Mathematicians and Dreams

Some time ago I wrote about "Cybernetics and Dreams" and how the cipher to John Wesley's coded journal was revealed to Nehemiah Curnock in a dream.

One of the most extraordinary stories about mathematical revelations through dreams was celebrated recently at the 125th anniversary of the birth of the Indian mathematician, Srinivasa Ramanujan. Ramanujan, a mathematical genius and prodigy.

Photo: Wikipedia

Wikipedia says...

Srinivasa Ramanujan FRS (22 December 1887 - 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. ...
Born at Erode, Madras Presidency (now Tamil Nadu) in a poor Hindu Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered by the age of 12; he even discovered theorems of his own, and re-discovered Euler's identity independently. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan had conducted his own mathematical research on Bernoulli numbers and the Euler-Mascheroni constant.

This remarkable man died at the age of 32. A Daily Mail article,  reported...

While on his death-bed in 1920, Ramanujan wrote a letter to his mentor, English mathematician G. H. Hardy, outlining several new mathematical functions never before heard of, along with a hunch about how they worked. 

Decades later, researchers say they've proved he was right - and that the formula could explain the behaviour of black holes.
....
Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.

The Durban Sunday Tribune elaborated, crediting the Daily Mail report...

Genius saw formulas in dreams 

Researchers have finally solved the cryptic deathbed puzzle renowned Indian mathematician Srinivasa Ramanujan claimed came to him in dreams...outlining several new mathematical functions never before heard of... Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.
...
Emory University mathematician said..... "No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,"
...
The findings were presented... at the Ramanajun 125 conference at the University of Florida, ahead of the 125th anniversary of the mathematician's birth on December 22.

- Tribune Herald, 6 January 2013

Hinduism Today featured an article posted by Dr Jai Maharaj in which he wrote:

.... Ramanujan possessed supernatural intelligence, a well of genius that leaves even brilliant men dumb-founded.  Ramanujan was a meteor in the mathematics world of the World War I era.  Quiet, with dharmic sensibilities, yet his mind blazed with such intuitive improvisation that British colleagues at Cambridge -- the best math brains in England -- could not even guess where his ideas originated.  It irked them a bit that Ramanujan told friends the Hindu Goddess Namagiri whispered equations into his ear.  Today's mathematicians -- armed with supercomputers -- are still star-struck, and unable to solve many theorems the young man from India proved quickly by pencil and paper.   

Ramanujan spawned a zoo of mathematical creatures that delight, confound and humble his peers.  They call them "beautiful," "humble," "transcendent," and marvel how he reduced very complex terrain to simple shapes.   

In his day these equations were mainly pure mathematics, abstract computations that math sages often feel describe God's precise design for the cosmos.  While much of Ramanujan's work remains abstract, many of his theorems are now the mathematical power behind several 1990's disciplines in astrophysics, artificial intelligence and gas physics.

Who is Namagiri?

In Hindu mythology Namagiri is the consort of Narasimha, the lionman avatar of Vishnu. Narasimha symbolises the omnipresence of God. Like the Sphynx of Giza, he is the everpresent guardian, an Aslan figure.

Srinivasa Ramanujan attributed his mathematical findings to the goddess Namagiri. According to Ramanujan, she appeared in his dreams, proposing mathematical formulae, which Ramanujan would then have to verify. One such event was described by him as follows:

"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing."

Dr. Jai Maharaj wrote:

"Debate still lingers as to the origins of Ramanujan's edifice of unique ideas.  Mathematicians eagerly acknowledge surprise states of intuition as the real breakthroughs, not logical deduction.  There is reticence to accept mystical overtones, though.... many can appreciate intuition “in the guise” of a Goddess.  But we have Ramanujan's own testimony of feminine whisperings from a Devi and there is the sheer power of his achievements.  Hindus cognize this reality."

Namagiri, the goddess of creativity, is akin to the Greek Muse, Urania, the muse of astronomy, science, and mathematics. As such she is an Anima figure inspiring, revealing, and unveling the mysteries of nature. Namagiri would be the feminine, guiding aspect, who can be thought of as a counterpart of the Jewish Hokmah or the Christian Sophia.

The genius of  dreams....let us pay attention to our dreams!

Also see: http://www.legacyoframanujan.com/index.html and http://www.hinduwisdom.info/quotes321_340.htm

Picture Credits: Wikipedia and Gustave Moreau, Hésiode_et_la_Muse

©Colin G Garvie HomePage: http://www.garvies.co.za