Research-page premise
Bourgain's work repeatedly converts a hard question into a quantitative core: a finite-dimensional obstruction, a frequency-localized inequality, a multiscale PDE induction, a sum-product growth theorem, a spectral-gap mechanism, or an inverse theorem. This page reconstructs those moves as an explicit decision tree.
Methodological rule: no posthumous development is assumed as part of Bourgain's own derivation. Later terminology is used only as retrospective labeling when it clarifies the reconstructed route.
Thirty-three reconstructed strategies
Select a strategy
Click a card above to see its inferred use, formula cue, and case evidence.
Overlapping prevalence ranking
Because each case may use several strategies, the percentages below are prevalence rates: count divided by 300 cases. They are not normalized to sum to 100%.
300 publication / chapter cases
| # | Year | Case / lecture title | Source | Thesis/result abstraction | Strategies |
|---|
Worked reconstructions
Source spine and limitations
This page uses bibliographic records as its case spine. It does not reproduce Bourgain's copyrighted papers or book chapters. The case summaries are compressed thesis/result abstractions intended for research navigation and methodological comparison.
The first 300 entries of the public publication list are used as a stable corpus even though the list continues beyond that point. Lecture-series and book/chapter records are incorporated when they occur in the bibliography and in the source-spine notes.