impose it on school kids? You might like jazz music, and are welcome to pursue it. But why insist that all school kids should learn jazz as the “universal” form of music? Indeed, I have repeatedly stated, right from the time of my Hawaii talk of 2000 that I do not object to the teaching of formal mathematics as an art form taught to a few specialists (but not in school, because it indoctrinates kids).
Secondly, why should the taxpayer support this sort of maths? More specifically, what I have publicly stated in my article on D. D. Kosambi [the son] (“Kosambi: the mathematician”, Economic and Political Weekly 44(20) May 16–22 (2009) pp. 33–45) is the following. In India, the Tata Institute of Fundamental Research is the bastion of formal mathematics—even their notion of “applied math” involves theorem-proving! It is funded by the Department of Atomic Energy. Why? If the aim is to pursue beauty, shouldn’t the funding come from the Department of Culture? If the aim is utility that should be shown. But none of the theorems proved by anybody there (barring Kosambi) over the last 65 years has even remotely contributed either to atomic energy or to the improvement of the life of even a single Indian (apart from the theorem-provers themselves). This demonstrable lack of practical benefits cannot be covered up by talk of a beauty which no one can see; they should talk of beauty while tabling the budget for atomic energy in parliament. In my opinion it is charlatanism to take money from the poor people of India in the name of atomic energy and then give nothing back in return, except empty talk of beauty, and this charlatanism of Western-oriented “mathmen”, like that of “godmen” should be exposed.
Thirdly, this talk of beauty, like all theological discourse, confounds all sorts of things. Yes, there definitely was beauty in Egyptian sacred geometry, nowadays called “Neoplatonic” geometry and today attributed to that fictitious character “Euclid”, invented during the Crusades to make math theologically correct. However, examine the story of Socrates and slave boy in Plato’s Meno. What Socrates demonstrates is the intuitive understanding of geometry which the slave boy has. What Socrates (or Plato) values is this intuition for (according to him) it awakens soul, like good music, and hence makes people virtuous.
However, Western math, which you believe in, long ago disconnected mathematics from the belief in that notion of the soul, which the church cursed. Formal math also disconnected mathematics from intuition. this is clear, for example, from your own dichotomy between “rigorous” and “intuitive” math, which is a common belief among formal mathematicians today. In fact, mathematicians, today, often value a theorem for how counter-intuitive it is! This just goes to show that Christian metaphysics (imparted through Western education) trains the mind in a way contrary to ordinary human intuition (with the deliberate aim of making it distrust human intuition and trust Western authority instead; for the belief among trained mathematicians is that the value of a mathematical theorem can only be correctly judged by Western authority, as in “international” publications, etc.). These are common theological tricks to train the human mind into subordination. As a teacher, it is my duty to warn you.
Formal mathematical proof involves Hilbert’s rigidly mechanistic ideas, it is addressed to a machine, and can be checked by one; it is as contrary to the human mind as assembly-language programming (which built on exactly that notion of formal proof). This point was driven home to me when my son objected to my praise for “Euclidean” geometry. I studied from the older texts of the Elements which followed the intuitive “Neoplatonic” treatment; he learnt from the newer texts which follow Hilbert’s formalism and synthetic postulates (and the rejection of the side-angle-side theorem and its replacement by the SAS postulate). According to me, then, intuitive math may have beauty, but formal math is, in a word, ugly.
And that is perhaps why so many people are intuitively repelled by it.
If any attraction still persists in formal math it is because of its “Neoplatonic” origins, so, if beauty is what you seek, you should certainly abandon formal math and go back to “Neoplatonic” math, or Egyptian sacred geometry. (But the West won’t approve, for that was started by blacks, who had a different religion.)
I will continue my response in my next mail.
All best,
C. K. Raju