The most powerful language for mathematics according to M. Gromov
José Manuel Rodríguez Caballero
josephcmac at gmail.com
Sat Feb 8 08:39:27 EST 2020
> What I don't like about these papers is that they fix there math, and
> then they take whatever they need to illuminate their math. They don't
> do it the other way around, for instance taking epithelial cells in the
> inner lining of the small intestines, see how they communicate e.g. the
> help of immunonutrients, and then observe some disease oriented problems
> (like Crohn or Celiac), and from there move on to phenomena to be
> modelled by math. Doing so would mean the problem driving the math, not
> the other way around. 99.9% of mathematicians do it the wrong way, I am
> blunt to say.
To make a mathematical study of biology and not only to use biology as a
means to illustrate a mathematical structure, the concept of information
must be more flexible than just a number. Gromov proposed to develop
information theory in a categorical framework and sometimes information
will be just a number as usual, but sometimes information will be another
mathematical object. There is a recent thesis  about this change of
paradigm, which may be seen as the achievement of Gromov's program. The
only problem is that this thesis is written in a language that may be hard
for people outside the mathematical community.
 Vigneaux, J., 2019. Topology of statistical systems. A cohomological
approach to information theory (Doctoral dissertation, Ph. D. Thesis, Paris
7 Diderot University, Paris, France).
URL = https://webusers.imj-prg.fr/~juan-pablo.vigneaux/these.pdf
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