When Distance Disappeared — Bridges, Holes, Knots, and the Shape of Data

Scene index

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1. 11736 · KönigsbergFolding a City Map into Four Dots and Seven Lines — The Bridge Problem
2. 21741 · Saint PetersburgProving a Walk Impossible without Trying Every Walk — Odd Degree
3. 31750 · BerlinFinding a Count That Survives Distortion — V−E+F
4. 41848 · GöttingenStudying Relations of Position instead of Measuring Position — Listing's Topologie
5. 51858 · LeipzigFollowing the Front and Returning without a Back — Möbius's Band
6. 61861 · GöttingenRecording a One-Sided Surface Independently — Listing's Twisted Ring
7. 71877 · EdinburghA Classification Table That Outlived a Failed Atomic Model — Tait's Knots
8. 81895 · ParisTranslating Holes into Algebra Richer than a Count — Analysis Situs
9. 91904 · ParisCould Loops Identify the Three-Dimensional Space We Inhabit? — The Poincaré Conjecture
10. 101911 · AmsterdamFolding a Plane toward a Line without Making Dimension Disappear — Brouwer
11. 111914 · LeipzigDiscarding Even the Rubber Sheet and Keeping Rules of Nearness — Hausdorff
12. 121925 · GöttingenFrom Numbers That Count Holes to Groups That Transform — Noether's Seminar Network
13. 131928 · PrincetonGiving a Knot a Polynomial Fingerprint — The Alexander Polynomial
14. 141956 · PrincetonThe Same Sphere Where Differentiation Works Differently — Milnor's Exotic 7-Sphere
15. 151961 · BerkeleyTaking High-Dimensional Spaces Apart by Handles — Smale
16. 161984 · BerkeleyA New Knot Fingerprint Emerging from Algebra outside Knot Theory — Jones
17. 172003 · Saint PetersburgLetting Space Flow until Its Shape Appears — Perelman's Three Preprints
18. 182005 · StanfordTracking Holes That Survive in a Cloud of Points — Persistent Homology