Table 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.