Web resources in Mathematics

Being a mathematics graduate I have a passion for mathematics and I am always fascinated by its beauty.Nevertheless I am interested in history of science and mathematics and computer science in particular and whenever I come to know any related web resource I will bookmark that.I discovered Diigo few months ago and it was the kind of tool I was looking for and I moved all my bookmarks from google to Diigo. In addition to just bookmarking it archives the pages bookmarked and it will be helpful if it gets lost in future(and it is very common).Also it is claimed to be a researcher's tool as it has facility to arrange items and highlight information ,share items with others etc.I suggest every one to try Diigo once.Coming back to mathematics I am listing below some links which will be interesting for any maths lover.

1) Wikipedia mathematics portal
Of cource wikipedia is the number one source for any topic.
2) Planet maths
Planet maths is an encyclopaedia for mathematics.It has article on almost every subject and it is reviewed by members. Each topic is owned by one member and so it will be more authentic and accurate.

3)Wolfram Math world and wolfram alpha online
Math world has rich set of details about almost all the branch of mathematics. Wolfram alpha knowledge engine uses mathematica software which helps you to compute so many mathematical functions online quickly.It is a powerful tool for mathematics students and teachers.
4) MacTutor History of Mathematics archive
The MacTutor History of Mathematics archive is the largest source of information in the web about the history of mathematics and also about mathematicians.
5)cut the knot
contains interesting mathematics puzzles and introduction to mathematics topics and problems
6)Springer encyclopaedia of mathematics
Springer encyclopaedia of mathematics acts as a quick reference for mathematics topics available with an index.
7)MIT open courseware
MIT open courseware from MIT is the largest source of learning materials on any subject .
8)Math forum
The Math Forum is a leading center for mathematics and mathematics education on the Internet.It has a lot of resources and links for learning and teaching mathematics.
9)Internet encyclopedia of philosophy
Internet encyclopedia of philosophy has a section about mathematics and logic which is helpful to understand the foundations and philosophy of mathematics.
10)Prime pages
Prime pages has lot of information about prime number research an interesting field in number theory.
11)Gresham college lectures in mathematics
A lot of interesting lectures in mathematics.I found these very interesting and informative.
12)The Math Open Reference Project
A free interactive math textbook on the web. Initially covering high-school geometry.
13)visualmathlearning.com
Understanding Mathematics through Insight, Concept, and Perception
14)math-atlas.org
Introductory articles on almost all the branches of mathematics.
15)NRICH
NRICH is a team of qualified teachers who are also practitioners in RICH mathematical thinking.NRICH aims to Enrich the experience of the mathematics curriculum for all learners.

I hope these links will be useful for all mathematics lovers seeking for resources and reference in web.

Erdős number

I was just reading the news of stepping down of Stephan hawking from the Lucasian professor of Mathematics in Cambridge University.I also came to know that Hawking has a Erdos number of 4. This evoked my interest to know more about Paul Erdos the great Hungarian mathematician.

Paul Erdos ,an immensely prolific mathematician has wrote around 1,475 mathematical articles in his lifetime, mostly with co-authors. This made his colleagues to coin the term Erdos number which indicates the collaborative distance between a person and Erdős, as measured by authorship of mathematical papers.Erdos has a number of 0 his co-authors has number of 1 and their co-authors will have number of 2 and so on.

The origin of this term won't be astonishing if you come to know more about Paul Erdos and his contributions .He stands only next to Euler in terms of the volume of mathematical work.Erdos also known to be of exceptional character for whom possessions meant nothing and spent most of his life as a vagabond.He has once told "You don't have to believe in God, but you should believe in The Book".The Book is an imaginary book that Erdos believes in which God had written down the best and most elegant proofs for mathematical theorems.See the wikipedia article and related links on Paul Erdos for more details.
Reference
Wikipedia

More lectures on mathematics from Gresham college

As a part of creating the previous note on "Hilbert's questions" i was just going through the Gresham college site for more luctures on mathematics and found many other interesting lectures in the site. As the one mentioned earlier all these are a good collection of lectures and will be enjoing for any mathematic student .
Follow these link and you are there.
Past lectures on geometry

Hilbert's questions to the future

Here is an interesting lecture on Hilbert's questions by Professor Robin Wilson of Grasham college,London delivered on 27/02/2008."From Hilbert's problems to the future"
This lecture is very informative and simple to understand the famous Hilberts questions .Hilbert's problems are a list of twenty-three problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900.
References
Wikipedia

Euler's equation of degree four solved

This post may be a little late(found in march 2008),but i just come across this .One of the unsolved problem proposed by Leonhard Euler in 1772 have a solution now. This problem asks for a solution in integers to the equation a⁴ + b⁴ + c⁴ + d⁴ = (a + b + c + d)⁴.
Mathematician Daniel J. Madden and retired physicist, Lee W. Jacobi, found solutions to a puzzle that has been around for centuries. Please see this link for the complete story. It is very interesting.
This is related to another disproved conjucture of Euler .In 1772, Euler, hypothesized that to satisfy equations with higher powers, there would need to be as many variables as that power. For example, a fourth order equation would need four different variables, like the equation above. Euler's hypothesis was disproved in 1987 by a Harvard graduate student named Noam Elkies. He found a case where only three variables were needed. Elkies solved the equation: (a)(to the fourth power) + (b)(to the fourth power) + (c)(to the fourth power) = e(to the fourth power), which shows only three variables are needed to create a variable that is a fourth power.
95800⁴ + 217519⁴ + 414560⁴ = 422481⁴.

Largest prime number

Good news for number theory enthusiasts. Two new larger prime numbers are discovered.
These are 2^37,156,667-1, and 2^43,112,609-1.Previousely the known largest prime was 2^110,503-1 discovered in 1988.
These are mersenne primes(primes which can be expressed as one minus a power of 2). Mersenne primes are very rare and till now only 46 numbers are discovered. For more details
see the GIMPS(Great Internet Mersenne Prime Search) home page.GIMPS is a is a collaborative project of volunteers who use Prime95 and Mprime software that can be downloaded from for free from net to search for mersenne primes.
References
Wikimedia News