Matrix multiplication

Wolfram demonstrations project provides a lot of interactive scripts on many mathematics concepts.
Here is the matrix multiplication:

You will have to download the free CDF player in order to interact with the script.

Matrix Multiplication from the Wolfram Demonstrations Project by Abby Brown

How to install OpenBugs on a macintosh using OSX in 5 simple steps

If you want to use OpenBugs on a macintosh there is a really simple solution: install it using wine.

1. First of all you have to install Wineskin (an Open Source implementation of the Windows API). Download the latest version from here:

http://wineskin.urgesoftware.com/
and double click on Wineskin Winery.app :






Click on the + sign to add an engine, just take the most recent one.






2. Then click on Create New Blank Wrapper, naming it as you wish:





3. Next, download the windows OpenBugs installer:

http://www.openbugs.net/w/Downloads


4. Then, double-click on the OpenBugs.app you have created (it resides on your ~/Applications folder in your home, not the /Applications folder of your disk, but you can move it later) and choose Install Software.

Click on Choose Setup Executable, point it to the OpenBugs installer you downloaded and here you are, installation begins.

At the end you will have an OpenBugs.app application in your ~/Applications folder and when you double click it you launch directly OpenBugs:

That's all. As I said, you can move your OpenBugs.app on the /Applications folder to make it available to all users of your macintosh.

For Ada Lovelace day: who were the first women in mathematics?

The Ada Lovelace day is a day to celebrate all women contributing in science.

On this occasion the first names coming to my mind are Marie Curie and Rosalind Franklin. 

But I wanted to pay a tribute to some of the first women of mathematics.

Going back in time, well before the great Sophie Germain and her pioneering work on prime numbers.

I believe almost everyone knows Hypatia from Alexandria and her work on conic sections. She was not only a mathematician but also a teacher and a philosopher of the end of the IV^th century. There are plenty of web sources you can find with her history but I recommend you read her complete biography by Maria Dzielska.

A few centuries earlier, in the 6^th century BC, Pythagoras accepted equally men and women in his school. Iamblichus cites 17 "illustrious Pythagorean women" (click to see the text).

The most famous is his wife, Theano, believed to be the first to study the golden ratio. She directed the school after Pythagoras death.

Damo, daughter of Pythagoras and Theano published the works of her father.

A woman was also the first teacher of Pythagoras, the priestess of Delphi, Themistokleia (click to read the text by Diogenes Laertius in "Lives of Eminent Philosophers").

It is difficult to attribute particular works to these Pythagorean women but clearly they actively participated and contributed to the school studies. 

Talking about prime numbers, twins, cousin, sexy and safe

There was a lot discussion on the net those last days concerning a big step toward the proof of a very old conjecture about prime numbers.
The conjecture states that there is an infinity of “twin prime numbers”, prime numbers separated only by two units, such as 11 and 13 for instance.
I was interested to the history of this conjecture and I tried some bibliographic research :

Some state that the conjecture was made by the Greek mathematician Euclid at 300 BC. Indeed Euclid had defined what a prime number is, and proved that there is an infinity of primes. (See the very elegant proof in Book 9 of the Elements, proposition 20, page 271 of this pdf). But I have not found the conjecture about twin primes in the Elements.

Most authors cite the French mathematician Alphonse de Polignac as the first to formulate the conjecture in a more general form at 1849 : in the Compte Rendus de l’Académie des Sciences, October 15th 1849, he published a paper on number theory, where he states among other theorems what has been later called the “de Polignac conjecture” :
“Every even number is equal to the difference of two prime numbers with an infinity of possibilities”.
If you consider the even number 2, you have the “twin primes” (like 11 and 13), with the number 4 you obtain what is called the “cousin primes” (like 13 and 17) and with the number 6 you have the so called “sexy primes” (like 11 and 17). And the infinity of possibilities implies that there is an infinity of each of these pairs, thus for n=2 we have the twin prime conjecture.

The “de Polignac conjecture” is a general case of the twin prime conjecture but is also a special case of the “Dickson conjecture” (formulated by the American mathematician Leonard Eugene Dickson at 1904), which covers also other special primes, such as the “Sophie Germain primes”, primes G such as 2*G+1 is also prime (2*G+1 is then called “safe prime”), named after the great French mathematician Marie-Sophie Germain. For instance 89 is a Sophie Germain prime because 2*89+1=179 is also prime, a safe prime.

Feel free to comment, especially if you find the proposition of Euclid about twin primes.