An Achievement India Never Celebrated. Unknown

Manindra Agrawal, Neeraj Kayal, Nitin Saxena.

These are the names associated with an achievement India never celebrated. This achievement happened in 2002. In a country obsessed with Cricket and Bollywood (or all things foolish), this stupendous and enormously important achievement didn't matter and went into quick oblivion, though I doubt if it ever came into limelight. The achievement in question is AKS Primality Test (Agrawal-Kayal-Sexena Primality Test). This is named after three minds behind this achievement. If you try to search 'AKS Primality Test' on Google, the first two pages of results doesn't contain any 'indian' link. Ok, only one result and that too from their alma mater Indian Institute Technology website, Kanpur. At the time they published their results, Manindra was professor of Computer Science at IIT Kanpur, while Neeraj and Nitin were his doctoral students.

Random Miscellany #1 - Pi Unknown

Sometime back, I noticed a widely circulated meme on Pi on Internet: That meme reads: -

"PI IS AN INFINITE, NON-REPEATING DECIMAL - MEANING THAT EVERY POSSIBLE NUMBER COMBINATION EXISTS SOMEWHERE IN PI. CONVERTED INTO ASCII TEXT, SOMEWHERE IN THAT INFINITE STRING OF DIGITS IS THE NAME OF EVERY PERSON YOU WILL EVER LOVE, THE DATE, TIME AND THE MANNER OF YOUR DEATH, AND THE ANSWER TO ALL THE GREAT QUESTIONS OF UNIVERSE."

I found this rather intriguing and it made me curious enough to note it down. Of course, Pi is an infinite and non repeating decimal. As on 2011, the value of Pi has been calculated to, hold your breath, up to 10 trillion digits (that is 10,000,000,000,050 digits). Do check here for detailed account of this endeavor.  Ten trillion digits because, well, it took one year, some restarts, numerous hardware failures. The thing is, Pi will always have a last laugh over our computational capabilities.

As such, this meme, however interesting and sensational, is useless. If you really think about it, you will know this exercise is futile and meaningless. But story of Pi, on the other hand, is enormously deep and mysteriously beautiful.

Mathematical Resources from Internet Unknown

Indeed, much of Newton’s intellectual development can be attributed to this tension between rationalism and mysticism. At the Stourbridge Fair in 1663, at age twenty, he purchased a book on astrology, “out of a curiosity to see what there was in it.” He read it until he came to an illustration which he could not understand, because he was of ignorant of trigonometry. So he purchased a book on trigonometry but soon found himself unable to follow the geometrical arguments. So he found a copy of Euclid’s ‘Elements of Geometry’, and began to read. Two years later he invented the differential calculus.

- An excerpt from ‘Cosmos’ by Carl Sagan

We take up something-we know it is finite; but as soon as we begin to analyze it, it leads us beyond our reason, and we never find an end to all its qualities, its possibilities, its power, its relations. It has become infinite.

- Swami Vivekananda

"Good, he did not have enough imagination to become a mathematician".

- David Hilbert's response upon hearing that one of his students had dropped out to study poetry.

  

I have compiled a list of websites which may be used as resources for Mathematics. The compilation is not exhaustive for the obvious reason that Internet is full of thousands of such websites. Besides, I haven’t tried to categorize those websites. Some of the websites listed below also contain resources for topics not related to Mathematics, though you may find them useful anyway.