Book contents
- Frontmatter
- Contents
- Foreword
- Participants
- On bounded languages and the geometry of nilpotent groups
- Finitely presented groups and the finite generation of exterior powers
- Semigroup presentations and minimal ideals
- Generalised trees and Λ-trees
- The mathematician who had little wisdom: a story and some mathematics
- Palindromic automorphisms of free groups
- A Freiheitssatz for certain one-relator amalgamated products
- Isoperimetric functions of groups and exotic cohomology
- Some embedding theorems and undecidability questions for groups
- Some results on bounded cohomology
- On perfect subgroups of one-relator groups
- Weight tests and hyperbolic groups
- A non-residually finite, relatively finitely presented group in the variety N2A
- Hierarchical decompositions, generalized Tate cohomology, and groups of type (FP)∞
- Tree-lattices and lattices in Lie groups
- Generalisations of Fibonacci numbers, groups and manifolds
- Knotted surfaces in the 4-sphere with no minimal Seifert manifolds
- The higher geometric invariants of modules over Noetherian group rings
- On calculation of width in free groups
- Hilbert modular groups and isoperimetric inequalities
- On systems of equations in free groups
- Cogrowth and essentiality in groups and algebras
- Regular geodesic languages for 2-step nilpotent groups
- Finding indivisible Nielsen paths for a train track map
- More on Burnside's problem
- Problem Session
The mathematician who had little wisdom: a story and some mathematics
Published online by Cambridge University Press: 05 April 2013
- Frontmatter
- Contents
- Foreword
- Participants
- On bounded languages and the geometry of nilpotent groups
- Finitely presented groups and the finite generation of exterior powers
- Semigroup presentations and minimal ideals
- Generalised trees and Λ-trees
- The mathematician who had little wisdom: a story and some mathematics
- Palindromic automorphisms of free groups
- A Freiheitssatz for certain one-relator amalgamated products
- Isoperimetric functions of groups and exotic cohomology
- Some embedding theorems and undecidability questions for groups
- Some results on bounded cohomology
- On perfect subgroups of one-relator groups
- Weight tests and hyperbolic groups
- A non-residually finite, relatively finitely presented group in the variety N2A
- Hierarchical decompositions, generalized Tate cohomology, and groups of type (FP)∞
- Tree-lattices and lattices in Lie groups
- Generalisations of Fibonacci numbers, groups and manifolds
- Knotted surfaces in the 4-sphere with no minimal Seifert manifolds
- The higher geometric invariants of modules over Noetherian group rings
- On calculation of width in free groups
- Hilbert modular groups and isoperimetric inequalities
- On systems of equations in free groups
- Cogrowth and essentiality in groups and algebras
- Regular geodesic languages for 2-step nilpotent groups
- Finding indivisible Nielsen paths for a train track map
- More on Burnside's problem
- Problem Session
Summary
The Story
If any of you who read this volume do not like stories, then I am sorry for you. Stories are the thread from which the fabric of the world is woven, and to dislike stories is to dislike life. But, to any such people, I would also say that if you read this story you will also learn some mathematics.
Once there was a mathematician who had little wisdom. One spring he attended a group theory conference in Scotland, which may or may not have been wise of him. Since the conference was long, he decided to take a couple of days off, which was certainly wise. He had heard much about the beauty of Scotland's rivers, and the fine salmon that swam in them, so he decided to go salmon-fishing. He did not think of the need for a licence, nor that a large charge is made for the right to fish for salmon in most places; indeed, he had not even checked whether there were salmon in the rivers at that time of year. This may seem foolish of him, but turned out not to be so.
He went to the Tweed, which was running sweetly. He saw many people fishing for salmon, but found a pool where no-one was. Not thinking that this might be because that was not a good place for salmon (for he had little wisdom, though, as we shall see, he was also lucky), he began fishing under a bright spring sky.
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- Chapter
- Information
- Combinatorial and Geometric Group Theory, Edinburgh 1993 , pp. 56 - 62Publisher: Cambridge University PressPrint publication year: 1994