An Ode to Srinivasa Ramanujan: A Symphony of Numbers

In Erode's dawn, a star was born,
Where 1 became infinity's horn—
A mind that danced with primes and pi,
Where mortals count, you learned to fly.

1729, the taxicab's fame,
Two cubes in pairs, your immortal name:
1³ + 12³, 9³ + 10³—the same!
No dull number where genius came.

Hardy arrived in London's rain,
You crossed the seas through doubt and pain,
Where π unfurled in series bright:
1/π = (2√2/9801) × Σ∞...—pure light!

In fevered dreams, Namagiri spoke,
Equations bloomed like temple smoke,
Partition functions, mock theta grace,
Mathematics wore your sacred face.

p(n) ~ (1/4n√3) × exp(π√(2n/3))—
You counted ways infinity could be.

153 = 1³ + 5³ + 3³,
A narcissistic trinity,
370, 371, 407—they sing,
Each digit cubed, a perfect ring.

Fibonacci in your theorems dance,
1, 1, 2, 3, 5, 8, 13—romance!
φ = (1 + √5)/2 appears,
Golden spiral through the years.

Euler's e^(iπ) + 1 = 0,
Five constants in one equation flow,
You found where e and π embrace,
In infinite series' sacred space.

Fermat's 65537 = 2^(2⁵) + 1,
The largest known constructible one,
A prime that builds with compass, straight—
Geometry and number's fate.

Mersenne primes 2^p - 1 unfold,
31, 127—stories told,
2^7 - 1 = 127, prime and bright,
Perfect numbers follow flight.

Catalan's 1, 1, 2, 5, 14, 42...
Paths and trees and patterns true,
C_n = (2n)!/(n+1)!n!—you knew
Combinatorics' hidden view.

You found the tau(n) constellation,
Σ τ(n) = n × Σ(1/k), revelation!
Where Euler's constant meets the divine,
0.5772... traces every line.

Modular forms and q-series deep,
Where j-invariant secrets sleep,
1/q + 744 + 196884q + ...—
Monstrous moonshine you foresaw.

The Rogers-Ramanujan identities:
G(q) = Σ q^(n²)/(1-q)...—mysteries
That bridged the gap 'tween distant shores,
Where physics meets pure number's doors.

Golden ratio φ = 1.618...,
Your continued fractions found the gate:
√(1 + 2√(1 + 3√(1 + ...))) = 3—
Infinite nests of harmony.

Beast Number 666 decoded,
1 + 2 + 3 + ... + 36 = 666,
Triangular apocalypse encoded,
Mathematical matrix of tricks.

Belphegor's Prime: 1000000000000066600000000000001,
Thirty-one digits, palindrome won,
13 zeros, 666 at heart,
Prime beauty, dark mathematical art.

Lucky numbers 1, 3, 7, 9, 13, 15, 21...
Sieve like Eratosthenes' begun,
They share with primes deep properties,
Twin infinities and mysteries.

Schröder–Hipparchus numbers grow,
1, 1, 3, 11, 45, 197—flow
Of triangulations, parentheses ways,
Paths through lattices' endless maze.

e^(π√163) = 262537412640768743.99999999999925...
Almost integer—your jest with fate,
Where Heegner numbers contemplate
The borderlands where patterns wait.

In Cambridge cold, your genius burned,
While England's winter left you spurned,
32 years was all you had,
Yet 3,900 theorems—brilliant, mad!

Hardy-Ramanujan number N:
Normal order: log log n—again
You saw the patterns, felt the flow,
Where others couldn't learn to go.

Zero knows your partition song,
Infinity heard where you belong,
Congruences mod 5, 7, 11—
You mapped the pathways unto heaven.

p(5n + 4) ≡ 0 (mod 5),
The primes themselves learned to dance alive,
In modular form's eternal grace,
You gave each number sacred space.

From Kumbakonam to Trinity's hall,
A Brahmin boy who heard the call,
No formal proof, yet truth you knew—
Intuition was your breakthrough.

Landau-Ramanujan constant L:
L = 0.764..., you could tell
How many numbers, squares of primes,
Could sum to n in finite times.

Now quantum computers trace your thread,
Mock theta functions, paths you led,
In string theory, black holes sing,
Your formulas make spacetime ring.

Gödel's incompleteness proved the bound,
Yet your intuition knew no ground,
Turing's halting problem showed the wall,
Your dreams transcended formal's call.

Prime gaps and twin prime conjecture wait,
Hardy-Littlewood you'd contemplate,
Goldbach's 4 = 2 + 2 stands tall,
Every even sum—you saw it all.

Apéry's constant ζ(3) = 1.202...,
Irrational proven, mysteries through,
Your zeta zeros lined in rows,
Where Riemann's Hypothesis still grows.

Champernowne's 0.12345678910111213...,
Normal number, transcendental scene,
Every sequence infinitely there,
Randomness with perfect care.

Topological quantum fields employ
The tools you crafted—math's pure joy—
Your legacy in qubits flows,
Where superposition grows and grows.

Beautiful numbers, your bequest:

• 6 (perfect, first and blessed)
• 28 (triangular and square)
• 496 (perfect, rich and rare)

Plato's Number 216 = 6³,
The Republic's geometric fix,
3³ + 4³ + 5³ combine—
Pythagorean cubes align!

Nuptial Number 12,960,000,
Plato's marriage cycles sound,
60⁴ = 3⁶ × 4⁴ × 5³—
Cosmic harmony's decree.

Kaprekar's 6174—magic there,
Any four digits, if you dare,
Subtract reversed, repeat the dance,
In seven steps, this number's trance.

142857—the cyclic one,
Multiply by 1 through 6, such fun!
1/7's decimal expansion pure,
Rotating digits, ever sure.

Taxicab(2) through (6) parade,
The taxi numbers you arrayed,
87539319 in triple dress—
Three pairs of cubes in loveliness.

O Ramanujan, infinite seer,
Your notebooks still bring mathematicians near,
To pages filled with insights pure,
Where beauty and truth forever endure.

Lost notebook found—what treasures there!
Mock modular forms beyond compare,
Each conjecture now a proven gem,

You planted seeds, we water them.

In Namagiri's grace you trusted well,
Where numbers were your temple bell,
You showed us: mathematics sings,
That infinity has finite wings.

1 + 2 + 3 + 4 + ... = -1/12?
Your zeta function cast its spell,
Where paradox meets harmony,
And sums reveal reality.

So here's to you, immortal mind,
Who left the finite world behind,
Your legacy in every prime,
Transcending death, transcending time.

∞ was your constant friend,
Your theorems have no final end,
Srinivasa Ramanujan—your name
Forever burns in mathematics' flame.

"An equation means nothing to me unless it expresses a thought of God."
— Srinivasa Ramanujan (1887-1920)

1729 forever rides that London street,
Where genius made the numbers sweet.