Srinivasa Ramanujan Was a Genius. Math Is Still Catching Up. | Quanta Magazine

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Abstraction: Rogers-Ramanujan partition identities resurface across modern mathematics branches

Key points:

Ramanujan, self-taught and largely isolated in India, produced thousands of results without proof before dying at 32 in 1920; G.H. Hardy called discovering Ramanujan his greatest mathematical contribution
Rogers-Ramanujan identities (proved 1917) connect infinite sums to infinite products via partition counting; their appearance across statistical mechanics, knot theory, string theory, representation theory, and algebraic geometry is unexplained
Hussein Mourtada connected arc spaces of algebraic singularities to partition identities in 2010, proving Rogers-Ramanujan structure underlies seemingly unrelated geometric objects
Pooneh Afsharijoo (2015–) discovered a third condition extending the original Rogers-Ramanujan identity, adding to Ramanujan's work a century later
Ken Ono, Craig, and van Ittersum (2024): partition functions can detect prime numbers — plugging any prime into their formula yields zero, any composite yields positive

Connections: Srinivasa Ramanujan · Gh Hardy · Partition Identities · Number Theory · Algebraic Geometry