NATIONAL MATHEMATICS DAY

NATIONAL MATHEMATICS DAY

22 December 23 

India celebrates National Mathematics Day on December 22 to honor the 144th birth anniversary of the remarkable mathematician Srinivas Ramanujan. 

Born in Erode, Tamil Nadu in 1887, Ramanujan’s mathematical brilliance was recognized when he worked as a clerk at the Madras Port Trust in 1912. His colleague referred him to Professor GH Hardy of Trinity College, Cambridge University, where he later received his Bachelor of Science (BSc) degree. Ramanujan’s contributions to the theory of numbers were groundbreaking, including pioneering discoveries related to the partition function.

In 2012, then Prime Minister Manmohan Singh declared December 22 as National Mathematics Day in India, paying tribute to this extraordinary mathematician who left an indelible mark on the field of mathematics. 

LET’S DELVE INTO SOME KEY HIGHLIGHTS:

PARTITION FUNCTION: Ramanujan made pioneering discoveries related to the properties of the partition function. His insights into this area significantly advanced our understanding of number theory.

EARLY GENIUS: At the age of 15, Ramanujan obtained a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics. This collection of theorems sparked his genius, and he went beyond it, developing his own theorems and ideas.

SCHOLARSHIP AND STRUGGLES: In 1903, he secured a scholarship to the University of Madras, but his intense focus on mathematics led to the loss of the scholarship. Undeterred, he continued his work in poverty, without formal employment.

RECOGNITION AND COLLABORATION: Ramanujan’s genius gradually gained recognition. In 1911, he published his first papers in the Journal of the Indian Mathematical Society. His correspondence with the British mathematician Godfrey H. Hardy led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge.

MATHEMATICAL MASTERY: Despite being unaware of modern developments in mathematics, Ramanujan’s knowledge was astounding. His mastery of continued fractions, Riemann series, elliptic integrals, and hypergeometric series was unparalleled. He even developed his own theory of divergent series using a technique known as Ramanujan summation.

JOURNEY TO ENGLAND: Overcoming religious objections, Ramanujan traveled to England in 1914, where Hardy tutored him and collaborated on research. His contributions left an indelible mark on the field of mathematics.

Ramanujan’s legacy continues to inspire mathematicians worldwide, and his brilliance remains a beacon of mathematical exploration and discovery. 

DID HE RECEIVE ANY AWARDS FOR HIS WORK?

Srinivasa Ramanujan, despite his relatively short life, left an indelible mark on the world of mathematics. While he did not receive numerous awards during his lifetime, his contributions were eventually recognized posthumously. Here are some notable honors and recognitions:

FELLOWSHIP OF THE ROYAL SOCIETY (FRS): In 1918, Ramanujan was elected a Fellow of the Royal Society in London. This prestigious honor acknowledged his exceptional mathematical achievements.

HARDY-RAMANUJAN NUMBER 1729: During his collaboration with G.H. Hardy, they encountered the number 1729. Hardy remarked that it seemed uninteresting, but Ramanujan quickly corrected him. He revealed that 1729 is the smallest positive integer that can be expressed as the sum of two cubes in two different ways: (1729 = 1³+ 12³ = 9³+ 10³). This unique property led to it being named the Hardy-Ramanujan number.

LOST NOTEBOOK : After Ramanujan’s death, a collection of his unpublished mathematical results was discovered. This notebook contained groundbreaking theorems and conjectures. Mathematicians continue to study and explore its contents, recognizing its immense value.

PADMA VIBHUSHAN: In 1954, the Indian government posthumously awarded Ramanujan the Padma Vibhushan, one of India’s highest civilian honors. This recognition celebrated his exceptional contributions to mathematics.

RAMANUJAN CENTENARY: In 1987, the Ramanujan Centenary was celebrated worldwide to commemorate the 100th anniversary of his birth. Conferences, seminars, and events were organized to honor his legacy.

RAMANUJAN MEDAL: The Indian National Science Academy established the Ramanujan Medal in his honor. It is awarded to outstanding mathematicians under the age of 32 for their significant contributions.

WHAT IS RAMANUJAN'S LOST NOTEBOOK.

Ramanujan’s Lost Notebook is a fascinating mathematical treasure that sheds light on the genius of the Indian mathematician Srinivasa Ramanujan. Here are the key details:

WHAT IS IT?: The Lost Notebook is a manuscript in which Ramanujan recorded his mathematical discoveries during the last year of his life, specifically from 1919 to 192012. It contains a wealth of previously unknown theorems, conjectures, and mathematical insights.

REDISCOVERY: For many years, the whereabouts of this notebook remained a mystery, known only to a select few mathematicians. However, in 1976, George Andrews made a remarkable discovery. He found the Lost Notebook among the effects of another mathematician, G. N. Watson, stored in a box.

MATHEMATICAL SIGNIFICANCE: The contents of the Lost Notebook cover various areas of mathematics, including q-series, continued fractions, and other topics. Ramanujan’s unique approach and novel results continue to captivate mathematicians and inspire further research.

EQUIVALENT TO FINDING BEETHOVEN’S TENTH SYMPHONY: The discovery of the Lost Notebook has been likened to finding a previously unknown masterpiece. Just as uncovering Beethoven’s tenth symphony would be monumental, Ramanujan’s mathematical revelations in this notebook are equally profound.

LEGACY: The notebook contains 90 sheets of work on q-series and other mathematical topics, along with 180 pages of unpublished papers and additional loose pages. Mathematicians continue to study and explore its contents, uncovering hidden gems left behind by this mathematical prodigy.

In the world of mathematics, Ramanujan’s Lost Notebook stands as a testament to the boundless creativity and brilliance of a mind that transcended conventional boundaries. 

RAMANUJAN MACHINE:

Scientists from Technion — Israel Institute of Technology have developed a concept they have named the Ramanujan Machine, after the Indian mathematician. It is not really a machine but an algorithm, and performs a very unconventional function.

What it does:

With most computer programs, humans input a problem and expect the algorithm to work out a solution. With the Ramanujan Machine, it works the other way round. Feed in a constant, say the well-known π, and the algorithm will come up with an equation involving an infinite series whose value, it will propose, is exactly pi. Over to humans now: let someone prove that this proposed equation is correct.

Why Ramanujan? 

The algorithm reflects the way Srinivasa Ramanujan worked during his brief life (1887-1920). With very little formal training, he engaged with the most celebrated mathematicians of the time, particularly during his stay in England (1914-19), where he eventually became a Fellow of the Royal Society and earned a research degree from Cambridge.

Throughout his life, Ramanujan came up with novel equations and identities —including equations leading to the value of pi — and it was usually left to formally trained mathematicians to prove these. In 1987, two Canadian brothers proved all 17 of Ramanujan’s series for 1/pi; two years earlier, an American mathematician and programmer had used one of these formulas to calculate pi up to over 17 million digits, which was a world record at the time (Deka Baruah, Berndt & Chan; American Mathematical Monthly, 2009).

What’s the point?

Conjectures are a major step in the process of making new discoveries in any branch of science, particularly mathematics. Equations defining the fundamental mathematical constants, including pi, are invariably elegant. New conjectures in mathematics, however, have been scarce and sporadic, the researchers note in their paper, which is currently on a pre-print server. The idea is to enhance and accelerate the process of discovery.

How good is it?

The paper gives examples for previously unknown equations produced by the algorithm, including for values of the constants pi and e. The Ramanujan Machine proposed these conjecture formulas by matching numerical values, without providing proofs. It has to be remembered, however, that these are infinite series, and a human can only enter a finite number of terms to test the value of the series. The question is, therefore, whether the series will fail after a point. The researchers feel this is unlikely, because they tested hundreds of digits.

Until proven, it remains a conjecture. By the same token, until proven wrong, a conjecture remains one. It is quite possible that the algorithm will come up with conjectures that may take years to prove — a famous example of a human conjecture is Fermat’s Last Theorem, proposed in 1637 and proved only in 1994.

Where to find it

The researchers have set up a website, ramanujanmachine.com. Users can suggest proofs for algorithms or propose new algorithms, which will be named after them.