
Can one explain schemes to biologists? (2014) - octatoan
http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html
======
avz
There seems to be a fair amount of reservation or even animosity towards maths
in many areas:

* among the general public people feel it is acceptable to admit lack of basic skill or understanding in mathematics (at times even arithmetics) whereas they would be ashamed to admit it with respect to reading or writing,

* popular science books are often written without a single formula (and according to a preface in one popular science book editors and publishers generally reject a book that tries to sneak some in, their apparent justification being that each formula halves the sales),

* and it turns out that even STEM scientists, in this case biologists, appear to have gaps in their understanding of basic mathematics like analysis and algebra.

I'm very curious as to what might be behind this isolation of mathematics. Bad
teachers? Mathematicians' own disregard for applications? Some sort of self-
perpetuating myth about inaccessibility of maths for the common person?

~~~
reagency
It is also shocking how mathematicians have huge gaps in their basic knowledge
of cell biology. What can be done to help mathematicians learn relevant
applications? Or even accept that applications merit more than an occasional
momentary thought, and that only to wave off a field as trivial?

~~~
TeMPOraL
Mathematics and biology are not interchangeable like that. One is specific
knowledge, other (at least the parts we're talking about here) is mental tools
and models, which are useful for every field.

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jamessb
Lior Pachter had a blog post about this incident ( _The two cultures of
mathematics and biology_ ): [https://liorpachter.wordpress.com/2014/12/30/the-
two-culture...](https://liorpachter.wordpress.com/2014/12/30/the-two-cultures-
of-mathematics-and-biology/)

It was previously discussed here:
[https://news.ycombinator.com/item?id=8819811](https://news.ycombinator.com/item?id=8819811)

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ganzuul
Mathematics has a massive problem with communication. There are communities
among mathematicians which exclude each other and these communities are
invisible to the outsider, so the field appears to be full of contradictions.
For example, ZFC is fine for calculus (most of engineering), but completely
inadequate for computer science. For CS you have to allow self-reference and
that is expressly verboten in ZFC. By extension, CS only needs the natural
numbers, forgoing Hilbert space for Banach space + process.

Hilbert said "Wir müssen wissen — wir werden wissen!", and just the day prior
Gödel demonstrated the futility of axiomatic set theory. Yet, still today, ZFC
set theory is assumed unless it is stated otherwise.

There are Luddites among mathematcians, and Turing died for their sins.

~~~
tel
I think there are definitely interesting things to talk about in foundations,
and also that many are now well motivated by computer science. It's not like
these are either unknown or special, though. For most "practical", pure math
arguing about foundations can't move your field forward as it is not holding
your field back.

Further, differences in communication rarely stem from foundational issues as
much as merely the social construct that practitioners in separate fields have
less to say to one another than those in the same field. This leads to
semantic drift and development of independent metaphor technologies.
Translation necessarily becomes more expensive and so higher ROI is required
in order to motivate it.

~~~
ganzuul
I think I can express my opinion simply now. Thank you. -

"Practical" pure math appears to be based on formalism rather than
intuitionism. Because foundations and therefore intuition does not hold
formalism back, these practitioners drift further away from being able to
communicate their metaphors to whose who rely on intuition; such as
biologists.

\- And this is my opinion.

~~~
tel
Are you uniting "intuitionism" and common "intuition"? I'm not personally sure
I disagree here at all, but I'm certain many would!

~~~
ganzuul
Strictly no... Then We would have to debate what common intuition is and that
is untenable.

What I am trying to say is that math is a discipline of philosophy, that the
integers are divine, and that the straightedge and compass ought to be enough
for anybody. ;) I often rely on my intuition for abstract thought, and
repeatedly find that others have reached the same conclusions that I do.
Therefore (my own) intuition is repeatable, and therefore intuition is
scientific.

Juxtapose formalism, which seems to say that math is solely the practice of
inventing rules and following them to the end. - I understand why this idea
has its own beauty, haughty as it might seem, but at the same time it is a
very strange and in my opinion frightening kind of beauty because it intends
to remain unknowable.

Turing, who I have apparently proclaimed a saint, seems to observe that both
of these paradigms are needed for some kind of universal, and altogether
anthropomorphic, program. I would be hard pressed to dismiss any idea which
appears beautiful...

------
avz
> Their editor wrote me that 'higher degree polynomials', 'infinitesimal
> vectors' and 'complex space' (even complex numbers) were things at least
> half their readership had never come across.

It appears to me that in software engineering the situation is a lot better.
Anecdotes from my own recent experiences:

\- polynomials (encountered when reading about CRC codes and elliptic curve
cryptography),

\- infinitesimals and vectors (encountered when recalling Newton's third law
when working on a small Android game using libGDX and box2d),

\- complex numbers (encountered when learning Go and reading about AC
circuits).

I haven't encountered complex space, but my guess is that it's similar to the
familiar real vector space but permits complex numbers as vector components
and coefficients in linear combinations.

~~~
TeMPOraL
Cool thing about software, at least when talking about coding up stuff for fun
and not programming career, is that it tends to expose you to a great amount
of different fields of knowledge.

~~~
duaneb
Bingo. I think the biggest problem CS students have is being under the
impression they're studying a career directly instead of learning the tools
they need to tackle unknown problems directly.

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Myrmornis
The version submitted in the comments is better than Mumford's IMO.

