My experiments with maths ...

Today I finished reading a book " The UNKNOWABLE " by Gregory J. Chaitin author of "The Limits of Mathematics " ....... I found that author has quite similar psychatric setup like me . Initally (his early research day ) he is interested in physics and concludes that maths is the key to unlock the mystry of Nature via physics . I started stressing upon maths on the very same lines few months back . He is interested in programming , so am I . He enjoys maths , so do I .

Hammmm , good enough . The author is a great mathematician and has done tremendous work about ramdomness , incompleateness and complexity . Offf you are you getting bored !! Actually I was to blog about how I came to this book / personality . Way back to my higher secondary school I loved prime numbers and wrote independently some fundamental programs . I remember running one of my program for few minutes , which told me that there are about 6000 prime numbers upto 64000 .. I discovered ( same thing which was known even to centuary old mathematican ) that we need only to test upto square root of a number to test it's primality . Well enough about primes .......
So here I was , looking for something in library and suddenly I came accross the book "MATHEMATICAL MYSTRIES : the magic and beauty of numbers " . I turned a few pages and found something about Ramanujam and some intriguing things ... I started reading it . First few chapters were quite interesting about history/beauty of mathematics. The author mentioned about "Stephan Hawking " being told by his respective publisher that EVERY EQUATION YOU WRITE IN YOUR BOOK WILL HALF THE SELLING !!!!!!!! .Then author justified his stand on this , and things like that . I found it interesting and started reading this book in leasure time , chapter by chapter . Almost all the chapters accept few were interesting . I recall : " Statememt A emply B " , this relationship about 'A' and 'B' was really great ( I am not using the exact numerical format for reasons anyone can guess ) and give some beautiful expressions . It generated a lot of highly symmetrical looking functions and things like that ...... Then that book told me to tie my seatbelt !! Something was going to comeout . Suddenly the book showed that same A~B relation gives

1 = sqrt( 0 + sqrt( 0 + sqrt( 0 + sqrt( 0 + sqrt( 0 + sqrt( 0 + ..................)))))
ooooo my god . How on earth !!!!

I moved on . Then author told me that he has kept the best thing for last (chapter) . I started reading the last chapter "Into the stratosphere" . I remember pausing for few minutes that "It has been proved that not everything is provable ". There exists truths whcih can neither be proved nor disproved. This was the consequence of the result by Godel (known as Mr Why in his childhood ) that either "Every truth is not provable " or "The whole mathematics is wrong ". What a beautiful blend of philosphy and mathematics ...... This is how I came accross the famous Incompleteness theorem . Once tested opon the flaver , I wanted more and I got hand on this book which I finished today , with more questions then answers .