The Ledger
Every pure-math field in the 1959 Mathematics Subject Classification that counts as “pure” and was established by 1960 — all 34 of them, not just the ones with a good story.
34
fields surveyed
8
named dismissal, later applied
19
never dismissed, applied anyway
3
real application, but specialized
1
no external application documented
Click a column header to sort. Filter by verdict below. Every row links to that field's own page: the exact founding date, the dismissal quote (or its absence, stated plainly), the application (or its absence, stated plainly), and a confidence grade. Full citations are on the Sources page.
| MSC | Field | Dismissed? | Applied? | Gap (yrs) | Verdict |
|---|---|---|---|---|---|
| 03 | Mathematical logic & foundations | Yes | Yes | 102 | Named dismissal, later applied |
| 04 | Set theory | No | No | — | No external application documented |
| 05 | Combinatorics | No | Yes | — | Never dismissed, applied anyway |
| 06/08 | Order, lattices & Boolean algebra | No | Yes | 83 | Never dismissed, applied anyway |
| 11 | Number theory | Yes | Yes | 176 | Named dismissal, later applied |
| 12 | Field theory & Galois theory | No | Yes | 130 | Never dismissed, applied anyway |
| 13 | Commutative rings & algebras | No | Yes | 107 | Never dismissed, applied anyway |
| 14 | Algebraic geometry | Yes | Yes | 155 | Mixed / doesn't fit cleanly |
| 15 | Linear & multilinear algebra; matrix theory | No | Yes | 67 | Never dismissed, applied anyway |
| 16 | Associative rings & algebras (quaternions) | Yes | Yes | 142 | Named dismissal, later applied |
| 17 | Lie algebras & nonassociative algebra | No | Yes | 87 | Never dismissed, applied anyway |
| 18 | Category theory & homological algebra | Yes | Yes | 44 | Named dismissal, later applied |
| 19 | K-theory | No | Yes (specialized) | 52 | Real application, but specialized — not mass-market infrastructure |
| 20/22 | Group theory & Lie groups | No | Yes | 37 | Never dismissed, applied anyway |
| 26/28 | Real analysis & measure theory | No | Yes | 31 | Never dismissed, applied anyway |
| 30 | Complex analysis | No | Yes | 68 | Never dismissed, applied anyway |
| 31 | Potential theory | No | Yes | 0 | Never dismissed, applied anyway |
| 32 | Several complex variables | No | Yes (specialized) | 69 | Real application, but specialized — not mass-market infrastructure |
| 33 | Special functions | No | Yes | 158 | Mixed / doesn't fit cleanly |
| 34 | Ordinary differential equations | No | Yes | 0 | Never dismissed, applied anyway |
| 35 | Partial differential equations | No | Yes | 0 | Never dismissed, applied anyway |
| 37 | Dynamical systems & ergodic theory | No | Yes | 73 | Never dismissed, applied anyway |
| 40/41 | Classical analysis: series & summability | Yes | Yes | 78 | Named dismissal, later applied |
| 42 | Fourier analysis | No | Yes | 50 | Never dismissed, applied anyway |
| 43 | Abstract harmonic analysis | No | Yes (specialized) | 66 | Real application, but specialized — not mass-market infrastructure |
| 44/45 | Integral transforms & integral equations | Yes | Yes | 0 | Never dismissed, applied anyway |
| 46/47 | Functional analysis & operator theory | Yes | Yes | 28 | Named dismissal, later applied |
| 49 | Calculus of variations & optimal control | No | Yes | 0 | Never dismissed, applied anyway |
| 51/52 | Geometry: classical, convex & discrete | No | Yes | 354 | Mixed / doesn't fit cleanly |
| 53 | Differential geometry | Yes | Yes | 61 | Named dismissal, later applied |
| 54 | General topology | No | Yes | 40 | Never dismissed, applied anyway |
| 55 | Algebraic topology | No | Yes | 107 | Never dismissed, applied anyway |
| 57/58 | Manifolds & low-dimensional topology (knot theory) | Yes | Yes | 143 | Named dismissal, later applied |
| 60 | Probability theory | No | Yes | 0 | Never dismissed, applied anyway |
“Gap” is years from founding to first documented real-world application, not from any dismissal — several fields were never dismissed at all.