“Antedisciplinary” Science

I'm currently in the middle of applying for graduate programs in [[Computational/Systems/Synthetic/Quantitative Biology]/Bioengineering/Biomedical Engineering/Bioinformatics/Biotechnology] and, after working in related fields for years and having combed through dozens of relevant departments, I couldn't tell you what any of those terms mean relative to another (or rather, for any of those terms, I could show you two important universities that seem to use them very differently.) They all indicate overlapping areas of a very poorly-defined space in between "normal" biology, computer science, and physical engineering (as well as several other fields.)

Pragmatically, for a prospective student, it's a giant pain simply because it's hard to tell what a program bearing one of these names will actually teach you! Some "computational biology" programs will include wet-lab work, others will never let you near a pipette. Some bioengineering programs are almost purely physical-machines engineering; others use the word interchangeably with "bioinformatics." And so on.

But somewhere in that mess is the future of biology, medicine, and probably some other things as well.

> Every generation, we somehow compress our knowledge just enough to leave room in our brains for one more generation of progress.

I imagine it'd be pretty easy to do that today given the state of math edjumacation in American schools (never went to one). Looks like the bulk of it is calculus and not even the rigorous kind or the kind that could at least be immediately applied to problems today. A 1368 pages calculus book doesn't have a word about something as immediately useful as Gamma function (comes up a lot in today's compsci). Wouldn't it be more fruitful to chop all the current calculus sequences and instead have a semester of finite-dimensional vector spaces first followed up by a semester of functional analysis while introducing only the important bits of analysis as one goes? The relevant bits of mulitvariable calculus and differential geometry of curves and surfaces could be easily introduced within the framework of linear algebra within the first or second semester. That way students could progress to the frontiers of math and bleeding edge of engineering and sciences much faster. As it stands right now, it seems to me the students are forced to waster time, energy, money, potential on memorizing how to solve old chestnuts like the optimization problems from the single variable calculus that were (probably) barely relevant in the middle of the last century.

> However these 3 years of work in isolation, when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law. [..] to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me, both at the lyé and at the university, that one shouldn't bother worrying about what was really meant when using a term like "volume", which was "obviously self-evident", "generally known", "unproblematic", etc. I'd gone over their heads, almost as a matter of course, even as Lesbesgue himself had, several decades before, gone over their heads. It is in this gesture of "going beyond", to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one - it is in this solitary act that one finds true creativity. All others things follow as a matter of course.

-- Alexandre Grothendieck, "The Life of a Mathematician - Reflections and Bearing Witness" (1986)