Treccani History of Science
The Nineteenth Century
H1 – Mathematics
Edited by Umberto Bottazzini
The roots of contemporary knowledge
• 1. The most difficult problem: life and transformations in Nature
• 2. The stars and their history
• 3. Symmetries and marche naturelle: Fourier and Comte
• 4. Space and time. From Kant to Poincaré
• 5. The riddles of electricity and magnetism
• 6. Newtonian philosophies and conservation of energy
• 7. From conservation to dissipation: still a conflict between the discrete and the continuous
• 8. Evolution without design and the discovery of neuron
• 9. The field, particles and the discovery of electron
• 10. Matter and radiation
Images of mathematics in the nineteenth century
• 1. Le grandes écoles
• 2. Contrasting images
• 3. The «honour of the human spirit»
• 4. A national revolution
• 5. Across the Channel
• 6. The decline of hegemony French
• 7. The schools of Berlin and Göttingen
• 8. On the eve of the new century
Rigor in analysis
• 1. Lagrange’s legacy
• 2. Fourier series
• 3. New criteria of rigor
• 4. In the footsteps of Cauchy
• 5. Between Göttingen and Berlin
• 6. Continuity and infinite sets of points
Complex analysis
• 1. The fundamental theorem of algebra.
• 2. Origins of complex function theory.
• 3. Riemann.
• 4. Weierstrass.
• 5. Elliptic functions and Abelian Functions.
• 6. The dominance of complex function theory
Ordinary differential equations
• 1. Real variable
• 2. Complex variable
Partial differential equations
• 1. Functions of several variables
• 2. Partial differential equations: first and second order
• 3. Potential theory and integral theorems
• 4. General theory of partial differential equations and potentials
Calculus of variation
• 1. The Euler problem.
• 2. Jacobi.
• 3. Mayer.
• 4. Weierstrass.
• 5. Hamilton-Jacobi theory.
• 6. Existence questions