What does the word "symplectic" mean? - MathOverflow

What does the word "symplectic" mean?

2010-11-07T11:43:47Z

I know the definition of symplectic structure, symplectic group, and so on. But what does the word "symplectic" itself mean?

Meta question: I have many other mathematical words whose etymologies are obscure to me. Is it OK for me to ask one question per such word?

Answer by Jim Conant for What does the word "symplectic" mean?

2010-11-07T11:50:56Z

There is a brief explanation here. It looks like the term was coined by Weyl, and was a result of modifying the Greek root "comp" from "complex" to the equivalent Latin root "symp". This is a pretty obscure way to coin a word if you ask me!

Answer by Andrey Rekalo for What does the word "symplectic" mean?

2010-11-07T11:51:53Z

The term "symplectic group" was suggested in The Classical Groups: their invariants and representations (1939, p. 165) by Herman Weyl:

The name "complex group" formerly advocated by me in allusion to line complexes, as these are defined by the vanishing of antisymmetric bilinear forms, has become more and more embarrassing through collision with the word "complex" in the connotation of complex number. I therefore propose to replace it by the corresponding Greek adjective "symplectic." Dickson calls the group the "Abelian linear group" in homage to Abel who first studied it.

Take a look at the Earliest Known Uses of Some of the Words of Mathematics web page.

Answer by Dick Palais for What does the word "symplectic" mean?

2010-11-07T14:19:37Z

The following is from page 1 of Lectures on symplectic geometry, by Ana Cannas da Silva:

As a curiousity, note that two centuries ago the name symplectic did not exist. If you consult a major English dictionary, you are likely to find that symplectic is the name of a bone in a fish's head. However ... the word symplectic in mathematics was coined by Weyl who substituted the Latin root in
complex by the corresponding Greek root, in order to label the symplectic group.

Answer by Patrick I-Z for What does the word "symplectic" mean?

2011-01-25T11:32:41Z

The word "sum-plectic" as a greek translation of "com-plexus" was needed also to differentiate the study of "complex geometry" (complex numbers etc) from the study of "complexes de droites" (the geometry of 'line complexes') where the Plücker coordinates are associated to a natural symplectic structure on the space of affines lines in any euclidean space.

The concept of "differential symplectic geometry" has been introduced I believe by J.-M. Souriau in is 1953 paper

@inproceedings{Sou53, Author = {Jean-Marie Souriau},
Booktitle = {Coll. Int. CNRS},
Pages = {53},
Publisher = {CNRS, Strasbourg},
Title = {G{\'e}om{\'e}trie symplectique diff{\'e}rentielle. Applications.},
Year = {1953}}

He introduces there the concept of "Variétés isotropes saturées", called today "lagrangian manifolds", name given later by V.-I. Arnold.

Answer by Giuseppe for What does the word "symplectic" mean?

2011-06-28T13:55:33Z

From Pietro Majer's comments I learn that "symplectic" is the past participle of a classic Greek verb which means "to embrace".
Consequently I would just remark then how surprising is the effectiveness of this adjective to reflect the pervasiveness of the ideas from symplectic geometry in modern mathematics, which interconnect many different subjects.
Infact, from the introduction to the paper "Symplectic Geometry" by A.Weinstein, I quote:

I think it is not unfair to say that symplectic geometry is of interest today, not so much as a theory in itself, but rather because of a series of remarkable "transforms" which connect it with various areas of analysis.