Science
Bernhard Riemann
Mathematician of geometry and curved spaces
Historical portrait · Image credit
Who they are
Bernhard Riemann investigated geometry in spaces whose metric and curvature need not follow ordinary Euclidean assumptions. His work supplied part of the mathematical background later used in general relativity. The timeline connects him to Einstein through the curvature construction, while his own lecture asks how geometrical assumptions relate to experience.
He explains a mathematical precursor to the geometric description of gravitation, rather than participation in Einstein’s 1915 paper.
Selected contributions
Selected works
Primary text · 1867
On the Hypotheses which lie at the Bases of Geometry
Riemann develops spaces with variable metric and curvature and asks which geometrical assumptions can be supported by experience. The lecture supplies mathematical background for later geometric theories of gravitation.
Posthumous German publication in 1867; linked text is W. K. Clifford’s 1873 English translation. Lecture date is not used as the publication year.
Reading scope & citation
Freshly read the plan, manifold and metric discussion, and application-to-space conclusion in the English transcription. Formula derivations were not independently checked.
In the timeline
Biography sources & portrait credit
- The Field Equations of Gravitation ↗Prussian Academy proceedings; translation on Wikisource
- Ueber die Hypothesen, welche der Geometrie zu Grunde liegen ↗Trinity College Dublin, History of Mathematics
- On the Hypotheses which lie at the Bases of Geometry ↗Bernhard Riemann; W. K. Clifford translation; Trinity College Dublin
Portrait credit
Unknown artist. Public domain (Commons file-specific copyright declaration). Via Wikimedia Commons.
Historical portrait. Cropped to 4:5, resized to 320 × 400 and converted to WebP.
Image source & identification ↗ · Public domain (Commons file-specific copyright declaration) ↗
