Motto: "Few, but ripe." (Gauss)
GREAT NEW PROOF of the Fundamental Theorem of Calculus
Stephen M. Walk: A Streamlined Proof of an Essential Calculus Fact, The American Mathematical Monthly, Vol. 117, No. 9 (November 2010), pp. 832-833.
One can build math starting from a simple original ideas. In terms of Kolgomorov complexity ( EN ) the "program for making math" is simple. The same appears when you put cocoa powder into milk. Just two ingredients in the beginning. When mixed a little it is an interesting fight between cocoa and milk. But quickly it will be well mixed and everything interesting disappears.
A question: Is math well mixed?
In 2002-2003 Agrawal, Kayal, and Saxena in a great breakthrough "PRIMES is in P" ( Wiki EN ) proved that the PRIMES function (prime number test) is O(log ^8 n), in other words polynomial of degree 8 of the number of digits (log n) of a given number n.
BTW, where in P is its real position? Any idea?
Newton discovered the Fundamental Theorem of Calculus. To keep its mystery hidden he has sent a mail to Leibnitz with a "mystery cache". For all cachers (reformulated to 2011 English setting) the message sounds
This cache is a virtual one. Opening it you will read the answer to the Fundamental Question of Calculus.
While in those years Newton prepared the cache as "not to be found" (NTBF), we provide a hint here below.