The blog post certainly illustrates the importance of a good copywriter...
"Tool to get rid of dust."
What do grad students in math do all day?
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Re: What do grad students in math do all day?
#42The blog post certainly illustrates the importance of a good copywriter... "Tool to get rid of dust."
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Re: What do grad students in math do all day?
#43I'm just finishing a math PhD. Talking to CS PhD's my impression is that we do pretty much the same thing, we just work on different domains.
I'm a CS PhD, and I agree. I always tell people I'm studying math because it gives them much more of a flavor for what I'm actually doing everyday. When I say computer science, people think I'm just programming something. Also, when people ask me, "So What do you actually do studying math?" I reply, "Sit and stare at the wall for several hours a day. Occasionally I write something down."
Presumably, when you tell people you're doing research in math they imagine you're multiplying long numbers all day.
Re: What do grad students in math do all day?
#44Earlier quoted context omitted.
You are just wrong. For example, algebraic topology is one of the most abstract subjects I hear conversations about week. It has applications in physics, data analysis, and numerical computing. Also, saying that reality is 4-dimensional is hooding yourself. The machine learning techniques we use everywhere depend on the math of higher-dimensional spaces, and they wouldn't work if reality couldn't be meaningfully view…
Please share a link to an example paper published by a pure math department.
http://arxiv.org/pdf/1303.2807.pdf
Went to the Arxiv into the Algebraic Topology category. Any comments?
Re: What do grad students in math do all day?
#45Yes, when as a math grad student I saw some of that, I developed some opinions and ideas to look for more productive approaches. Somewhere I read: "There is a famous recipe for rabbit stew that starts out, 'First catch a rabbit'.", and I changed that to, "There is a recipe for how to do applied mathematics, first get an application.". For more, commonly the main criteria for 'research' is that it be "new, correct, an…
Computer science isn't something that is becoming increasingly more mathematical, but quite the opposite way: computer science was seen as just another branch of mathematics. Alan Turing didn't quite have physical machines at his disposal to develop a theory of computation on, so he invented an abstract machine. Von Neumann thought that the foundational trouble in mathematics with Gödel meant that pure mathematics would soon be a sterile field, so he went on to design the Von Neumman architecture of computing machines we still basically use now. Read some Knuth or Dijkstra. They're mathematicians first, specifically, computer scientists.
It was only in the 80's or so that computer science started to be seen as its own thing instead of a branch of mathematics. It's around this time that university departments separate from the mathematics department started to be created.
When modern "CS" graduates come out of university thinking that an "algorithm" is some irrelevant theoretical tool that is only useful for implementing standard libraries of programming languages and forever forgotten, I weep a little.
Re: What do grad students in math do all day?
#46Funny stuff, and no doubt often accurate, but it wasn't my experience. I wanted to work in game theory, and there weren't an game theorists in the Harvard mathematics department; there were, however, in the business school. So I went over there, and Elon Kohlberg told me of an outstanding problem, and gave me a couple of papers to explain. I worked until I had a proof of the conjecture, and that was that, even though it had in fact been proved elsewhere (the Mertens-Neyman Theorem) a couple of months before I finished.
The whole thing took about a year, after which I stared my post-doc in public policy. After that, I became a stock analyst. After that, I tried some startups (not successfully). Then I became a self-employed industry analyst.
What could be more straightforward than that? :)
Re: What do grad students in math do all day?
#47> Fortunately, math has an incredibly powerful tool that helps bridge the gap. Namely, when we come up with concepts, we also come up with very explicit symbols and notation, along with logical rules for manipulating them. It's a bit like being handed the technical specifications and diagrams for building a vacuum cleaner out of parts. Just to play the devil's advocate ... math has wonderful symbols and methods, but…
> The consequences of the Incompleteness theorems are often overstated, but they do falsify the idea that mathematics is logically consistent, or that a set of symbols, however clear and unambiguous, will prevent basic misunderstandings in even the most fertile minds.
The incompleteness theorems don't falsify the idea that mathematics is logically consistent; they do falsify the idea that any reasonable mathematical theory could prove its own logical consistency.
They also don't remove the possibility that there is some metamathematical justification for an unambiguous interpretation of the concept of the natural numbers or even of a set (see all of the work in large cardinals, culminating in Hugh Woodin's recent work on extender models for supercompact cardinals).
Re: What do grad students in math do all day?
#48Earlier quoted context omitted.
You are just wrong. For example, algebraic topology is one of the most abstract subjects I hear conversations about week. It has applications in physics, data analysis, and numerical computing. Also, saying that reality is 4-dimensional is hooding yourself. The machine learning techniques we use everywhere depend on the math of higher-dimensional spaces, and they wouldn't work if reality couldn't be meaningfully view…
Please share a link to an example paper published by a pure math department.
Here's one I've been struggling with lately: Parallel coordinates representations of smooth hypersurfaces. I'm not aware of extensive reseach of the parallel coordinates geometry prior to 50 years ago.
Re: What do grad students in math do all day?
#49Yeah, if you're lucky enough to never have to teach, pass quals, take classes of your own, etc. In reality, research takes up less than 30% of your average day.
Re: What do grad students in math do all day?
#50The blog post certainly illustrates the importance of a good copywriter... "Tool to get rid of dust."
Tool not get rid of all dust, only dust tool can get to.