While I agree that it's very questionable that Nature would invite someone to write an obituary (or what have you) and then reject it, I fail to see what's so controversial about the text being overly technical. I work in Physics, and "[...] locus of solutions of sets of polynomial equations by combining the algebraic properties of the rings of polynomials with the geometric properties of this locus, known as a variety" is still an incredibly tough sentence to parse on the first pass. I cannot imagine how it would read for someone who is either unfamiliar (or only passingly familiar) with, for example, the concept of a ring; "algebraic properties of a ring of polynomials"? This just seems like a case of https://xkcd.com/2501/ , with a hint of arrogance in thinking everyone working in STEM must be as comfortable with abstract concepts of mathematics as mathematicians are.
The two cultures of mathematics and biology (2014)
11–20 of 38 posts
Re: The two cultures of mathematics and biology (2014)
#12While I agree that it's very questionable that Nature would invite someone to write an obituary (or what have you) and then reject it, I fail to see what's so controversial about the text being overly technical. I work in Physics, and "[...] locus of solutions of sets of polynomial equations by combining the algebraic properties of the rings of polynomials with the geometric properties of this locus, known as a varie…
Just curious if you removed the words “rings of” would you have the same objections?
Re: The two cultures of mathematics and biology (2014)
#13There are currently 251131639 sequenced proteins in UniProt[^1], so, that's a very lower bound on the number of things a modern biologist has to amuse themselves with. Many still consider biology as the study of each individual biological organism, system, or protein. But since there are so many of those, I argue that biology must become a science of methods of understanding, and not a science of bare understanding.…
Why is there any science at all above pure maths? Why isn't physics, chemistry, geology etc etc just maths? That's because choosing the right level of abstraction is really important for making practical progress. For example penicillin was discovered and used to save millions of lives without any rigorous mathematical understanding of how the drug interacts with it's target. I'm not saying maths isn't incredibly use…
Also I do wonder sometimes whether mathematicians don't actually understand some of the maths they work on
We don’t. One of the first steps to mathematical maturity is learning to let go of the need to understand, the need to visualize. Much of mathematics is a formal affair of making arguments to satisfy necessary and sufficient conditions. Trying to understand infinite-dimensional spaces or highly abstract sets and objects is too much, and unnecessary.
”Young man, in mathematics you don't understand things. You just get used to them.”
— John von Neumann
Re: The two cultures of mathematics and biology (2014)
#14The estrangement he observes aren't that surprising, in either direction. Many universities have both Math and Applied Math departments. Why have both unless the mathematicians in the Math department don't want to work on applications? I have spoken with people who say if you're working on an application, "it's not really math."
In biology, there is almost certainly a self-selection effect in which the field attracts people who want to study science but are not comfortable with math, or just people who have a particular interest in plants or animals, which is uncorrelated with math skills.
I suspect there is a self-selection effect in the other direction too. I was always good at math, but I never wanted to major in it or go to grad school in it. I got a PhD in AI and machine learning, which was quite mathematical enough, and yet I can't recall ever interacting with anyone from the math department. As far as I knew, they wanted to do "pure math" and weren't interested in applications. So the people who want to do practical things select them selves into other majors like physics, engineering, and computer science.
Re: The two cultures of mathematics and biology (2014)
#15Earlier quoted context omitted.
Why is there any science at all above pure maths? Why isn't physics, chemistry, geology etc etc just maths? That's because choosing the right level of abstraction is really important for making practical progress. For example penicillin was discovered and used to save millions of lives without any rigorous mathematical understanding of how the drug interacts with it's target. I'm not saying maths isn't incredibly use…
Also I do wonder sometimes whether mathematicians don't actually understand some of the maths they work on We don’t. One of the first steps to mathematical maturity is learning to let go of the need to understand, the need to visualize. Much of mathematics is a formal affair of making arguments to satisfy necessary and sufficient conditions. Trying to understand infinite-dimensional spaces or highly abstract sets and…
I would disagree. Mathematicians certainly don't need to visualize everything but "intuition" is a commonly used phrase which is a notion of understanding.
Although math merely requires proving some statement, often having an intuition / understanding of how concepts interact with each other helps figure out which things are likely to be true.
Re: The two cultures of mathematics and biology (2014)
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Re: The two cultures of mathematics and biology (2014)
#17The estrangement he observes aren't that surprising, in either direction. Many universities have both Math and Applied Math departments. Why have both unless the mathematicians in the Math department don't want to work on applications? I have spoken with people who say if you're working on an application, "it's not really math." In biology, there is almost certainly a self-selection effect in which the field attracts…
Each field has its own culture and its own way of thinking. People are often socialized to a particular culture in the university or even earlier, and it sticks. You can learn other fields on your own, but it's hard to adopt the culture without socialization.
I did theoretical computer science in the university, leaning towards more applied stuff by the end of my PhD. I'm still a computer scientist at heart. I can follow some topics in research mathematics, but I don't think like a mathematician and I'm not interested in the same things. I work in bioinformatics these days, but I often zone out when people start talking about the stuff that goes in the results section of a paper. I'm not a bioinformatician, and I'm not interested in the same things. I've seen a similar culture gap between bioinformatics and "proper" biology, but I don't have first-hand experience with that.
Re: The two cultures of mathematics and biology (2014)
#18The estrangement he observes aren't that surprising, in either direction. Many universities have both Math and Applied Math departments. Why have both unless the mathematicians in the Math department don't want to work on applications? I have spoken with people who say if you're working on an application, "it's not really math." In biology, there is almost certainly a self-selection effect in which the field attracts…
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Re: The two cultures of mathematics and biology (2014)
#19This article was written in 2014 and I do not know if the specifics are still true. However, I think mathematicians and biologists work in two different levels of abstraction. One is a lawful good with occasional venture into chaotic good, only to reform the chaos. The other is a true neutral with lot of expeditions into chaotic evil just for fun.
Well, it's 2024, I'm a biologist, I read the thing about schemes, and I still don't understand what they are or how they would help me understand biology any better.
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Re: The two cultures of mathematics and biology (2014)
#20This article was written in 2014 and I do not know if the specifics are still true. However, I think mathematicians and biologists work in two different levels of abstraction. One is a lawful good with occasional venture into chaotic good, only to reform the chaos. The other is a true neutral with lot of expeditions into chaotic evil just for fun.
Well, it's 2024, I'm a biologist, I read the thing about schemes, and I still don't understand what they are or how they would help me understand biology any better.
I'm an applied mathematician (Ph.D. in math but never a professor) and I did not want to try to understand the description of schemes in the obituary. I thought that the obituary was too technical for me. On the other hand, if I thought that schemes were useful for my work, then I would dig into them and try to understand them.