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Today is the birth centenary of G.H.Hardy, great English Mathematician.Hardy is most famous outside of mathematics for his “A Mathematician’s Apology”. book . The book, talks among other things about how mathematics is young man’s game. He is also known for his association with Ramanujan and for being the person responsible for bringing him to Cambridge where his greatest mathematics unfolded.

Some quotes:

1. Asked if he believes in one God, a mathematician answered: “Yes, up to isomorphism”.
2. “I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.”

Wikipedia :

It is never worth a first class man’s time to express a majority opinion. By definition, there are plenty of others to do that.

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.


Quoting one of the mathematicians, C Snow, that Hardy worked with:


A mathematicians apology is, if read with the textual attention it deserves, a book of haunting sadness. Yes, it is witty and sharp with intellectual high spirits: yes, the crystalline clarity and candor are still there: yes, it is the testament of a creative artist. But it is also, in an understated stoical fashion, a passionate lament for creative powers that used to be and that will never come again. I know nothing like it in the language: partly because most people with the literary gift to express such a lament don’t come to feel it: it is very rare for a writer to realize, with the finality of truth, that he is absolutely finished.

Hardy was a sort of purist mathematician, one who did his mathematics not for the sake of its applicability to anything, but for the sake of doing great mathematics. Hardy, along with Littlewood and Ramanujan, is also mentioned in Apostolos Doxiadis’ “Uncle Petros and the Goldbach Conjecture”. The link above gives a short summary on his life.


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Today is the 121 Birth Anniversary of Srinivas Ramanujan,a famous Indian Mathematician,who, with almost no formal training in pure mathematics, made substantial contributions to mathematical analysis,number theory,infinite series and continued fractions.Recently his contributions have found applications in crystallography and string theory.

In the memory of Ramanujan, Tamil Nadu every year celebrates 22 December as ‘State IT Day’. His contributions to Mathematics are well known.The contribution of G.H. Hardy a famous mathematician is also equally important, but when some body asked him what was his biggest contribution to Mathematics, Hardy told, Ramanujan was his biggest contribution to Mathematics,such was the genius of Ramanujan.

Here is his brief Profile.

Profile

Born : 22 Dec 1887
Died : 26 April 1920
Birth Place : Erode, Tamil Nadu, India

Contributions to Mathematics :

1. Landau- Ramanujan Constant
2. Mock Theta Fuction
3. Ramanujan Prime
4. Ramanujan – Soldner Constant
5. Rogers- Ramanujan Identities

Applications of his contributions :

1. Crystallography
2. String Theory

I wrote this post to pay tribute to him & his genius.

Here is a nice Song i found on the Net, which reminds us about the Famous Unsolved Mathematical Problem P = NP .

its a love story
of two strange people
who never knew they could
fall for each other
when they first met
they only ended up fighting
but slowy it became clear to them
that they sure shared something

a small problem happened
when pride overtook him
he thought she was
less smarter than him
she would solve a puzzle
and he would solve it again
he would tell her
that she was simply
an idea away from him…
he said that he always gets this idea
and then he does all that she can
and probably much more…

one day she decided
his behaviour had to be checked
she thought for a while and
then she said…
fine, then you sure
can do everything
but if you are strictly more smart
you have to do the following
think of some puzzle
that you can easily do
and then give it to me
to solve and lets see if
i can’t do….

all the king’s men and
all the king’s horses
could not come up
with a puzzle like this
the duo got closer and
the world around more curious

today as it stands
the puzzle is still not found
and hence the duo
lives happily close bound
they two are well known
as simply, inseparable
P is the queen and
NP the king of our fable…

Hope you all enjoy it…….
Source : Nutan’s Blog

A prime number (or prime integer, often simply called a “prime” for short) is a positive integer 1″ border=”0″ height=”15″ width=”33″> that has no positive integer divisors other than 1 and p itself. (More concisely, a prime number p is a positive integer having exactly one positive divisor other than 1.) For example, the only divisors of 13 are 1 and 13, making 13 a prime number, while the number 24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization 24==2^3.3), making 24 not a prime number. Positive integers other than 1 which are not prime are called composite numbers.

Prime numbers are therefore numbers that cannot be factored or, more precisely, are numbers n whose divisors are trivial and given by exactly 1 and n.

The number 1 is a special case which is considered neither prime nor composite (Wells 1986, p. 31). Although the number 1 used to be considered a prime (Goldbach 1742; Lehmer 1909; Lehmer 1914; Hardy and Wright 1979, p. 11; Gardner 1984, pp. 86-87; Sloane and Plouffe 1995, p. 33; Hardy 1999, p. 46), it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own. A good reason not to call 1 a prime number is that if 1 were prime, then the statement of the fundamental theorem of arithmetic would have to be modified since “in exactly one way” would be false because any n==n.1. In other words, unique factorization into a product of primes would fail if the primes included 1. A slightly less illuminating but mathematically correct reason is noted by Tietze (1965, p. 2), who states “Why is the number 1 made an exception? This is a problem that schoolboys often argue about, but since it is a question of definition, it is not arguable.” As more simply noted by Derbyshire (2004, p. 33), “2 pays its way [as a prime] on balance; 1 doesn’t.”

With 1 excluded, the smallest prime is therefore 2. However, since 2 is the only even prime (which, ironically, in some sense makes it the “oddest” prime), it is also somewhat special, and the set of all primes excluding 2 is therefore called the “odd primes.” Note also that while 2 is considered a prime today, at one time it was not (Tietze 1965, p. 18; Tropfke 1921, p. 96).

The nth prime number is commonly denoted p_n, so p_1==2, p_2==3, and so on.

The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, …
A mnemonic for remembering the first seven primes is, “In the early morning, astronomers spiritualized nonmathematicians”

In the Season 1 episode “Prime Suspect” (2005) of the television crime drama NUMB3RS, math genius Charlie Eppes realized that character Ethan’s daughter has been kidnapped because he is close to solving the Riemann hypothesis, which allegedly would allow the perpetrators to break essentially all internet security by factoring large numbers.

The numbers of decimal digits in p_(10^n) for n==0, 1, … is given by 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, …

Source :http://mathworld.wolfram.com