Srinivasa Ramanujan – Migoro Media

Srinivasa Ramanujan: The Self-Taught Genius Who Reshaped Mathematics

From humble beginnings to infinity—how one man’s mind transformed modern math

Srinivasa Ramanujan (1887–1920) was an Indian mathematician whose short but brilliant life forever changed the landscape of mathematics. Born into a modest Brahmin family in southern India, Ramanujan was largely self-taught. With little formal training and working in near isolation, he independently developed thousands of mathematical formulas—many of which were groundbreaking, some of which were centuries ahead of their time, and others that are still not fully understood today.

Despite initial obscurity and repeated academic rejection, his extraordinary intuition for numbers eventually caught the attention of British mathematician G.H. Hardy at the University of Cambridge. Their correspondence and collaboration would go on to produce some of the most influential work in number theory, infinite series, continued fractions, and modular forms.

Ramanujan’s contributions include elegant formulas for calculating π (pi), innovations in partition theory, and the mysterious mock theta functions, which only decades later found profound applications in quantum physics, string theory, and black hole thermodynamics.

More than a mathematician, Ramanujan was a phenomenon. He worked from what he called “visions” from a Hindu goddess and often wrote down results without proofs, relying on a deep, almost mystical intuition that both fascinated and baffled his peers.

He passed away at the young age of 32, leaving behind a legacy that scholars are still unraveling more than a century later. His life continues to inspire not only mathematicians, but anyone who believes that raw passion and genius can break through even the most difficult barriers—be they cultural, institutional, or personal.

In this biography, we will explore Ramanujan’s life in depth—from his early childhood in Tamil Nadu, his groundbreaking work in Cambridge, to the rediscovery of his “lost notebook” decades after his death. Along the way, we’ll uncover the math, the man, and the mysteries that still surround one of history’s most extraordinary intellects.

🧒 Early Life and Background

🏡 Birth and Family

Srinivasa Ramanujan was born on 22 December 1887 in the town of Erode, in the Madras Presidency of British India (present-day Tamil Nadu). His birth took place in his maternal grandparents’ home, but he was raised in Kumbakonam, a culturally rich temple town.

👪 His father, K. Srinivasa Iyengar, was a clerk in a cloth shop, and his mother, Komalatammal, was a homemaker and a singer of devotional songs in temples. The family belonged to a Tamil Brahmin (Iyengar) community and lived in modest conditions.

🛐 Raised in a deeply religious household, Ramanujan was heavily influenced by Hindu rituals, traditions, and spiritual beliefs—especially the worship of the goddess Namagiri of Namakkal, whom he later credited as the source of his mathematical visions.

📚 Early Schooling and Signs of Genius

Ramanujan began his formal education at age five. He quickly showed himself to be an exceptional student, especially in arithmetic. By age 10, he had already mastered advanced trigonometry, and by age 12, he was independently working through college-level math.

📝 He excelled in school but struggled to focus on anything other than mathematics. He would often neglect other subjects entirely—a pattern that would follow him through his life.

At age 13, he began working on sophisticated mathematical concepts, such as solving cubic equations and developing his own methods for summing geometric and arithmetic series.

📖 The Book That Changed Everything

At age 16, Ramanujan encountered a book that would change his life forever:
“A Synopsis of Elementary Results in Pure Mathematics” by G.S. Carr, a compilation of around 5,000 theorems with very few explanations or proofs.

📗 While most students would have been overwhelmed, Ramanujan treated it like a treasure map. He worked through it line by line, often re-deriving or extending the results entirely on his own. The book gave him a framework—but not a method—forcing him to invent his own approach to mathematics.

This experience shaped his unusual, intuition-driven style of thinking and set the foundation for his future breakthroughs.

🧮 Isolation and Independent Exploration

Without access to formal guidance or modern textbooks, Ramanujan worked in near isolation. He filled countless notebooks with formulas—many without proof, driven by patterns he “saw” in his mind.

✍️ These early notebooks, later referred to as The Notebooks of Ramanujan, already contained many of the ideas that would later astound the mathematical world.

Despite having no formal degree, no mentors, and no recognition, he believed deeply in his ability and the truth of his ideas. But this obsession with math would soon come at a cost.

🧑‍🎓 Early Struggles with Formal Education

Ramanujan earned a scholarship to Government Arts College in Kumbakonam in 1904. However, his focus on mathematics came at the expense of other subjects like English and Sanskrit.

📉 He failed his exams—twice—and lost his scholarship. Over the next few years, he enrolled in and dropped out of multiple colleges, unable to pass non-math subjects. Though he was clearly gifted, the education system at the time had no place for a student who didn’t follow conventional standards.

This marked the beginning of a period of academic failure, poverty, and struggle for recognition, but Ramanujan never stopped pursuing mathematics. His notebooks grew, even as his future became more uncertain.

🎓 Education and Early Mathematical Exploration

After showing early signs of mathematical brilliance, Srinivasa Ramanujan’s formal education turned out to be both a foundation and a frustration. His passion for mathematics was unmatched—but his refusal to focus on other subjects led to repeated academic setbacks. At the same time, these years laid the groundwork for his most original and astonishing discoveries.

🏫 Scholarship and Collapse at Government College

In 1904, Ramanujan completed secondary school and was awarded the K. Ranganatha Rao Prize for mathematics. He earned a scholarship to Government Arts College, Kumbakonam—a rare achievement for someone from his socioeconomic background.

📚 However, Ramanujan’s obsession with mathematics consumed him. He spent all his time working through equations and deriving new formulas, ignoring every other subject. Within a year, he lost his scholarship for failing in non-mathematical courses like English and Sanskrit.

This began a pattern: he would enter a college, show flashes of brilliance in math, but eventually drop out due to his inability or unwillingness to meet broader academic requirements.

🏠 Years of Isolation and Poverty

Between 1905 and 1910, Ramanujan lived in near-total isolation, without a degree, job, or institutional support. He relied on his parents and, later, his wife, Janaki Ammal, whom he married in 1909. Despite domestic responsibilities and severe financial strain, he continued writing mathematical theorems and working on number theory, algebra, and infinite series.

📝 During this time, he filled three notebooks with thousands of results—many original, some rediscoveries, others containing errors due to lack of formal grounding. These notebooks would later become famous for their content and unusual methods.

💡 While his techniques were not always rigorous by European standards, the sheer volume of correct and profound results marked him as a rare mathematical talent. He independently arrived at identities and results that were previously known only to top mathematicians—or not known at all.

📘 Work Influenced by G.S. Carr’s Book

The only substantial mathematical reference Ramanujan had was G.S. Carr’s A Synopsis of Elementary Results in Pure Mathematics. The book, which listed over 5,000 results without proofs, served as Ramanujan’s primary textbook for years.

Instead of being discouraged by the lack of explanation, Ramanujan used this to:

Reconstruct the proofs himself 🧠
Extend the ideas beyond what was listed
Begin developing entirely new theorems based on patterns he perceived

📌 This created his signature style: intuition-driven, result-focused, and deeply original. Though his lack of formal structure frustrated European mathematicians later, it also freed him from traditional constraints—allowing him to explore ideas few dared to imagine.

🧮 Emergence of a Distinct Mathematical Voice

By 1910, Ramanujan’s reputation began to grow locally in Madras (now Chennai), especially among mathematicians and educated patrons who recognized his unusual abilities.

Despite:

No formal degree 🎓
No academic position
No support from universities

He continued to produce high-level mathematics that hinted at a once-in-a-century genius waiting to be discovered. But for that, he would need support, recognition—and a connection to the wider mathematical world.

📬 Struggles and Attempts to Gain Recognition

Despite his brilliance, Ramanujan’s early attempts to gain recognition were met with frustration, rejection, and uncertainty. Without formal credentials or institutional backing, he was forced to knock on doors, seeking someone who could understand and support the genius hidden in his notebooks.

📎 Life on the Margins

By 1910, Ramanujan was still without a degree, job, or formal mentorship. His family’s financial situation was increasingly strained, and his health was fragile due to years of poverty and inadequate nutrition.

💼 In 1912, he finally secured a modest job as a clerk at the Madras Port Trust. The job was arranged with the help of S. Narayana Iyer, a fellow Iyengar and mathematician who recognized Ramanujan’s talent and wanted to support him. Though clerical work was far below his potential, the position gave Ramanujan enough financial stability to resume his mathematical writing during his free time.

🤝 Finding Patrons and Supporters in Madras

Ramanujan’s mathematical ideas eventually reached people with influence. His work began to circulate locally in Madras’s academic circles thanks to intermediaries like:

S. Narayana Iyer (Madras Port Trust)
P.V. Seshu Aiyar (Professor at Presidency College)
R. Ramachandra Rao (Collector of Nellore and amateur mathematician)

📜 Ramanujan presented some of his work to Ramachandra Rao, who was initially skeptical. However, after testing Ramanujan’s abilities and seeing the depth of his understanding, Rao became one of his first real patrons—offering financial help so Ramanujan could focus entirely on mathematics.

💬 Rao later described Ramanujan as a man who “walked with the gods” in the realm of numbers.

🖊️ First Publication and Growing Reputation

With the support of Seshu Aiyar, Ramanujan submitted his first paper in 1911 to the Journal of the Indian Mathematical Society. Titled “Some Properties of Bernoulli Numbers”, it was modest in scope but marked his official entry into the mathematical community.

📈 Over the next two years, he submitted more results to local journals, including infinite series identities, work on prime numbers, and continued fractions.

Though these early papers barely scratched the surface of his deeper findings, they earned him respect within South India’s small but growing mathematical network.

🇬🇧 Correspondence with G.H. Hardy and the Journey to Cambridge

In 1913, a handwritten letter from a little-known Indian clerk would spark one of the most extraordinary collaborations in the history of mathematics. Srinivasa Ramanujan’s correspondence with G.H. Hardy, a leading British mathematician at Cambridge University, marked the turning point from obscurity to global recognition.

✉️ The Letter That Changed Everything

In January 1913, Ramanujan sent a nine-page letter to Godfrey Harold Hardy, accompanied by more than 120 mathematical theorems and formulas. These included:

Infinite series approximations of π
Identities involving continued fractions
Concepts related to elliptic functions, gamma functions, and more
Early indications of what would later be known as modular forms and mock theta functions

📎 The letter was unconventional—there were no proofs, just conclusions. Yet Hardy recognized something astonishing: this was not a crank, but an untutored genius who had arrived at deep mathematical truths entirely on his own.

📜 Hardy later wrote:

“The letter contained theorems enough to make a dozen papers in any reputable journal, and most of them were rather startling.”

🧑‍🏫 Hardy’s Reaction and the Mathematical World’s Awakening

Initially skeptical, Hardy reviewed the formulas with fellow mathematician J.E. Littlewood. The two spent hours going over the letter’s contents. The results were so unusual—and in some cases, so far ahead of their time—that Hardy was both mystified and intrigued.

🎓 Hardy recalled scoring Ramanujan’s letter on a scale of 0 to 100 for originality, depth, and difficulty:

He gave himself 25
Littlewood 30
Ramanujan: 100

This began an effort to bring Ramanujan to Trinity College, Cambridge. Hardy wrote back, expressing his admiration and encouraging Ramanujan to publish and collaborate further.

🕊️ Cultural and Religious Dilemma

Though thrilled by Hardy’s response, Ramanujan faced a profound inner conflict. As a devout Tamil Brahmin, he had been raised to follow strict dietary and cultural codes, including a prohibition against crossing the ocean (kala pani), which was believed to cause ritual impurity.

💭 His decision was not made lightly. Ramanujan wrestled with the idea, torn between:

Loyalty to his faith and family
And a once-in-a-lifetime opportunity to work with the world’s leading mathematicians

🙏 According to later accounts, Ramanujan’s mother had a dream in which the family deity Namagiri instructed her to let him go. With her reluctant blessing, Ramanujan agreed to make the journey.

⛴️ The Journey to England

In March 1914, funded by a scholarship arranged by Hardy and the University of Madras, Ramanujan boarded the S.S. Nevasa bound for England. He carried:

His mathematical notebooks
A basic understanding of English
And a mind filled with centuries’ worth of untapped ideas

🌊 The voyage was difficult. Ramanujan, a lifelong vegetarian, struggled to find suitable food. He also had chronic health issues and suffered during the cold, damp passage.

🏫 Arrival at Trinity College, Cambridge

Ramanujan arrived in April 1914 and was formally admitted to Trinity College, one of the most prestigious institutions in the Western world. There, he began his intense and fruitful collaboration with Hardy.

📚 For the first time, Ramanujan had access to:

A complete mathematical library
Leading mathematicians to discuss ideas with
Resources to validate, refine, and publish his findings

His arrival at Cambridge marked the beginning of the most productive—and most demanding—period of his life.

📘 Life and Work in Cambridge (1914–1919)

When Srinivasa Ramanujan arrived at Trinity College, Cambridge, in April 1914, he entered a world vastly different from the one he had known in India. The weather was cold and damp, the food unfamiliar, and the academic environment rooted in strict formalism. Despite these challenges, the next five years would see an extraordinary outpouring of mathematical creativity, with Ramanujan producing work that would establish him as one of the greatest mathematical minds of all time.

🧊 Adapting to Life in England

Life in Cambridge was difficult from the start. Ramanujan:

Adhered strictly to a vegetarian diet, which limited his food options
Struggled with the cold British climate, especially in the absence of central heating
Felt culturally isolated, surrounded by Western scholars in a foreign land

⚠️ These conditions would take a toll on his health. Nevertheless, Ramanujan remained committed to his work, often spending long hours at his desk, scribbling equations in chalk and pen.

👨‍🏫 Working with G.H. Hardy

Ramanujan’s collaboration with G.H. Hardy was the intellectual core of his Cambridge years. While their personalities and mathematical styles were vastly different, their partnership was highly productive:

Hardy was logical, methodical, and a champion of rigor
Ramanujan was intuitive, symbolic, and driven by insight rather than proof

🧠 Hardy later said:

“It was his insight into algebraic formulae, transformations of infinite series, and so on, that was most amazing. One could check a formula and find it was right. But where had it come from? Why was it true?”

Together, they published several groundbreaking papers, with Hardy helping Ramanujan translate his ideas into the formal mathematical language of Western academia.

✍️ Major Contributions During Cambridge Years

While at Cambridge, Ramanujan produced over 30 significant papers, some jointly with Hardy, including results that are still central to modern mathematics:

🔢 Partition Theory

Developed asymptotic formulas for p(n), the number of ways to partition a natural number
Introduced the Ramanujan tau function
Resulted in the Hardy–Ramanujan formula, a major advance in combinatorics

🔁 Infinite Series and Continued Fractions

Found beautiful new representations for π (pi), including rapidly converging infinite series
Created original formulas involving gamma functions, hypergeometric series, and modular equations

🌗 Mock Theta Functions

In his final years, Ramanujan introduced the concept of mock theta functions, mysterious expressions related to modular forms
These remained poorly understood until the 21st century and are now vital in areas such as string theory and black hole physics

🧮 Highly Composite Numbers

Introduced and analyzed highly composite numbers—integers with more divisors than any smaller number
This work had deep implications in number theory and the distribution of prime numbers

🏆 Recognition and Honors

Despite initial skepticism from Western mathematicians, Ramanujan’s originality and depth earned him significant recognition:

📜 Elected Fellow of the Royal Society (FRS) in 1918 — the second Indian and first Indian mathematician to receive the honor
🎓 Elected Fellow of Trinity College, Cambridge, in the same year

These honors placed him among the highest academic ranks of the British Empire—an extraordinary achievement for someone with no formal degree.

⚕️ Health Decline and War Years

Unfortunately, the triumphs of Ramanujan’s Cambridge years were shadowed by illness.

He suffered from recurrent health problems, possibly related to malnutrition, tuberculosis, or a parasitic liver infection (amoebiasis)
The First World War (1914–1918) caused food shortages and poor living conditions, which worsened his condition
He was frequently hospitalized between 1917 and 1919, at times hovering near death

Despite this, Ramanujan continued to write and submit papers, often from his hospital bed.

💌 Final Works Before Returning to India

In 1919, Ramanujan prepared to return home. Before leaving, he sent a final letter to Hardy, filled with new mathematical insights, including expanded notes on mock theta functions.

Hardy later described it as “the most fruitful single letter he had ever received.”

In July 1919, Ramanujan left England after five years, his health severely deteriorated but his notebooks filled with revolutionary ideas.

🏡 Declining Health and Return to India (1919–1920)

After five intense years in Cambridge, Srinivasa Ramanujan returned to India in 1919, celebrated abroad but weakened in body and spirit. Though he had achieved remarkable mathematical success and international recognition, the harsh English climate, wartime shortages, and years of personal and cultural isolation had left him gravely ill.

⚠️ Struggling with Chronic Illness

Ramanujan had battled recurring illness since 1917. During his time in England, he suffered from:

Extreme weight loss and persistent fevers
Symptoms consistent with tuberculosis, malaria, or hepatic amoebiasis
Ongoing nutritional deficiencies from his strict vegetarian diet in wartime England

🏥 He was in and out of hospitals during his final years in Cambridge, including the Matlock House Sanatorium, but his condition showed only brief improvement.

📚 Despite this, he continued to produce deep mathematical work, sometimes writing from his hospital bed—a testament to his unstoppable dedication to mathematics.

🚢 Return to India and Brief Period of Hope

In July 1919, Ramanujan boarded a ship back to India. He arrived in Madras (now Chennai) in late August 1919, where he was warmly welcomed by family, friends, and fellow Indian scholars who now recognized his greatness.

🏠 He moved into a small house in Kodambakkam, a suburb of Madras, where he was looked after by his wife Janaki Ammal and his family.

During this time, he began to feel marginally better, and for a brief period, there was hope he might recover. However, his health soon deteriorated again.

✍️ Final Contributions from His Sickbed

Even during the final months of his life, Ramanujan remained intellectually active.

📜 He continued developing his theories on mock theta functions, which he had introduced in his last letter to Hardy. These strange and beautiful functions—named by Ramanujan himself—remained largely misunderstood until they were rediscovered and developed further in the late 20th and early 21st centuries, now playing a role in:

String theory
Black hole entropy
Modern number theory and combinatorics

📝 These notes, filled with unproven but profound results, would later become known as Ramanujan’s “Lost Notebook”, and would spark a new era of research decades after his death.

🕯️ Death and Legacy in India

On 26 April 1920, Ramanujan passed away at the age of 32 at his home in Madras.

His official cause of death was tuberculosis, complicated by malnutrition and liver complications. Later medical historians have debated other possibilities, including vitamin deficiencies, autoimmune disorders, or parasitic infections.

🪔 His funeral was conducted with traditional Hindu rites. Though his passing was deeply mourned, it also marked the beginning of a lasting legacy—both in India and across the global mathematical community.

🏛️ Posthumous Recognition in India

While Ramanujan was not fully appreciated in India during his early life, his reputation soared after his death:

Memorials and institutions were established in his honor
His birth date, 22 December, was declared National Mathematics Day by the Government of India in 2012
The Ramanujan Institute for Advanced Study in Mathematics was founded at the University of Madras
His contributions are now celebrated annually in Indian schools and universities

🎓 Today, Ramanujan is viewed as India’s most revered mathematician, a symbol of intellectual brilliance, spiritual discipline, and the power of untapped potential.

📓 The Lost Notebook: A Mathematical Treasure Rediscovered

More than 50 years after Srinivasa Ramanujan’s death, one of the most significant mathematical discoveries of the 20th century came not in the form of a new theory—but in the rediscovery of Ramanujan’s “lost” work. Known today as the Lost Notebook, this collection of handwritten pages contains some of his deepest and most mysterious ideas, many of which are still being unpacked by mathematicians today.

🗃️ Discovery in the Wren Library (1976)

In 1976, American mathematician George E. Andrews was visiting the Wren Library at Trinity College, Cambridge, to examine the papers of British mathematician G.N. Watson. There, among old documents and unsorted materials, he found a set of 87 unbound pages in Ramanujan’s handwriting.

📜 These pages contained hundreds of formulas and mathematical identities—many of which had never been published or referenced in any previous collection of Ramanujan’s known work.

Andrews immediately recognized the significance of what he had found. He named it:

“The Lost Notebook of Ramanujan”

🧠 Though not technically a notebook (it was a sheaf of loose papers), the title stuck, capturing the mystery and allure of a genius whose ideas had once again emerged from obscurity.

🧾 Contents of the Lost Notebook

The Lost Notebook contains material written during the last year of Ramanujan’s life, when he was bedridden in Madras. It reflects a profound shift in his thinking—his focus had moved toward:

🌗 Mock theta functions
🔁 q-series and theta functions
🧮 Modular forms and modular equations
➗ Hypergeometric series
💡 And numerous unproven conjectures, many of which were decades ahead of their time

🔍 What makes the Lost Notebook so remarkable is that many of its results were completely unknown to the mathematical community—and some were later found to anticipate techniques developed only in the late 20th century.

🔬 Modern Impact and Continued Research

The rediscovery of the Lost Notebook triggered a new wave of mathematical research, particularly in the areas of:

Number theory
Combinatorics
Mathematical physics
String theory and quantum gravity

In fact, Ramanujan’s mock theta functions—introduced in these final pages—are now recognized as mock modular forms, a concept formally defined only in the early 2000s by mathematicians such as Sander Zwegers, Don Zagier, and others.

⚛️ These functions have since appeared in black hole entropy calculations in physics and in advanced areas of conformal field theory, making Ramanujan not just a historical figure but a contributor to modern theoretical science.

📚 Collaborations and Publications

After Andrews’ discovery, a major collaborative project was launched to analyze and publish the contents of the Lost Notebook.

George Andrews, Bruce C. Berndt, and other mathematicians worked for decades to provide proofs, explanations, and historical context for each entry
Multiple volumes have since been published under the title “Ramanujan’s Lost Notebook: Part I–IV”

Their work revealed just how far ahead of his time Ramanujan had been—and how much modern mathematics still owes him.

✨ A Timeless Mind Reawakened

The Lost Notebook is often referred to as Ramanujan’s final gift to the world. It serves as a reminder that:

Many of his ideas remain unexplored frontiers
His intuition continues to guide modern discovery
Mathematical truth, once revealed, transcends time, place, and culture

📌 For students and scholars alike, the Lost Notebook is a symbol of unbounded creativity, mystical intuition, and the power of pure thought. In a very real sense, Ramanujan’s mind continues to speak to us—one formula at a time.

🌍 Legacy and Modern Impact

Though Srinivasa Ramanujan died at the young age of 32, his influence on mathematics has only grown over the past century. From number theory to physics, cryptography to computer science, his ideas have become embedded in the foundation of modern mathematics and beyond. Ramanujan’s life also stands as a testament to the power of raw genius, perseverance, and the importance of recognizing talent in all its forms—regardless of background or circumstance.

🧠 Influence on Modern Mathematics

Ramanujan’s work continues to inspire and shape some of the most advanced areas in mathematics today:

🔢 Number Theory

His discoveries in partition functions, modular forms, and prime number distribution are foundational to much of modern number theory. The Hardy–Ramanujan asymptotic formula for p(n), the number of partitions of a number n, is still widely used in analytical and computational mathematics.

🔁 Mock Theta Functions

Initially mysterious and poorly understood, Ramanujan’s mock theta functions are now recognized as mock modular forms. These functions are central to:

String theory
Black hole entropy
Quantum modular forms
Moonshine theory (connections between modular functions and algebraic structures)

🔬 Modern mathematical physicists and number theorists alike are still unpacking the depths of these final contributions.

🧮 Algebra, Continued Fractions, and Infinite Series

His continued fractions and rapidly converging series for π (pi) are not only mathematically elegant but also used in algorithm design for high-precision calculations.

💻 Applications in Science and Technology

Ramanujan’s legacy stretches far beyond pure math:

🔐 Cryptography

His work on number theory has implications for modern encryption algorithms, including those used in secure communication and digital security.

⚛️ Physics

Mathematical physicists use Ramanujan’s formulas in studies of:

Black hole entropy
Modular symmetry in quantum gravity
Partition functions in string theory

🧬 Computer Science

In algorithm design, especially in symbolic computation and automated theorem proving, his formulas are used for optimizing calculations and exploring new problem-solving techniques.

🏫 Honors, Institutions, and Memorials

Ramanujan is widely celebrated across the world, and especially in India:

📅 National Mathematics Day

Declared by the Government of India in 2012
Celebrated annually on December 22 (his birthday) to honor his contributions

🏛️ Institutions in His Name

Ramanujan Institute for Advanced Study in Mathematics, University of Madras
Srinivasa Ramanujan Centre, affiliated with SASTRA University, Tamil Nadu
The Ramanujan Math Park, Andhra Pradesh – an interactive museum for students

🧾 The Ramanujan Journal

A specialized international journal launched in 1997, dedicated to areas of mathematics influenced by Ramanujan’s work.

🧑‍🏫 Ramanujan Prize

Awarded annually by the International Centre for Theoretical Physics (ICTP) for outstanding work in mathematics by researchers from developing countries.

🎬 Popular Culture and Global Recognition

Ramanujan’s story continues to inspire millions:

📘 Books

The Man Who Knew Infinity by Robert Kanigel (1991)
Numerous academic biographies and popular science books

🎥 Film

The Man Who Knew Infinity (2015)
Starring Dev Patel as Ramanujan and Jeremy Irons as G.H. Hardy
Based on Kanigel’s book, the film brought his life story to a global audience

🖼️ Postage Stamps and Statues

Featured on Indian postage stamps, coins, and currency
Statues and busts installed at Trinity College, Cambridge, and in several Indian academic institutions

✨ A Symbol of Intuition, Inspiration, and Imagination

Ramanujan’s legacy transcends equations and formulas. He remains a symbol of:

Self-taught brilliance
Unconventional genius
Cross-cultural collaboration
Spiritual and intellectual depth

📚 His life encourages students and researchers to trust their curiosity, honor their heritage, and pursue truth wherever it leads—even if it lies beyond the boundaries of formal education or mainstream recognition.

“An equation has no meaning unless it expresses a thought of God.”
— Srinivasa Ramanujan

His work, driven by intuition and guided by faith, reminds the world that genius can come from anywhere—and that, sometimes, the greatest minds walk unseen among us.

🧮 Ramanujan’s Mathematical Style and Philosophy

More than just a list of accomplishments, Srinivasa Ramanujan’s mathematical work reveals a unique way of thinking—one that blended deep intuition, symbolic abstraction, and a spiritual reverence for numbers. His methods were unconventional by Western academic standards, yet they produced results that were not only correct, but revolutionary. Understanding his style and philosophy is essential to appreciating the true depth of his genius.

🧘‍♂️ Intuition Over Formalism

Unlike most mathematicians of his era—or even today—Ramanujan was largely self-taught, and as such, he never developed the habit of writing detailed proofs. Instead, he relied heavily on intuition, pattern recognition, and what he described as a sort of inner vision of mathematical truth.

His notebooks are filled with hundreds of results presented without justification

Many of them were later proved correct, while some required refinement

A few were incorrect or incomplete, but remarkably rare considering his isolated learning

📖 He often viewed proofs as less important than the results themselves, once saying that he had no time to prove things that were “obviously true” to him.

🌌 Mathematics as Divine Inspiration

Ramanujan famously credited his mathematical insights to spiritual inspiration—specifically, visions granted by the Hindu goddess Namagiri of Namakkal.

🗣️ He once said:

“An equation for me has no meaning unless it expresses a thought of God.”

To Ramanujan, numbers were not just tools—they were sacred, and he felt it was his duty to uncover their hidden truths. His religious upbringing deeply shaped his view of mathematics as a form of divine communication.

This mystical worldview clashed with the logical, atheistic mindset of G.H. Hardy, yet the contrast between them made their collaboration all the more fascinating.

🔍 Obsession with Patterns and Identities

Ramanujan had an uncanny ability to spot deep, elegant patterns in seemingly unrelated areas of mathematics. He could:

Derive new identities involving infinite series, continued fractions, and modular functions

Predict the behavior of complex functions without using formal tools like limits or epsilon-delta proofs

Compress dense mathematical truths into compact formulas few could decipher at first glance

🧠 This rare ability allowed him to leap to conclusions that others might only reach through pages of careful derivation. Hardy often remarked that Ramanujan’s leaps were “startling”—mathematically correct, but unreachable by ordinary reasoning.

📚 A Blend of Eastern Philosophy and Western Math

Ramanujan’s mathematical output reflects a unique fusion of cultures:

From the East, he brought spiritual depth, metaphorical thinking, and a meditative approach to discovery

From the West (especially through Hardy), he learned structure, presentation, and the rigor required to communicate his ideas formally

While he never fully adopted the Western style of proof-based mathematics, his influence eventually helped broaden the mathematical community’s view of what constitutes a valid approach to discovery.

📝 Legacy of His Working Style

Ramanujan’s distinctive style has influenced generations of mathematicians and continues to teach valuable lessons:

💡 Intuition matters: Insight and pattern recognition are as vital as formal logic

📈 Untrained minds can still contribute: Genius doesn’t need credentials—it needs space and encouragement

⌛ Ideas ahead of their time are often misunderstood: Ramanujan’s mock theta functions were mysterious for decades but are now central to modern theory

Though his approach lacked formalism, his results often stood the test of time—proof that there is more than one path to mathematical truth.

📜 Selected Works and Publications

Though Srinivasa Ramanujan’s career was tragically brief, his mathematical output was astonishingly rich. His work spans number theory, infinite series, continued fractions, modular forms, and more—fields that continue to be influenced by his results today.

Despite lacking formal academic training, Ramanujan authored and co-authored numerous papers, many of which were published in the most prestigious journals of his time. His notebooks, letters, and final manuscripts have since become foundational texts in mathematical research.

🧾 Notebooks and Lost Notebook

📘 The Notebooks (Pre-Cambridge)

Before traveling to England, Ramanujan had already compiled three extensive notebooks filled with formulas, conjectures, and identities. These notebooks were:

Written between 1904 and 1914
Contained over 3,000 results, most without proofs
Rediscovered and studied extensively after his death
Published in annotated form by Bruce C. Berndt in a multi-volume series

📓 The Lost Notebook (Final Year of Life)

Discovered in 1976 by George Andrews in the Wren Library at Trinity College, this collection includes:

About 87 unbound pages written in 1919–1920
New and mysterious work on mock theta functions
Insights decades ahead of their time
Published in parts by Andrews and Berndt under the title “Ramanujan’s Lost Notebook”

🖊️ Key Published Papers

During his time at Cambridge (1914–1919), Ramanujan published or co-authored 21 papers, including 5 with G.H. Hardy. Some of the most significant include:

🟢 “Highly Composite Numbers” (1915–1916)

📍 Proceedings of the London Mathematical Society
One of his longest and most detailed solo papers, in which Ramanujan analyzed integers with more divisors than any smaller number. The work introduced deep concepts related to:

Divisor functions
Prime factorization
Logarithmic density
Applications to analytical number theory

This paper was ahead of its time and later extended by mathematicians like Paul Erdős.

🔵 “On Certain Arithmetical Functions” (with G.H. Hardy, 1917)

📍 Transactions of the Cambridge Philosophical Society
Introduced the now-famous Hardy–Ramanujan asymptotic formula for the partition function p(n):

This formula was a breakthrough in analytic number theory and remains a cornerstone of the field today.

🟣 “Modular Equations and Approximations to π” (1914)

📍 Quarterly Journal of Mathematics
In this paper, Ramanujan introduced rapidly converging infinite series for π, some of which are used in modern computer algorithms to compute millions of digits of π.

Example of a Ramanujan-type π formula:

These results are both aesthetically elegant and computationally powerful.

🟡 “A Class of Multiple Series” (1918)

📍 Proceedings of the Cambridge Philosophical Society
This paper explored advanced techniques in summation of multiple series and revealed Ramanujan’s innovative manipulations of infinite series, many of which anticipated modern analytic techniques.

🟤 “On Certain Infinite Series” (1916)

This paper demonstrated Ramanujan’s mastery in transforming and evaluating infinite series and continued fractions, laying groundwork for future explorations in special functions.

📚 Collected Works and Edited Volumes

📘 The Collected Papers of Srinivasa Ramanujan (1927)

Edited by G.H. Hardy, P.V. Seshu Aiyar, and B.M. Wilson
Contains all of Ramanujan’s published papers
Still a primary reference for students and researchers

📕 Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (1940)

Authored by G.H. Hardy
A deeply personal and scholarly tribute that analyzes and contextualizes Ramanujan’s contributions

🧮 Fields Influenced by His Work

📐 Combinatorics (Partition theory, integer sequences)
🔢 Number Theory (Modular forms, prime distributions)
♾️ Mathematical Analysis (Infinite series, continued fractions)
🧬 Mathematical Physics (String theory, black hole entropy)
🔐 Cryptography and Algorithm Design

Ramanujan’s published work and posthumously studied notebooks continue to be mined for new insights, with mathematicians still proving, generalizing, and applying his results today. His legacy is a living body of work, inspiring generations of mathematicians to think differently, explore boldly, and trust in the power of pure insight.

📅 Timeline and Key Events

This timeline offers a chronological overview of the major milestones in Srinivasa Ramanujan’s life and legacy—from his humble beginnings in India to his enduring impact on global mathematics. It’s especially helpful for students, educators, and anyone seeking a quick reference to the key chapters in his extraordinary story.

🧒 Early Life and Education

📆 Date	🗓️ Event
22 Dec 1887	Born in Erode, Tamil Nadu, India, to K. Srinivasa Iyengar and Komalatammal
1892–1898	Attends primary school in Kumbakonam; shows early signs of mathematical ability
1903	Discovers G.S. Carr’s Synopsis, which becomes the foundation of his self-taught mathematical journey
1904	Wins the K. Ranganatha Rao Prize for mathematics; enters Government Arts College, Kumbakonam
1905–1906	Drops out of college due to poor performance in non-math subjects
1909	Marries Janaki Ammal at the age of 21

🔬 Mathematical Development and Search for Support

📆 Date	🗓️ Event
1910	Gains attention from local mathematicians in Madras, including P.V. Seshu Aiyar and R. Ramachandra Rao
1911	Publishes first paper: Some Properties of Bernoulli Numbers
1912	Employed as a clerk at the Madras Port Trust; supported by S. Narayana Iyer
1913	Writes to G.H. Hardy at Cambridge, sending over 120 theorems

🛳️ Move to England and Cambridge Years

📆 Date	🗓️ Event
March 1914	Travels to England to study at Trinity College, Cambridge
1914–1919	Collaborates with Hardy; publishes 21 papers (5 jointly); elected Fellow of the Royal Society (1918) and Fellow of Trinity College
1917–1919	Suffers recurring illness; hospitalized frequently
1918–1919	Develops the theory of mock theta functions, outlined in letters to Hardy

🏡 Return to India and Final Year

📆 Date	🗓️ Event
July 1919	Returns to India due to worsening health
Late 1919	Settles in Madras; continues working on mathematics despite illness
26 April 1920	Passes away at the age of 32 in Madras

📓 Posthumous Recognition and Rediscovery

📆 Date	🗓️ Event
1927	The Collected Papers of Srinivasa Ramanujan published, edited by Hardy, Seshu Aiyar, and Wilson
1976	Mathematician George Andrews discovers the Lost Notebook at Trinity College
1987	100th birth anniversary celebrated globally; India issues commemorative stamp
1997–2018	Ramanujan’s Lost Notebook published in four volumes by Andrews and Berndt
2012	National Mathematics Day established in India on his birthday, 22 December
2015	Biopic The Man Who Knew Infinity released, bringing his story to a global audience

🌍 Ongoing Legacy

📆 Ongoing	🗓️ Impact
Continued mathematical research based on Ramanujan’s notebooks and mock theta functions
Applications of his work in string theory, black hole physics, modular forms, and cryptography
Inspiration for young mathematicians worldwide, especially in India and the Global South

This timeline summarizes a life that defied convention, challenged expectations, and continues to unfold through modern science. Ramanujan’s impact is not confined to the past—it lives on in equations, algorithms, and theories that shape our world today.

📚 References / Sources

📘 Books and Biographies

Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. Washington Square Press, 1991.

Widely considered the definitive biography of Ramanujan, combining historical research with narrative storytelling.
Hardy, G.H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work. AMS Chelsea Publishing, 1940.

A personal and technical tribute by Ramanujan’s closest collaborator.
Berndt, Bruce C. Ramanujan’s Notebooks (Volumes I–V). Springer, 1985–1998.

A comprehensive analysis of Ramanujan’s original notebooks, annotated with proofs and historical notes.
Berndt, Bruce C., and George E. Andrews. Ramanujan’s Lost Notebook (Parts I–IV). Springer, 2005–2013.

Explores the content and significance of the “Lost Notebook,” discovered in 1976.

📄 Academic Papers and Journals

Hardy, G.H., and Ramanujan, S. “Asymptotic Formulae in Combinatory Analysis.” Proceedings of the London Mathematical Society, 1918.
Hardy, G.H., and Ramanujan, S. “Une formule asymptotique pour le nombre des partitions de n.” Comptes Rendus, 1917.
Ramanujan, S. “Highly Composite Numbers.” Proceedings of the London Mathematical Society, 1915–1916.
Andrews, George E. “An Introduction to Ramanujan’s Lost Notebook.” The American Mathematical Monthly, 1988.
Zagier, Don. “Ramanujan’s Mock Theta Functions and Their Modern Importance.” Bulletin of the AMS, 2009.

🏛️ Archives and Primary Sources

Trinity College Library, Cambridge – Wren Library Manuscripts Collection

Original manuscripts and the Lost Notebook (discovered in the papers of G.N. Watson).
Indian Mathematical Society – Journal Archives (1911–1920)

Contains Ramanujan’s first published works.
Ramanujan Institute for Advanced Study in Mathematics, University of Madras

Hosts digitized versions of original papers and historical commentary.

🌐 Online Resources

MacTutor History of Mathematics Archive (University of St Andrews):
🔗 https://mathshistory.st-andrews.ac.uk/Biographies/Ramanujan/

A detailed and reputable academic overview of Ramanujan’s life and contributions.
The Ramanujan Journal (Springer):
🔗 https://www.springer.com/journal/11139

A peer-reviewed journal devoted to areas of mathematics influenced by Ramanujan.
National Mathematics Day (India):
🔗 https://dst.gov.in/national-mathematics-day

Official government portal explaining Ramanujan’s importance to Indian education and science.

🎓 Suggested Reading for Students

The Great Mathematicians by Raymond Flood and Robin Wilson
Letters and Commentary between Hardy and Ramanujan (compiled by Berndt & Rankin)
Ramanujan for Students: Exploring Numbers Beyond Infinity (Educational series, India-based publishers)

❓ Frequently Asked Questions (FAQs)

🔹 Who was Srinivasa Ramanujan?

Srinivasa Ramanujan (1887–1920) was a self-taught Indian mathematician whose intuitive and groundbreaking work in number theory, infinite series, and modular forms revolutionized mathematics. Despite no formal training, he developed thousands of original theorems and became one of the most celebrated mathematicians of the 20th century.

🔹 What is Ramanujan famous for?

Ramanujan is best known for:

His partition function formula
Mock theta functions
Highly composite numbers
His rapidly converging series for π (pi)
His collaboration with G.H. Hardy at Cambridge

His work on modular forms and infinite series continues to influence modern number theory and physics.

🔹 Why is 1729 called the “Ramanujan Number”?

1729 is known as the Hardy–Ramanujan number because of a famous anecdote:

When G.H. Hardy visited Ramanujan in the hospital, he remarked that 1729 seemed like an unremarkable number. Ramanujan replied:

“No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”

$1^3 + 12^3 = 9^3 + 10^3$

🔹 What are mock theta functions?

Mock theta functions are a class of functions introduced by Ramanujan in the final year of his life. Though mysterious for decades, they are now known to be mock modular forms, essential in fields like:

String theory
Quantum black hole entropy
Number theory

🔹 Why didn’t Ramanujan provide proofs for his theorems?

Ramanujan was largely self-taught and focused on the results rather than formal Western-style proofs. He believed the truth of a theorem was self-evident if it “came from the goddess.” Later, many of his results were rigorously proved by others and found to be correct.

🔹 What is the “Lost Notebook”?

The Lost Notebook is a collection of about 87 pages of Ramanujan’s final unpublished work, discovered in 1976 by mathematician George Andrews in the archives at Trinity College, Cambridge. It contains many previously unknown formulas, especially on mock theta functions.

🔹 What challenges did Ramanujan face?

Poverty and poor health
Lack of formal education
Cultural and religious barriers (e.g., hesitations about traveling abroad)
Isolation as a non-Western thinker in the British academic world
Serious illness in his final years

Despite these, he made lasting contributions with limited resources.

🔹 How did Ramanujan die?

Ramanujan died on 26 April 1920, at age 32, in Madras (Chennai). His official cause of death was listed as tuberculosis and a severe vitamin deficiency, though modern researchers have proposed other possible medical explanations such as hepatic amoebiasis.

🔹 Why is he important today?

Ramanujan’s work:

Continues to influence mathematics, physics, and cryptography
Is still being researched and extended today
Inspires mathematicians around the world
Shows that formal training isn’t the only path to discovery
Symbolizes the global nature of genius and cross-cultural intellectual collaboration

🔹 Where can I read more about Ramanujan?

You can explore:

📘 The Man Who Knew Infinity by Robert Kanigel
📚 Collected Papers of Ramanujan (edited by Hardy, Seshu Aiyar, and Wilson)
🧾 Ramanujan’s Notebooks (Bruce C. Berndt)
🔗 Online sources like the MacTutor History of Mathematics Archive and The Ramanujan Journal