Treccani History of Science
The second Scientific Revolution
I5 – Mathematics and logic
Part E - The mathematics of nature and society. Mathematical schools
Edited by Umberto Bottazzini, Jeremy Grey
The probability
• 1. Evolution of the notion of probability
• 2. Limit theorems and laws of large numbers
• 3. Random processes
• 4. The 'schools' of probabilists
Statistical methodology
• 1. The tests of significance
• 2. The hypothesis tests
• 3. The estimate
• 4. The maximum likelihood
• 5. Interval estimation
• 6. The probabilistic prediction
The mathematization of biology and the biomathematics
• 1. Conceptual and practical sources
• 2. The nineteenth-century stasis
• 3. The golden age of theoretical biology: 1920-1940
• 4. Mathematical biology between mechanism and modeling
Mathematical economy 1870-1950
• 1. Marginalism
• 2. The post-war years
• 3. Wald and von Neumann's contributions
• 4. Linear programming
Numerical analysis
• 1. The computational science: arithmetic and efficient algorithms
• 2. Discretization processes
• 3. Fixed-point techniques
• 4. Stability and complexity
Systems theory and control
• 1. The development of the theory of automatic control in the nineteenth century
• 2. Theory of automatic control in the first decades of the twentieth century
• 3. The foundations of the classical theory of automatic control
• 4. Evaluation of the stability of the system
• 5. Quality of the control process
• 6. Non-linear problems in the theory of automatic control
• 7. Variational approach to control problems
Moscow school of mathematics
• 1. Mathematics in St. Petersburg and Moscow
• 2. The Egorov-Luzin School before the Revolution
• 3. Mathematics in the Revolution years
• 4. Mathematics in Moscow in the Twenties and Thirties
• 5. The ideological repressions of the Thirties and the beginning of a new phase
• 6. The transfer to Moscow of the Steklov Mathematical institute
• 7. World War II and the postwar period
Mathematics in the United States
• 1. Mathematics at the turn of the century
• 2. The rise of the American mathematical community
• 3. Mathematics and the First World War
• 4. The 1920s: 'the dawn of a new era'
• 5. The Institute for advanced study
• 6. The immigration of Jewish scholars to the United States in the 1930s
• 7. Mathematics and the Second World War
• 8. Applied mathematics
• 9. Government support for post-war research
• 10. Mathematics in the early post-war years
Bourbakism
• 1. Bourbaki and his methods
• 2. Sets
• 3. Algebra
• 4. General topology
• 5. Functions of a real variable
• 6. Topological vector spaces
• 7. Integration
• 8. Commutative algebra
• 9. Algebraic varieties
• 10. Lie groups and algebras
• 11. Spectral theories