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While on his death bed , the bright Indian mathematician Srinivasa Ramanujan cryptically write down functions he said arrive to him in dreaming , with a hunch about how they behaved . Now 100 years later , investigator say they ’ve prove he was good .
" We ’ve solved the job from his last cryptical letter . For people who run in this area of math , the problem has been subject for 90 years , " Emory University mathematician Ken Ono say .
Srinivasa Ramanujan
Ramanujan , a ego - taught mathematician behave in a rural settlement in South India , spent so much clock time thinking about math that he flunked out of college in India twice , Ono say .
But he institutionalise mathematicians letter depict his work , and one of the most preeminent ones , English mathematician G. H. Hardy , recognized the Indian boy ’s champion and invited him to Cambridge University in England to study . While there , Ramanujan print more than 30 composition and was inducted into the Royal Society . [ Creative Genius : The World ’s Greatest Minds ]
" For a abbreviated window of time , five years , he litthe world of mathon fire , " Ono told LiveScience .
A visualization of a theta function
But the insensate weather finally sabotage Ramanujan ’s health , and when he was dying , he went home to India .
It was on his deathbed in 1920 that he described orphic functions that mimic theta use , or modular forms , in a letter to Hardy . Like trigonometric functions such as sine and cosine , theta function have a repeating radiation pattern , but the pattern is much more complex and elusive than a simple sine curve . Theta map are also " super - symmetric , " meaning that if a specific type of numerical subprogram called a Moebius transformation is applied to the functions , they flex into themselves . Because they are so symmetrical these theta functions are utile in many eccentric of mathematics and physics , admit string theory .
Ramanujan believed that 17 Modern role he discover were " mock modular forms " that looked like theta functions when write out as an infinte sum ( their coefficients get large in the same agency ) , but were n’t super - symmetrical . Ramanujan , adevout Hindu , thought these patterns were give away to him by the goddess Namagiri .
Ramanujan died before he could prove his hunch . But more than 90 years later , Ono and his squad proved that these routine indeed mimicked modular forms , but do n’t share their defining characteristics , such as superintendent - proportion .
The expansion of mock modular form helps physicists compute theentropy , or level of disorder , ofblack holes .
In developing mock modular variant , Ramanujan was decades ahead of his time , Ono said ; mathematician only figured out which branch of math these equations belonged to in 2002 .
" Ramanujan ’s legacy , it grow out , is much more authoritative than anything anyone would have guessed when Ramanujan died , " Ono said .
The findings were deliver last calendar month at the Ramanujan 125 group discussion at the University of Florida , onwards of the hundred-and-twenty-fifth day of remembrance of the mathematician ’s birth on Dec. 22 .
