Misha Gromov's recent Bull. AMS article "Crystals, proteins, stability and isoperimetry" (2011) can be read as a 29-page essay on the requested topic, with a focus particularly on mathematical inspiration arising in evolutionary biology, neurophysiology, and cognitive science. Gromov sets the stage as follows:

One may conjecture that neither cell nor brain would be possible if not for profound mathematical “somethings” behind these, Nature’s inventions. But what are these “somethings”? Why do we, mathematicians, remain unaware of them? … The history of mathematics shows how slow we are when it comes to inventing/recognizing new structures even if they are spread before our eyes, such as hyperbolic space, for instance. … One has to browse through myriad stars—structural specks of Life revealed by biologists—in order to identify the “essential ones”, and when (if ?) we find them, we may start on the long road toward new mathematics.

Gromov then goes on to suggest many dozens of concrete questions, arising in many bio-related disciplines, that uniformly direct our vision (to use Scott Aaron's nice similes) from the "leaves" of life to the "roots" of fundamental mathematics.

What does Gromov see (that everyone sees) that inspires him so frequently to conceive mathematics (that no one previously has conceived (Szent-Gyrgyi))? Gromov has written this essay, to tell us precisely what it is, that he presently sees.

Since this is a community Wiki, I will informally suggest that it is great fun to read Gromov's inspiring essay either immediately before, or immediately after, viewing Stephane Guisard and Jose Salgado's similarly inspiring VLT (Very Large Telescope) HD Timelapse Footage.

Gromov is concerned largely with very small (molecular-scale) evolved systems, while Guisard and Salgado are concerned mainly with very large (galactic scale) evolved systems … and yet they are tapping the same source.

Misha Gromov's recent Bull. AMS article "Crystals, proteins, stability and isoperimetry" (2011) can be read as a 29-page essay on the requested topic, with a focus particularly on mathematical inspiration arising in evolutionary biology, neurophysiology, and cognitive science. Gromov sets the stage as follows:

One may conjecture that neither cell nor brain would be possible if not for profound mathematical “somethings” behind these, Nature’s inventions. But what are these “somethings”? Why do we, mathematicians, remain unaware of them? … The history of mathematics shows how slow we are when it comes to inventing/recognizing new structures even if they are spread before our eyes, such as hyperbolic space, for instance. … One has to browse through myriad stars—structural specks of Life revealed by biologists—in order to identify the “essential ones”, and when (if ?) we find them, we may start on the long road toward new mathematics.

Gromov then goes on to suggest many dozens of concrete questions, arising in many bio-related disciplines, that uniformly direct our vision (to use Scott Aaron's nice similes) from the "leaves" of life to the "roots" of fundamental mathematics.

What does Gromov see (that everyone sees) that inspires him so frequently to conceive mathematics (that no one previously has conceived (Szent-Gyrgyi))? Gromov has written this essay, to tell us precisely what it is, that he presently sees.

Since this is a community Wiki, I will informally suggest that it is great fun to read Gromov's inspiring essay either immediately before, or immediately after, viewing Stephane Guisard and Jose Salgado's similarly inspiring VLT (Very Large Telescope) HD Timelapse Footage.

Gromov is concerned largely with very small (molecular-scale) evolved systems, while Guisard and Salgado are concerned mainly with very large (galactic scale) evolved systems … and yet they are tapping the same source.

Misha Gromov's recent Bull. AMS article "Crystals, proteins, stability and isoperimetry" (2011) can be read as a 29-page essay on the requested topic, with a focus particularly on mathematical inspiration arising in evolutionary biology, neurophysiology, and cognitive science. Gromov sets the stage as follows:

One may conjecture that neither cell nor brain would be possible if not for profound mathematical “somethings” behind these, Nature’s inventions. But what are these “somethings”? Why do we, mathematicians, remain unaware of them? … The history of mathematics shows how slow we are when it comes to inventing/recognizing new structures even if they are spread before our eyes, such as hyperbolic space, for instance. … One has to browse through myriad stars—structural specks of Life revealed by biologists—in order to identify the “essential ones”, and when (if ?) we find them, we may start on the long road toward new mathematics.

Gromov then goes on to suggest many dozens of concrete questions, arising in many bio-related disciplines, that uniformly direct our vision (to use Scott Aaron's nice similes) from the "leaves" of life to the "roots" of fundamental mathematics.

What does Gromov see (that everyone sees) that inspires him so frequently to conceive mathematics (that no one previously has conceived (Szent-Gyrgyi))? Gromov has written this essay, to tell us precisely what it is, that he presently sees.

Since this is a community Wiki, I will informally suggest that it is great fun to read Gromov's inspiring essay either immediately before, or immediately after, viewing Stephane Guisard and Jose Salgado's similarly inspiring VLT (Very Large Telescope) HD Timelapse Footage.

Gromov is concerned largely with very small (molecular-scale) evolved systems, while Guisard and Salgado are concerned mainly with very large (galactic scale) evolved systems … and yet they are tapping the same source.

Misha Gromov's recent Bull. AMS article "Crystals, proteins, stability and isoperimetry" (2011) can be read as a 29-page essay on the requested topic, with a focus particularly on mathematical inspiration arising in evolutionary biology, neurophysiology, and cognitive science. Gromov sets the stage as follows:

One may conjecture that neither cell nor brain would be possible if not for profound mathematical “somethings” behind these, Nature’s inventions. But what are these “somethings”? Why do we, mathematicians, remain unaware of them? … The history of mathematics shows how slow we are when it comes to inventing/recognizing new structures even if they are spread before our eyes, such as hyperbolic space, for instance. … One has to browse through myriad stars—structural specks of Life revealed by biologists—in order to identify the “essential ones”, and when (if ?) we find them, we may start on the long road toward new mathematics.

Gromov then goes on to suggest many dozens of concrete questions, arising in many bio-related disciplines, that uniformly direct our vision (to use Scott Aaron's nice similes) from the "leaves" of life to the "roots" of fundamental mathematics.

What does Gromov see (that everyone sees) that inspires him so frequently to conceive mathematics (that no one previously has conceived (Szent-Gyrgyi))? Gromov has written this essay, to tell us precisely what it is, that he presently sees.

Since this is a community Wiki, I will informally suggest that it is great fun to read Gromov's inspiring essay either immediately before, or immediately after, viewing Stephane Guisard and Jose Salgado's similarly inspiring VLT (Very Large Telescope) HD Timelapse Footage.

Gromov is concerned largely with very small (molecular-scale) evolved systems, while Guisard and Salgado are concerned mainly with very large (galactic scale) evolved systems … and yet they are tapping the same source.