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.
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.
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.
Inhaltsangabe
* 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
* 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
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