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This book tells the history of impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square.
List of contents
- 1: Introduction
- 2: Prehistory: Recorded and Non-Recorded Impossibilities
- 3: The First Impossibility Proof: Incommensurability
- 4: The Classical Problems in Antiquity: Constructions and Positive Theorems
- 5: The Classical Problems: The Impossibility Question
- 6: Diorisms and Conclusions about the Greeks and the Medieval Arabs
- 7: Cube Duplication and Angle Trisection in the 17th and 18th Centuries
- 8: Circle Quadrature in the 17th Century
- 9: Circle Quadrature in the 18th Century
- 10: Impossible Equations Made Possible: The Complex Numbers
- 11: Euler and the Bridges of Königsberg
- 12: The Insolvability of the Quintic by Radicals
- 13: Constructions with Ruler and Compass: The Final Impossibility Proofs
- 14: Impossible Integrals
- 15: Impossibility of Proving the Parallel Postulate
- 16: Hilbert and Impossible Problems
- 17: Hilbert and Gödel on Axiomatization and Incompleteness
- 18: Fermat's Last Theorem
- 19: Impossibility in Physics
- 20: Arrow's Impossibility Theorem
- 21: Conclusion
About the author
Jesper Lützen is a historian of mathematics and the physical sciences. He is Professor Emeritus at the Department of Mathematical Sciences at the University of Copenhagen, where he has taught since 1989.
Summary
This book tells the history of impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square.
Additional text
This book is intended as a semi-popular volume: in it, the author eschews mathematical or historical technicalities, instead providing succinct yet rich accounts that neatly convey the main conceptual innovations and transformations at the heart of the episodes discussed therein...The writing is clear and engaging.
