Why Would a Mathematician Care About Embryology?
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Reason number one was given by Lewis Wolpert: It is not birth, marriage, or death, but gastrulation, which is truly the most important time in your life.
But mathematicians do not care about things and people just because they are “important.” (If mathematicians study the “marriage problem,” it is not for the reasons that motivate normal people to get married.) Let us try again: Embryonic development is, structurally speaking, a damn interesting process, something that is very hard to understand. This is better. We, mathematicians, are supposed to understand everything worth understanding and be able to solve any hard problem deserving a solution. Tell me – a nut-cracker mathematician exclaims – just tell me in rigorous mathematical terms what the main problem in embryology is, and I will solve it. OK, here is the problem: What is the mathematical formulation of the main problem(s) in embryology? There are two opposite directions to take for a mathematician who enters a field in biology. The most productive one is to concentrate on a particular class of phenomena, learn as many specific details as possible from biologists, and work out a specific model in agreement with the data. You will find several fascinating talks along these lines in these pages. But this does not lead, at least not directly, to the solution of the main problem. No matter how many successful models you have, there remains a lingering feeling of being a blind man touching different parts of an elephant. What is the elephant?
M. Gromov (*) Institut des Hautes E´tudes Scientifiques, France e-mail: [email protected] V. Capasso et al. (eds.), Pattern Formation in Morphogenesis, Springer Proceedings in Mathematics 15, DOI 10.1007/978-3-642-20164-6_1, # Springer-Verlag Berlin Heidelberg 2013
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M. Gromov
Fig. 1 Bats by Ernst Haeckel. Lithograph from “Kunstformen der Natur” (1900) -“Chiroptera”, Plate 67-Vampyrus, 1-15: Plecotus auritus; Nyctophilus australis; Megaderma trifolium; Vampyrus auritus; Lonchorhina aurita; Natalus stramineus; Mormops blainvillei; Anthops ornatus; Phyllostoma hastatum; Furipterus coerulescens; Rhinolophus equinus; Centurio flavigularis; Vampyrus spectrum (permission to copy under the terms of the GNU Free Documentation License)
Why Would a Mathematician Care About Embryology?
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Rene´ Thom suggested an approach in the framework of the catastrophe theory, but, from a biologist’s point of view, that was rather more about the shadow of an elephant on a wall, not about the real animal. Earlier, John von Neumann proposed a model of “morphogenesis” of automata, but one still cannot adequately formulate the theorem that von Neumann proved. It seems that the general ideas of von Neumann and of Thom, imaginative as they are, still fall short of addressing the main problem. But where should a mathematician go, where can we start from? I think all you can do is to proceed like a child learning a language, a child mathematician, though you be biology-blind as a bat (Fig.1): you ask questions and listen to the echoes – the answ
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