Srinivasan Ramanujan F.R.S.
 

Today we commemorate Srinavsa Ramanujans 117the birth anniversary.
[1887-1920].
He was tutored by the great English mathematician G.H. Hardy. Together they collaborated on numerous papers which startled the worlds leading. mathem’cians
When Hardy was asked ‘What was your greatest discovery?’ He replied Ramanujan.
When Hardy visited Ramanujan during his illness he remarked that the number of the Taxi cab was 1729 a rather dull number and hoped it was not a bad omen..
‘No Hardy’ said Ramanujan. ‘It is the smallest number that expresses the sum of two cubes in two different ways---1729 = 12^3 + 1^3 = 10^3 + 9^3.

In 1942 Freeman Dyson was then a 2nd. Yr. student at Winchester Hardy’s alma mater where he won a prize in Mathematics. Later this is what he had to say of Srinivasa.
“He discovered so much and yet he left so much in his garden for other people to discover. In the 44 yr.s since then I have been intermittently coming back to Ramanujans garden. . Every time I come back I find fresh flowers blooming” a fitting tribute from such an eminent mathem’cian.

As a sample of srinivasa’s genius Hardy recorded his appx. of pi as
63/25(17 + 15 sq.rt.5)/ 7 + sq.rt.5) correct to 9 places and that too without the aid of an electronic calculator !

He reflected his life in these words “An equation for me has no meaning unless it expresses a thought of God”

Sou: ‘The Man who knew Infinity” by Robert Kanigel

S. Ramanujan
 

If I may opine on the subject I'd like to add that Ramanujan was compared to the greats like Jacobi & Euler mainly for sheer manipulative ability. His, Ramanujan’s, main interest was in problems that had solutions & to provide formulas for the same. This reason could be why he was uninterested in Fermat’s Last Theorem.

"Euler could calculate with no apparent effort as men breathe or as eagles sustain themselves in the wind." I think the same could be said of the Indian mathematical genius Srinivasa Ramanujan.

From: lxef

Bertrand Russell
 

:sad: Im a day late but lets remember Old Russell who baffled many a mathematician in his day.

Mathematical moments

Bertrand Russell - Born: 18th of May 1872 in Ravenscroft, Wales
Died: 2nd of February 1970 in Penrhyndeudraeth, Wales

Bertrand Russell was one of the most influential logicians of the 20th century. He held the view that all maths can be reduced to formal logic, and played a major role in developing formal logic and what is known as "first-order predicate calculus". But what he's maybe most famous for is the paradox which carries his name. It goes like this: take any set and ask if it's a member of itself. For example, the set consisting of all dogs on Earth is not a member of itself, because a set of dogs is not a dog. But the set consisting of everything that is not a dog is a member of itself, since it's itself not a dog. Now look at the set which consists of all sets that are not members of themselves. If this is a member of itself, then it's not a member of itself. If it's not a member of itself, then it's a member of itself. Have fun puzzling...:surprised Mally :coffee:

Always nice to see such a thing.

Silly English Knnnnnnnigggits...

[quote=Fusion_power][URL="http://news.bbc.co.uk/2/hi/science/nature/4569656.stm"]http://news.bbc.co.uk/2/hi/science/nature/4569656.stm[/URL]
[/quote]
Notice Sir John's resemblance to the current heir to the throne?

Knighthood for a British mathematicin
 

[QUOTE=Fusion_power][url]http://news.bbc.co.uk/2/hi/science/nature/4569656.stm[/url]

Slightly interesting. Any comments Paul?[/QUOTE]

An extract from the url/
"Professor Ball studied for his undergraduate degree in mathematics at the University of Cambridge, and obtained a D.Phil in 1972 at the University of Sussex."
Do you personally know him Paul?
Mally :coffee:

Abel prize for Swede
 

:bow:
One up for the Swedes!

[url]http://www.sci-tech-today.com/news/Swede-Wins-Abel-Mathematics-Prize/story.xhtml?story_id=11300BSASHFI[/url]
1. [url]http://www.p2pnet.net/story/8306[/url]

Mally :coffee:

Do they shake left hands in Sweden?

[QUOTE=victor]Do they shake left hands in Sweden?[/QUOTE]
That took me some time to understand. :lol:

[QUOTE=mfgoode][url]http://www.p2pnet.net/story/8306[/url][/QUOTE]:rant: :rant: Proxy-firewall:rant: :rant:

[quote=victor]Do they shake left hands in Sweden?[/quote]Another example of carelessness in craftsmanship. :furious: The left/right flip is one of the worst things a graphic artist can do when there is asymetry. Tabloids will often flip pix of celebs to orient the picture so that the person faces the center of the page and not the edge or fold. With someone with obvious asymetry like Marilyn Monroe, Gorbachev, or Bob Dole they don't so often, but others like Denzel Washington (who has the highest degree of symetry of any current movie star), they flip all the time and only background parts of the image may be a give away.:rant:

Mathematical moments
 

:flex:
Jean Baptiste Fourier - Born 21st of March 1768 in Auxerre, France
Died 16th of May 1830 in Paris, France

Every periodic function can be expressed as an infinite sum of sine and
cosine functions. This probably is Fourier's most famous result and his
name remains attached to these infinite sums. Fourier analysis, the
process
of splitting a function into its constituent sine and cosine parts, is
invaluable when it comes to analysing anything that travels in waves.
Music, speech and image analysis, as well as the compression of sounds
and
images, and analysis of weather and seismic data are just a few
examples of
the applications of Fourier analysis. It has particularly come into its
own
since the rise of computers, because our digital and finitely-minded
computers can only understand complicated wave forms - like those
coming
from music - if they are approximated by their constituent sine and
cosine
waves.
For more from Plus magazine.

[url]http://us.f521.mail.yahoo.com/ym/ShowLetter?MsgId=2910_2177976_844374_3121_3579_0_19786_7258_2080935897&Idx=0&YY=78036&inc=25&order=down&sort=date&pos=0&view=&head=&box=Inbox[/url]

Mally :coffee:

[QUOTE=mfgoode]:flex:
Jean Baptiste Fourier - Born 21st of March 1768 in Auxerre, France
Died 16th of May 1830 in Paris, France

Every periodic function can be expressed as an infinite sum of sine and
cosine functions. This probably is Fourier's most famous result and his
name remains attached to these infinite sums. Fourier analysis, the
process
of splitting a function into its constituent sine and cosine parts, is
invaluable when it comes to analysing anything that travels in waves.
Music, speech and image analysis, as well as the compression of sounds
and
images, and analysis of weather and seismic data are just a few
examples of
the applications of Fourier analysis. It has particularly come into its
own
since the rise of computers, because our digital and finitely-minded
computers can only understand complicated wave forms - like those
coming
from music - if they are approximated by their constituent sine and
cosine
waves.
For more from Plus magazine.

[url]http://us.f521.mail.yahoo.com/ym/ShowLetter?MsgId=2910_2177976_844374_3121_3579_0_19786_7258_2080935897&Idx=0&YY=78036&inc=25&order=down&sort=date&pos=0&view=&head=&box=Inbox[/url]

Mally :coffee:[/QUOTE]
...and don't forget its utility in convolving the binary representations of very large integers (mod 2^(P-1)). :grin:

There is a story about this in the local newspaper today, Upsala Nya Tidning.

firewall.
 

[QUOTE=Uncwilly]:rant: :rant: Proxy-firewall:rant: :rant:
:razz:
I just clicked on that website and found no problem. Its as clear as day.
Maybe it was your off day. Why dont you give it a try again.
Mally :coffee:

Congrats Lennart Carleson! You deserve the Abel Prize (~1 $million).

I remember the elegance of the proof that every square integrable
(hence every continuous) function equals the sum of its Fourier Series
except at a "small" set of points (finite,nowhere dense,or measure zero?).

Very important result!!!!! Thank you, sir!

-- davar55 (David Yablon).

Please excuse my ignorance, but if this stuff was originally made to deal with waves, how does it connect to determining primality?

Please keep in mind, if you try to explain, that while I'm fairly intelligent, my education was cut short near the beginning of my 11th grade school year(by illness)

[QUOTE=jasong]Please excuse my ignorance, but if this stuff was originally made to deal with waves, how does it connect to determining primality?
[/QUOTE]

FFT stands for Fast Fourier Transform. Google on "FFT multiplication" for some good descriptions of how FFTs are used for multiplying large numbers.

Normally to do a Lucas-Lehmer test the following is done

S (1) = 4
S (2) = (4 * 4 – 2) mod 127 = 14
S (3) = (14 * 14 – 2) mod 127 = 67
S (4) = (67 * 67 – 2) mod 127 = 42
S (5) = (42 * 42 – 2) mod 127 = 111
S (6) = (111 * 111 – 2) mod 127 = 0

With 2^P - 1 being 2^7 - 1 = 127 which is why the steps are mod 127.
Mod 127 means integer division by 127
with a remainder in the range 0 to 126.

Using DWT a form of FFT (Fast Fourier Transforms) instead of multiplying
111*111 then modding (dividing) by 127 for the remainder,
it gets both done at once using considerably less calculations and time.
I ignored the - 2.

For large numbers in the range that are being tested by Prime95
for example 2^37654321 - 1 is a number that is 4706791 bytes long.
Squaring a number of that size then modding it by 2^37654321 - 1
by the math operations of multiplication and integer division
for the remainder, requires alot more calculations then doing a DWT.