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How Maths 'Nobel' winner Manjul Bhargava solved a 200-year-old number theory puzzle via Sanskrit tex

Skull and Bones

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Manjul Bhargava, a maths professor who just won the Fields Medal, once simplified a 200-year-old number theory law with help of an Indian mathematician's work from 6th century CE and the popular Rubik's Cube.

According to an interview the Princeton University professor gave to Quanta Magazine, he said German maths wizard Carl Friedrich Gauss showed that if two numbers - each sum of two perfect squares - are multiplied, the result will also be the sum of two perfect squares.

Bhargava, whose grandfather was a Sanskrit professor in Rajasthan, said he had once seen in Sanskrit manuscripts a generalisation of this same law, credited to Brahmagupta - an Indian mathematician in 628 CE.

The generalisation was this: If two numbers are each the sum of a perfect square and a given whole number times a perfect square are multiplied together, the product will again be sum of a perfect square and that whole number times another perfect square, said the report.

So when Bhargava came across Gauss' famous 18th century composition law on binary quadratic forms, which had him 20 pages to prove, Bhargava looked for a simpler way to describe the same process.

The process was if one multiplies two binary quadratic forms, the law tells which quadratic form will appear.

The eureka moment, as Bhargava told the magazine, came via Rubik's Cubes and Mini-Cube (with four squares on each side).

According to the magazine report, Bhargava saw that if he placed numbers on each four corners of the mini-cube and cut the cube in half, the eight corner numbers could be combined to produce a binary quadratic form.



In fact, the cube could generate three binary quadratic forms since there were three ways to cut a cube in half - making front-back, left-right or top-bottom divisions, said the report.

These three forms added up to zero with respect to Gauss' law. So the cube-slicing method gave a new reformulation of Gauss' law. Bhargava also found out that if he arranged numbers on a Rubik's Domino, he could produce a composition law for cubic forms, ones whose exponents are three.

Eventually, he have found 12 more such compositions that became part of his PhD thesis and later, a Benedict Gross, a Harvard mathematician, said the thesis was "first major contribution to Gauss' theory of composition of binary forms for 200 years".

When he was awarded the Infosys Prize two years ago, this feat was also cited : "Among Prof. Bhargava's contributions is the answer to a problem that had eluded the legendary Carl Friedrich Gauss (1777-1855).

"One of Gauss' discoveries was a law of composition on binary quadratic forms, i.e. expressions of the type ax2+ bxy + cy2, with a, b and c being whole numbers that are fixed, and x and y being the variables. It was an open question as to whether this was isolated or part of a bigger theory.

"Prof. Bhargava showed that quadratic forms were not the only forms with such composition, but that other forms such as cubic forms also have such composition. He was also able to show that the Gauss composition is in fact only one of at least 14 such laws".

http://indiatoday.intoday.in/story/...0-year-old-number-theory-puzzle/1/376911.html
 
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ppl who crave for attention in threads like these.

seems i got your attention for a comment where i said "who cares". :lol:

well, i was always one of those - "love him or hate him, you cannot ignore him".

ppl who couldnt do jack shit in their own life and have gall to point fingers at others :D

haan bhai, main hi ek nikamma nitthalla nikla warna aap aur aap ke dost toh kisi zamaane mey che guevara ke saath inqilaabon me shaamil the aur kuch dost elon musk ke saath das saal ek andar mars duniya ko one-way jaane waale hain.
 
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busy with the work Bro :)
where have you been since the last 2 weeks,missed you yara:cry:---and how many times i quoted,not a single reply from rana sahab:mad:
ppl who crave for attention in threads like these.

ppl who couldnt do jack shit in their own life and have gall to point fingers at others :D
panday tenoo phainti pyn vali hoi ay:butcher:
 
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seems i got your attention for a comment where i said "who cares". :)

well, i was always one of those - "love him or hate him, you cannot ignore him".

Naah !! its more like a good for nothing Nikamma Nithalla showing his envy over other's achievements :)

haan bhai, main hi ek nikamma nitthalla nikla warna aap aur aap ke dost toh kisi zamaane mey che guevara ke saath inqilaabon me shaamil the aur kuch dost elon musk ke saath das saal ek andar mars duniya ko one-way jaane waale hain.

Good that u admit that u are good for nothing attention seeker :)
panday tenoo phainti pyn vali hoi ay:butcher:
isnu Chhadd yara.

dass ki hal aan ?

where have you been since the last 2 weeks,missed you yara:cry:---and how many times i quoted,not a single reply from rana sahab:mad:

Kataaai season chal raha hai yar, and fir vyah bhi to tha :D
 
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Naah !! its more like a good for nothing Nikamma Nithalla showing his envy over other's achievements :)



Good that u admit that u are good for nothing attention seeker :)

isnu Chhadd yara.

dass ki hal aan ?



Kataaai season chal raha hai yar, and fir vyah bhi to tha :D
fit fat have you earned a wife yet:P

Kataaai season chal raha hai yar, and fir vyah bhi to tha :D
great, when did it happen? and how is bhabi g treating you:azn: chavla koi mithay nae khilay:pissed:
 
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Naah !! its more like a good for nothing Nikamma Nithalla showing his envy over other's achievements :)

go to some socialist country or to the jnu campus or the 'hyderabad university' and announce your utter usefulness to humanity in detail.

they will laugh at you at the minimum, and that will teach you who's the nikamma nitthalla.

yahaan pey main akela mil gaya hoon toh tum log ghair lete ho... one such person thanked your post too and i am not talking about @Mentee .

see, people like you may be hot shots among your family and like-minded peers but you can neither be a good progressive leader nor a good progressive student... buss ek bheed ka hissa ho. :)

Good that u admit that u are good for nothing attention seeker :)

i admitted no such thing.

stop being deluded.
 
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