(14) When Mathematics Met Ramanujan.
Pankaj Khanna
9424810575
Previous/Next Blog Posts:
(1) Beauty Squarely Introduction & Kuber Yantra
(2) Murphy Radio!? अले वाह!! My first Experience of Magic Square.
(3) Decoding the Quadratum Mirabile! How to solve 3x3 Magic Squares.
(4) Lo Shu Square History of Chinese Magic Square.
(5) The Unhurried Odyssey of a Turtle!! History of Magic Squares in short.
Brief Introduction.
(7) Khajuraho Magic: Introduction.
(8) Chautisa Yantra: Mytho-math Spice.
(9) Dürer Square
(11) Tona Lisa as a Rock Star!
(14) When Mathematics Met Ramanujan.
In December 2011, India Post once again honoured Srinivasa Ramanujan with a commemorative postage stamp, marking his 125th birth anniversary. The occasion carried extra weight: the Government of India also declared his birthday—22 December 1887—as National Mathematics Day, hoping that a little Ramanujan might help students lose their fear of mathematics and discover the joy behind the numbers.
Presented below are the major contributions of Srinivasa Ramanujan to mathematics—each accompanied by a brief, intuitive description. We keep the technical jargon/formula at bay and focus instead on the ideas, insights, and quiet brilliance that continue to inspire mathematicians around the world.
(1) Partition Theory (His Crown Jewel)
Ramanujan discovered astonishing patterns in the partition function —the number of ways to write a number as a sum of positives.
He found exact congruences nobody had imagined:
These are so surprising that reknowned mathematician Hardy said: “It was a clairvoyant kind of insight.”
Today, modern string theory and black hole entropy depend on these very formulas.
(2) Modular Forms & Mock Theta Functions (Years Ahead of His Time)
Ramanujan discovered mock theta functions—mysterious cousins of modular forms.
Nobody understood them fully until 2002, when Zwegers proved that they behave like “shadows” of modular forms.
In short: Ramanujan anticipated a major 20th-century mathematical revolution by 80 years.
(3) Continued Fractions (Monuments of Beauty)
His formulas for continued fractions are jaw-dropping, especially the Rogers–Ramanujan continued fraction.
This is not just pretty—
It links number theory, combinatorics, and even modern physics.
(4) Highly Composite Numbers
Ramanujan classified integers with the greatest number of divisors for their size—highly composite numbers.
This became foundational in: Analytic number theory, Multiplication algorithms,
Computer-science optimization.
(5) Infinite Series & Pi Formulas (Lightning Calculations)
Ramanujan produced outrageously fast-converging series for π. One of his formulas underlies the modern Chudnovsky algorithm, used today to compute trillions of digits of π.
That’s why our smartphone knows π to millions of digits—Ramanujan is inside!
(6) Elliptic Functions, q-Series & Identities Everywhere.
He generated hundreds of identities involving theta functions, q-series, hypergeometric series, and elliptic integrals—many still being rediscovered and proved.
Hardy famously said:
“Each of his theorems was one that I could not have obtained by my own methods.”
(7) The Tau Function & Ramanujan’s Conjectures.
His conjectures about the tau function were so deep that proving them took decades and led directly to the proof of the Modularity Theorem, which eventually led to the proof of Fermat’s Last Theorem in 1995 after almost 350 years of hypothesis.
Yes—Ramanujan indirectly contributed to the proof of Fermat’s Last Theorem also!
In one line: Ramanujan’s main contribution to mathematics is the discovery of deep, unexpected, and near-mystical patterns in numbers—decades ahead of his time—which reshaped number theory, modular forms, and even modern physics.
In 2016, India Post celebrated Srinivasa Ramanujan once again—this time with a definitive ₹4 stamp issued as part of its 11th series, cheerfully carrying his immense contributions to mathematics into everyday circulation.
Srinivasa Ramanujan is also fondly remembered for creating his famous Birthdate Magic Square. In the grand hierarchy of his mathematical achievements, this little square is actually a minor footnote—standing far below his monumental work on infinite series, partitions, and number theory. But ask a magic-square enthusiast, and you may hear a very different story!
For many lovers of magic squares, the Birthdate Magic Square is not just one of Ramanujan’s creations—it is the creation! Forget the terrifying equations and fearsome formulas; those belong to a realm accessible only to mortals with divine intuition and endless notebooks. Simple numerical magic, however, feels comfortably human—and delightfully achievable.
And so begins the ritual: people eagerly construct magic squares from their own birth dates, feel a pleasant mathematical thrill, and—if only for a moment—harbour the joyful illusion that they might just be the next Srinivasa Ramanujan. It may not lead to groundbreaking theorems, but it certainly leads to happy numbers, proud smiles, and a renewed love for playful mathematics.
In the next blog post, we’ll finally turn to Ramanujan’s actual Birthdate Magic Square—examining its structure, uncovering its patterns, and even building simple formula and generator so you can conjure similar magic squares for any birth date of your choice.
Pankaj Khanna
9424810575
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मेरे कुछ अन्य ब्लॉग:
हिन्दी में:
तवा संगीत : ग्रामोफोन का संगीत और कुछ किस्सागोई।
रेल संगीत: रेल और रेल पर बने हिंदी गानों के बारे में।
साइकल संगीत: साइकल पर आधारित हिंदी गाने।
कुछ भी: विभिन्न विषयों पर लेख।
तवा भाजी: वन्य भाजियों को बनाने की विधियां!
मालवा का ठिलवा बैंड: पिंचिस का आर्केस्टा!
ईक्षक इंदौरी: इंदौर के पर्यटक स्थल। (लेखन जारी है।)
अंग्रेजी में:
Love Thy Numbers : गणित में रुचि रखने वालों के लिए।
Epeolatry: अंग्रेजी भाषा में रुचि रखने वालों के लिए।
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