Crystalls, Proteins and Isoperimetry.
Misha Gromov
September 18, 2009

Abstract
We attempt to formulate several mathematical problems suggested by
structural patterns present in bio-molecular assemblies. Our description of
these assemblies, by necessity brief, is self-contained, albeit on a supercial
level. If a reader stumbles upon something confusing, this, hopefully, will
become clearer at a later point in the article.
1 Is there Mathematics in Biology?
Day-Night, Day-Night, Day-Night. Summer-Winter, Summer-Winter… .
What is the structure behind this. Where should we look to uncover it? Is
it in the singing of birds, in the
ows of rivers, in the changes of temperature?
We know, with hindsight, what we should do.
Look up into the night sky, nd a few specks of light { planets { that slowly
crawl amongst the unmoving stars, imagine how their routes appear if seen from
the sun, invent calculus, guess dierential equations for the planetary routes,
unravel symmetries of these…. and the world of mathematical wonders opens
to you: Lie groups, algebraic varieties, symplectic manifolds… .
Now try: Alive-Dead, Alive-Dead, Alive-Dead,… . Where do we go from
here?
«… living matter, while not eluding the «laws of physics» as established
up to date, is likely to involve «other laws of physics» hitherto unknown, which