Wednesday, November 19, 2008

Some thoughts on India's moon mission

One article came in Knowledge wharton in oct 16 2008 before the lunar mision found very informative. Describing various views on lunar mission ,its benefits and some criticisms it tries to explain what india is going to achieve my the mission. The criticisms were especially about the appropriateness of huge amount money being spent(386 crore) on this mission while a large part of the population is living below the povert line. But in light of its huge success and the confidence the indian scientific communinity gained by this mission ,and its far reaching benefits ,makes all criticisms week. It is sure that india gained a good position in the world space arena by this mission .

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

Tuesday, November 18, 2008

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 237,156,667-1, and 243,112,609-1.Previousely the known largest prime was 2110,503-1 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