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I actually do agree that math isn't necessary for many types of software development. This is one of the reasons I'm angling to get more into data science - I
by geebee 13y ago
I actually do agree that math isn't necessary for many types of software development. This is one of the reasons I'm angling to get more into data science - I was a math major, and I'd actually like to be doing more math. I would also tend to agree that studying math can sharpen your mind in a way that would help for programming, but you could say that about a lot of mentally challenging fields.
It is, of course, possible to agree with a conclusion while disagreeing with the reasoning behind it. I completely disagree with a couple of statements here. Again, this is probably because as a math major (and as a short-lived doctoral student in an engineering department that was heavy on proof based math theory around optimization and stochastic processes), I've experienced "math" very differently from most people, including engineering or science students who have done a substantial amount of math (say, the calculus sequence through differential equations).
Math (I'm talking about the US based university approach) changes dramatically once you get to "upper division" coursework. Real Analysis is very, very different from the differential equations course that is about one-fifth math majors and four fifths engineering or hard science majors. There's very little "applying an equation" going on. And the notion that there is "one answer" is remarkably incorrect (I suppose it's correct if you define "TRUE" as the one correct answer to fermat's last theorem, but there are often so many different correct ways to go about a proof).
I remember a story about Graham Nash (the Nash equilibrium guy - this is all from memory based on his biography, so I may have some of the details wrong). Nash proved a very difficult and elusive theorem early in his career. It was later discovered that a different mathematician had completed a proof for the same theorem a short time earlier (I think it was a few months). Nash was apparently very depressed by this. However, he shouldn't have been - the other proof was by contradiction, whereas Nash's proof was more direct and contained the structure for an algorithm, and would probably be more influential.
This isn't at all unusual in math. There are a huge number of different angles on a problem.
Part of the problem here is what is meant by "math"... it is a shame that someone could get as far as second year university math in the US and still see it as a field where you simplify things to the point where you can apply a formula to arrive at the one right answer. In Ross Hunter's defense, he didn't say that's all that math is, he said "People who are good at math are good at breaking problems down into parts, recognizing patterns, and applying known formulae to those parts to arrive at the one right answer."
But you know, people who are good at math do far, far more than that. I know, because oh my god math got harder after the standard "calc through diff eq" sequence.
- scelerat 13y ago> Graham Nash the Nash equilibrium guy John Forbes Nash, Jr. is the math guy. Graham Nash was the lead singer of the Hollies and a member of Crosby, Stills, Nash and Young. Both of these guys' work is worth checking out.
- jackmaney 13y agoKing Graham was the guy in the King's Quest games. I think we now need a PC adventure game where the main character is a musician king who discovers new mathematical ideas and then goes horribly insane.
- geebee 13y agoOops, sorry! But eh, too late for an edit, I'll leave it up now. Agree with you about Graham Nash, also worth checking out ;)
- mrbrowning 13y ago> Part of the problem here is what is meant by "math"... it is a shame that someone could get as far as second year university math in the US and still see it as a field where you simplify things to the point where you can apply a formula to arrive at the one right answer. In Ross Hunter's defense, he didn't say that's all that math is, he said "People who are good at math are good at breaking problems down into parts, recognizing patterns, and applying known formulae to those parts to arrive at the one right answer." I think it's reasonable to assume, given what he stated, that Ross does in fact conceive of math that way. It blows my mind that one can get through a discrete math class and still think of math as basically computational in nature, since as far as I know most curricula treat the course as an opportunity to introduce the sort of concepts that typically figure into an introduction-to-higher-mathematics-type course, such as proof techniques, basic number theory, and so on.
- jackmaney 13y ago(Disclosure: I taught college mathematics courses (almost entirely from the calculus sequence on up) for one semester as an undergrad, 4.5 years in grad school, and 4 more years as an assistant professor.) > Math (I'm talking about the US based university approach) changes dramatically once you get to "upper division" coursework. It's not just a dramatic change; for most, it's a cliff thrown in the middle of the learning curve. There are many reasons for it: some high schools passing students along when they shouldn't, some professors doing the same thing when students get to college, and the ever-so-fetishized focus on applications over concepts. In short, it's a cultural problem. And at this point, I have no idea how--or if--it can be resolved.