### Ramanujan

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Dimensions: 18” H X 24” W X 1.5” D. Landscape orientation.

Acrylic paint, open-sourced printed materials overlaid with high gloss varnish.

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Srinivasa Ramanujan

This collage celebrates Srinivasa Ramanujan’s life at Trinity College, his formulas, and contributions to understanding partitions, summation, and mock theta functions in the subject of pure mathematics. The vibrant colors, papers, and 3D red beads reflect his vivid culture and brilliant mind. The pattern of overlapping lines represents the depth, layering, and interaction of the bold, bright ideas which made up his genius. He was born on December 22, 1887, in Madras, India. He was the mathematician depicted in the movie “The Man Who Knew Infinity.” Ramanujan had little formal training in pure mathematics. However, his brilliance enabled him to make substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan corresponded with a well-known mathematician G.H. Hardy at Trinity College, Cambridge, England. Hardy was impressed by Ramanujan’s work and invited him to England in order to advance Ramanujan’s work as well as to collaborate. Once in England, Ramanujan’s work earned him the prestigious Fellowship of the Royal Society. He became one of the youngest Fellows of the Royal Society and the first Indian to be elected a Fellow of Trinity College, Cambridge. He tragically became sick in 1919, traveled home to India, where he died in 1920. His work is still being researched today and has been used to understand black hole physics and types of string theory.

Elements of Art

Portrait of Ramanujan

Ramanujan’s signature

Photo of Trinity College

Quote from Ramanujan

Mathematics

Number theory

Infinite Series

Ramanujan’s mock theta functions

Infinity symbol

Special case integrals for constants in a Ramanujan theta function

Graphic of a theta function

1729/Vintage taxi with the cab number 1729

Partitions

Graphic explanation of partitions

The Hardy-Ramanujan Asymptotic formula

Photo of Ramanujan outside the Senate House at the University of Cambridge

Ramanujan Summation

A portion of the numerical proof for the Ramanujan summation

The final formula for the Ramanujan summation

The Om symbol

Explanation of Elements

Portrait of Ramanujan before 1920. Unknown photographer.

Ramanujan’s signature from Wikipedia.

Photo of Trinity College in Cambridge, England, where Ramanujan went to study with British mathematician G.H. Hardy in 1914.

Quote from Ramanujan. “An equation means nothing to me unless it expresses a thought of God.” Ramanujan was a deeply religious Hindu and followed the traditions of the Brahmin culture, including ceremonial worship called Puja and vegetarianism. He believed that the family goddess Namagiri Thayer endowed him with mathematical knowledge, revealed formulas to him and that all his mathematical skills were God speaking through him.

Mathematics is the abstract science of numbers, quantity, and space.

Number theory is the branch of mathematics that deals with the properties and relationships of numbers, especially positive integers.

Infinite series is the sum of infinitely many numbers related in a given way and listed in a given order.

Ramanujan's mock theta functions can be thought of as repeating trigonometric functions such as sine and cosine waves with more complex and subtle patterns. In addition, mock theta functions are “super-symmetric,” and their patterns turn into themselves, which is called a Mobius transformation. Ramanujan described the first examples of mock theta functions in his last letter to G.H. Hardy in 1920. Research continues on these functions, and they are currently used to help physicists compute the entropy, or level of disorder, of black holes and better understand string theory.

The infinity symbol is called a lemniscate and represents something that is boundless or endless. It was introduced in the 17Th century as mathematicians developed and worked with calculus, infinite series, and infinitely small quantities.

Special case integrals for constants in a Ramanujan theta function are included in this collage to show the span and complexity of this type of mathematics.

Graphic of a theta function which is related to a mock theta function. This graphic was created using a function by Carl Gustav Jacob Jacobi. Ramanujan studied in detail the theta functions generalizing the Jacobi theta functions. These functions have highly delicate analytical properties, which is why they are used to determine the critical dimensions in Bosonic String theory, M theory, and certain types of String theory.

1729/ Vintage taxi with the cab number 1729

The story about G.H. Hardy’s taxi and the number 1729.

Hardy was the professor of mathematics who invited Ramanujan to study at Trinity College. They worked closely together and became friends. Once when Ramanujan was ill, Hardy went to visit him in the hospital. When Ramanujan discovered he had taken a taxi, he inquired about its number. Hardy said that it was just a boring number: 1729. Ramanujan replied that 1729 was not a boring number as all and explained that it was the smallest number that could be expressed by the sum of two cubes in two different ways. This story is very famous among mathematicians, and the number, 1729, is sometimes called the “Hardy-Ramanujan number.”

1729 = 1^3 + 12^3

= 9^3 + 10^3

Partitions:

In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For example, p(4) = 5 because the integer 4 has five partitions 1+1+1+1, 1+1+2, 1+3, 2+2, and 4.

Graphic explanation of partitions which is comprised of young diagrams (rows of boxes) for the partitions of the numbers from 1 to 7.

The Hardy-Ramanujan Asymptotic formula was created by G.H. Hardy and Ramanujan in 1918.

Photo of Ramanujan outside the Senate House at the University of Cambridge. Ramanujan is in the center together with his colleague G.H. Hardy (extreme right).

The Ramanujan summation formula shows that if you add all the natural numbers, that is 1,2,3,4, and so, all the way to infinity, you will find that it is equal to -1/12. He was able to prove this by manipulating different series of numbers. This type of summation has applications in complex analysis, quantum field theory, and the original string theory.

A portion of the numerical proof for the Ramanujan summation

The final formula for the Ramanujan summation formula shows that if you add all the natural numbers, that is 1,2,3,4, and so, all the way to infinity, you will find that it is equal to -1/12.

The Om symbol is considered the highest sacred symbol of Hinduism. It refers to Atman (soul) and Brahman (ultimate reality, entirety of the universe, truth, divine, supreme spirit, and knowledge). Ramanujan was a devout Hindu and greatly valued this symbol.

References:

“Infinite Series.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., www.britannica.com/science/infinite-series.

“Infinity.” Wikipedia, Wikimedia Foundation, 5 June 2021, en.wikipedia.org/wiki/Infinity.

“Mock Modular Form.” Wikipedia, Wikimedia Foundation, 7 May 2021, en.wikipedia.org/wiki/Mock_modular_form#:~:text=In%20mathematics%2C%20a%20mock%20modular,and%20in%20his%20lost%20notebook.

“Möbius Transformation.” Wikipedia, Wikimedia Foundation, 4 May 2021, en.wikipedia.org/wiki/M%C3%B6bius_transformation.

“Om.” Wikipedia, Wikimedia Foundation, 7 June 2021, en.wikipedia.org/wiki/Om.

“Oxford Languages and Google - English.” Oxford Languages, languages.oup.com/google-dictionary-en/.

“Partition (Number Theory).” Wikipedia, Wikimedia Foundation, 30 Apr. 2021, en.wikipedia.org/wiki/Partition_(number_theory).

“QUOTES BY SRINIVASA RAMANUJAN: A-Z Quotes.” A, www.azquotes.com/author/21463-Srinivasa_Ramanujan.

“Ramanujan Summation.” Wikipedia, Wikimedia Foundation, 10 May 2021, en.wikipedia.org/wiki/Ramanujan_summation.

“Srinivasa Ramanujan.” Wikipedia, Wikimedia Foundation, 31 May 2021, en.wikipedia.org/wiki/Srinivasa_Ramanujan.

“Taxicab Number.” Wikipedia, Wikimedia Foundation, 29 Mar. 2021, simple.wikipedia.org/wiki/Taxicab_number.

“Trinity College, Cambridge.” Wikipedia, Wikimedia Foundation, 31 May 2021, en.wikipedia.org/wiki/Trinity_College,_Cambridge.

Weisstein, Eric W. “Ramanujan Theta Function.” Wikipedia, Wikimedia Foundation, 30 Apr. 2021, en.wikipedia.org/wiki/Ramanujan_theta_function.