Dear Neeraj or Amartya\u00a0(or whoever you are),
\n\u00a0
\nYou say
\n\u00a0
\n>One of the chief reasons why most
\n> of us are drawn to the notion of rigor today however, is not religious
\n> but simply because of the elegant, sublime, almost surreal nature of
\n> rigorous mathematical proofs.<\/p>\n
First, I established in my previous mail\/post,\u00a0that the notion of “rigor” to which you refer is a culturally-specific notion of\u00a0“rigor” according to Christian metaphysics, and that it is non-rigorous, and contrary<\/em> to the notion of “rigor” in various other systems of philosophy. Certainly,\u00a0the church aims to dominate\u00a0and 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\u00a0please don’t pretend\u00a0like the church that\u00a0that the notion of “rigor” is already universal, by using it without qualifying adjectives as your Western indoctrination taught you to\u00a0do. Try to be\u00a0honest and\u00a0at least call it “rigor according to Christian theology”, or “rigor according to Christian mathematics”.\u00a0The moment you apply those adjectives it becomes clear that\u00a0this “rigor”\u00a0is a matter of culturally-specific\u00a0belief; that itself is\u00a0enough to justify why I\u00a0call it religious. (There are other reasons, but I won’t go into them here. My forthcoming book Euclid and Jesus <\/em>explains this in more detail.) Dear Neeraj or Amartya\u00a0(or whoever you are), \u00a0 You say \u00a0 >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,\u00a0that the notion of “rigor” to which you refer is a culturally-specific notion of\u00a0“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,\u00a0the church aims to dominate\u00a0and 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\u00a0please don’t pretend\u00a0like the church that\u00a0that the notion of “rigor” is already universal, by using it without qualifying adjectives as your Western indoctrination taught you to\u00a0do. Try to be\u00a0honest and\u00a0at least call it “rigor according to Christian theology”, or “rigor according to Christian mathematics”.\u00a0The moment you apply those adjectives it becomes clear that\u00a0this “rigor”\u00a0is a matter of culturally-specific\u00a0belief; that itself is\u00a0enough to justify why I\u00a0call 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.) \u00a0 I have no objection if you want to do math because you find it beautiful. (But why so many adjectives?\u00a0 (“elegant, sublime, surreal”)\u00a0\u00a0That\u00a0suggests lack of confidence in what you are saying, for most people\u00a0do not see that beauty; so maybe you are afraid\u00a0that you are\u00a0just deluding yourself, as so many people\u00a0do about so many things.) \u00a0 My first objection\u00a0to formal math is this:\u00a0why impose it on school kids?\u00a0<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,3],"tags":[],"class_list":["post-48","post","type-post","status-publish","format-standard","hentry","category-education","category-history-and-philosophy-of-mathematics"],"_links":{"self":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=48"}],"version-history":[{"count":0,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/48\/revisions"}],"wp:attachment":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=48"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=48"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\u00a0
\nI have no objection if you want to do math because you find it beautiful. (But why so many adjectives?\u00a0 (“elegant, sublime, surreal”)\u00a0\u00a0That\u00a0suggests lack of confidence in what you are saying, for most people\u00a0do not see that beauty; so maybe you are afraid\u00a0that you are\u00a0just deluding yourself, as so many people\u00a0do about so many things.)
\n\u00a0
\nMy first objection\u00a0to formal math is this:\u00a0why impose it on school kids?\u00a0You might like\u00a0jazz\u00a0music, and are welcome to pursue it. But why insist that all school kids should learn jazz as the “universal” form of music?\u00a0Indeed, 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).\u00a0
\n\u00a0
\nSecondly, why should the taxpayer support this sort of maths? More specifically, \u00a0what \u00a0I have publicly stated in my article on\u00a0D. D. Kosambi\u00a0[the son]\u00a0(“Kosambi: the mathematician”, Economic and Political Weekly\u00a0 <\/em>44<\/strong>(20) May 16\u201322 (2009) pp. 33\u201345) <\/span><\/span><\/span>is the following.\u00a0In India,\u00a0the Tata Institute of Fundamental Research is the bastion of formal mathematics—even their\u00a0notion of “applied math” involves theorem-proving!\u00a0It is funded by the Department of Atomic Energy. Why? If the aim is to pursue beauty, shouldn’t the funding\u00a0come from the\u00a0Department of Culture?\u00a0If the aim is utility that should be shown. But none of the theorems proved by anybody there\u00a0 (barring Kosambi) over the last 65 years\u00a0has even remotely contributed either to atomic energy or to the improvement of the life of even a single Indian\u00a0(apart from the theorem-provers themselves). This demonstrable lack of practical benefits cannot be covered\u00a0up by talk of a beauty which no one can see; they should talk of beauty while tabling the budget for atomic energy in parliament.\u00a0\u00a0In my opinion it is charlatanism to take money from the poor people of India in the name of\u00a0atomic energy and then give nothing back in\u00a0return, except\u00a0empty talk of\u00a0beauty, and\u00a0this charlatanism of Western-oriented “mathmen”, like that of “godmen” should be exposed.
\n\u00a0
\nThirdly,\u00a0this talk of beauty, like all theological discourse,\u00a0confounds all sorts of things. Yes, there definitely was\u00a0 beauty\u00a0in 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<\/em>. What Socrates demonstrates\u00a0is the intuitive <\/em>understanding of\u00a0geometry which the slave boy has. What Socrates (or Plato)\u00a0values is this intuition for (according to him) it awakens soul, like good music, and hence makes people virtuous.\u00a0
\n\u00a0
\nHowever,\u00a0Western math,\u00a0which you\u00a0believe in,\u00a0long ago disconnected mathematics from the belief in that notion of the\u00a0soul, which the church cursed.\u00a0Formal math also\u00a0disconnected mathematics from intuition.\u00a0this is clear, for example, from your\u00a0own dichotomy between “rigorous” and “intuitive” math, which is a common belief among formal mathematicians today.\u00a0 In fact,\u00a0mathematicians, today, often value a theorem for how counter<\/em>-intuitive it is! This just goes to show that Christian metaphysics\u00a0(imparted through Western education) trains the mind in a way contrary<\/em> to ordinary human intuition (with the deliberate aim of making it distrust human intuition and\u00a0trust 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\u00a0theological tricks to train the human mind into subordination. As a teacher, it is my duty to warn you.
\n\u00a0
\nFormal mathematical proof involves Hilbert’s rigidly mechanistic ideas, it is addressed to a machine, and can be checked by one; it\u00a0is as contrary to\u00a0the human mind as assembly-language programming (which built on exactly\u00a0that notion of formal proof).\u00a0This 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\u00a0<\/em>which followed the intuitive\u00a0“Neoplatonic” treatment; he learnt from the newer texts which follow Hilbert’s formalism and\u00a0synthetic postulates (and the rejection of\u00a0the side-angle-side\u00a0theorem and its replacement by\u00a0the SAS\u00a0postulate).\u00a0According to me, then, intuitive math may have beauty, but formal math is, in a word,\u00a0ugly.
\n\u00a0
\nAnd that is perhaps why so many people are intuitively repelled by it.
\n\u00a0
\nIf any attraction still persists in formal math it is because of\u00a0its “Neoplatonic” origins,\u00a0so, if beauty is what you seek,\u00a0you should certainly\u00a0abandon formal math and go back to “Neoplatonic” math, or Egyptian sacred geometry. (But the West won’t approve, for that was\u00a0started by blacks, who had a\u00a0different religion.)
\n\u00a0
\nI will continue my response in my next mail.
\n\u00a0
\nAll best,
\n\u00a0
\nC. K. Raju
\n\u00a0
\n\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"