A googol is 10100 - 101 digits the inspiration for a mispelling that names a search company and sometimes taught to kids as a really big number. Beyond that is 10googol - the googolplex with about 17 million digits. But this is tiny - very tiny - compared with the scale of Graham's Number:
Change ringing refers to the playing of long sequences of permutations of the order of the ringing of bells - usually church bells. The Simons Foundation has a nice video explanation. An interesting combination of stamina, mathematics and art dating back about four centuries.
Neil deGrasse Tyson talks about the history of scientific progress and what happens when figures like the 12th century figure Hamid al-Ghazali can hit the brakes. It makes you wonder about the modern House in America with the sharia house rules of a party aiming itself at the distant past.
At least where people write a calendar as month.day and where biblical precision is all that s necessary (unless you get into hours, minutes and seconds as some do). But celebrations are often fun and an excuse to eat pie is welcome (note that e is another great irrational number).
Something curious is to look for interesting strings in pi. It is not known if the digits of irrational numbers are random, but pi gives the appearance. One of the first interesting strings comes at the 762nd decimal place where there are six 9s in a row. Richard Feynman noted if you are memorzing pi, to it to that level and then you can end by saying "... two, one, one, three, four, nine, nine, nine, nine, nine, and so on ..." suggesting pi is rational:)
For short strings it is easy to calculate pi to a few million digits and then find the string. So you can represent your initials by numbers (ascii for example) and find where they first occur in the number..
In the spirit of fun there is this video. Someone sent it yesterday and asked what it was - it is a joke .. see if you can figure it out:-)
But mathematicians also star in some of the most dramatic stories in science. The lone, unrecognized genius laboring away on a groundbreaking theory over many years is more fiction than fact for most of modern science—but not in mathematics. Andrew Wiles’ 1995 proof of Fermat’s last theorem, which had defied all efforts to prove it for more than 300 years, was made all the more dramatic by the secrecy with which it was conducted. But Wiles was already ensconced in the elite circles of mathematics when he did his work.
Not only did Zhang work in relative secrecy, he was also a complete unknown. He had found work as a lecturer at the University of New Hampshire (UNH) in 1999, eight years after he finished his Ph.D., with the help of connections at his undergraduate institution, Peking University. Then, in April of this year, Zhang announced a proof that cracked open a century-old problem in mathematics, called the twin prime conjecture. “It was like climbing Everest,” says Ayalur Krishnan, a math professor at CUNY’s Kingsborough community college.
(tip of the hat to Frank)
Explaining something technical is a real challenge. Here Margot Geeritsen talks about a great piece of applied math - the Navier-Stokes equation. If you have seen a bit of calculus you should be ok with it and learn why this is so useful. A nice job and she uses a real chalkboard...
Elliptic curve cryptography (ECC) is one of the most powerful but least understood types of cryptography in wide use today. An increasing number of websites make extensive use of ECC to secure everything from customers' HTTPS connections to how they pass data between data centers. Fundamentally, it's important for end users to understand the technology behind any security system in order to trust it. To that end, we looked around to find a good, relatively easy-to-understand primer on ECC in order to share with our users. Finding none, we decided to write one ourselves. That is what follows.
Be warned: this is a complicated subject, and it's not possible to boil it down to a pithy blog post. In other words, settle in for a bit of an epic because there's a lot to cover. If you just want the gist, here's the TL;DR version: ECC is the next generation of public key cryptography, and based on currently understood mathematics, it provides a significantly more secure foundation than first-generation public key cryptography systems like RSA. If you're worried about ensuring the highest level of security while maintaining performance, ECC makes sense to adopt. If you're interested in the details, read on.