All strategies are restricted to mathematics available before 1920. Post-Ramanujan frameworks (formal modular forms theory, Zwegers mock-theta shadows, Garsia–Milne bijection, Deligne’s proof) are excluded from the reconstruction.
Strategy probability ranking — all 33 strategies
Estimated from 80 sampled Ramanujan formulae · click any bar
Original 30 formulae used to build the first-pass tree, plus 50 additional from the notebooks and lost notebook, each traced back through the algorithm. verified = algorithm correctly routes the derivation. updated = algorithm required an update to route it. extended = derivation requires an additional strategy.
| # | Formula | Category | Primary strategy | Starting point | Status |
|---|
What Ramanujan actually used as raw material
Modern equivalent starting points
The following are today's analogues of the raw material Ramanujan started from — accessible without post-1920 theoretical frameworks, but in 2026 form.
Each demonstration starts from a modern equivalent of a Ramanujan-era starting point and traces the algorithm to a verifiable result, none of which Ramanujan knew about.
Techniques Ramanujan would have learned or encountered through Hardy, Littlewood, and the broader international analytic tradition — extended to the worldwide frontier as of 2026. Eighty-two methods across twenty branches, spanning Stokes (1850) through Kelley–Meka (2023): oscillatory integrals, Laplace-type integrals, exponential sums (Weyl, van der Corput, Vinogradov, Bourgain–Demeter–Guth), circle method and additive number theory, sieve methods, spectral and trace formulae, special function asymptotics, random matrix theory, resurgence and trans-series (Écalle, QED perturbation theory), modern additive combinatorics (Gowers, Green–Tao, Kelley–Meka), motivic periods and the cosmic Galois group (Brown, Broadhurst–Roberts), and Teichmüller dynamics and spectral counting (Wu–Xue, Pollicott–Sharp, Mirzakhani, Eskin–Mirzakhani–Mohammadi). School attribution and frontier status are marked for each.
Selection criterion: top-tier, globally competitive practice. No school — Cambridge, Princeton, Paris, Moscow, Beijing, Tokyo, Seoul, Tel Aviv — is privileged. The criterion is the strongest known result for each problem class.