  Brackets by another name, Whitehead or Samelson products, have a history
parallel to that in Kosmann-Schwarzbach's From Schouten to Mackenzie: notes on
brackets. Here I sketch the development of these and some of the other brackets
and products and braces within homotopy theory and homological algebra and with
applications to mathematical physics. In contrast to the brackets of Schouten,
Nijenhuis and of Gerstenhaber, which involve a relation to another graded
product, in homotopy theory many of the brackets are free standing binary
operations.
  My path takes me through many twists and turns. The path leads beyond binary
to multi-linear n-ary operations, either for a single n or for whole coherent
congeries of such assembled into what is known now as an $\infty$-algebra, such
as in homotopy Gerstenhaber algebras. It also leads to more subtle invariants.
Along the way, attention will be called to interaction with `physics'; indeed,
it has been a two-way street.
