Treccani History of Science
The second Scientific Revolution
I4 – Mathematics and logic
Part D - The mathematics of structures
Edited by Umberto Bottazzini, Jeremy Grey
Origins of the structural approach to algebra
• 1. Dedekind’s lectures
• 2. Serret’s and Jordan’s textbooks
• 3. Weber’s Lehrbuch
• 4, Further research by Dedekind
• 5. Hilbert
• 6. The success of the structural approach
Algebraic theory
• 1. Between the nineteenth and twentieth centuries
• 2. The period 1918-1939
• 3. Algebraic geometry and algebraic number theory
• 4. The Riemann-Roch theorem
• 5. Intrinsic algebraic geometry
Differential geometry
• 1. The situation in the 19th century
• 2. Intrinsic geometry: 1900-1917
• 3. The period 1918-1939
• 4. Connections
Algebraic topology at the beginning of the XX Century
• 1. Homology
• 2. Homotopy
• 3. Conclusions
Analytic number theory
• 1. Additive analytic number theory
• 2. Multiplicative analytic number theory
Algebraic number theory
• 1. Algebraic number fields
• 2. Class fields
• 4. Artin's reciprocity law
Algebra
• 1. Commutative algebra
• 2. Homological algebra
• 3. The representation theory
• 4. The group theory
• 5. Logic, combinatorics and K-theory