Good programmer = Bad mathematician

[Alphabit]

This is something I've been thinking about for a while and it occurred to me that I don't know anyone who is both good at math and programming (and I know a lot of good and bad programmers).

At uni, I know this guy who switched out of software engineering to do a bachelor of maths because he kept getting excellent results in his maths subjects but kept failing his programming courses. (and he put more work into programming than math)

I'm not saying that it's true for everyone, but I think that there is a definite tendency for people who are good at Math to be crap programmers and vice-versa.
I think it has something to do with intuition. Math requires a lot of intuition, while programming requires that you have no intuition.

Here's my theory on the subject:
When you're programming, it's very important to be fully aware of your assumptions and possible alternatives at any given time; so if you have a bug, you know the weaknesses in your program and you can go and fix them fairly quickly (because you have an idea of where to look).
In math, if you try to keep track of all the assumptions that you make all the time (and the alternatives that you didn't use), then you end up with information overload and ultimately you just lose your train of thought.

What do you think?
Is anyone here both good at math and good at programming?

I'm a very average math students, I get decent results, but I seriously struggle... Exams are like brain torture; when I come out of that exam room, I feel like I've been through electroshock therapy.

[adam2510]

yea i find this to be true but the thing is there are certain aspects of programming where you do need maths

i hate maths but i understand programming very well

[Cinjection]

I'm not sure I agree. I know plenty of people who are very good at both. At the lowest level, both math and computer science are often simply about solving problems. They are both fundamentally rooted in logic and abstraction.

I think that the reason mathematicians struggle with computer science is that they are not comfortable with "baby feeding" a computer with very precise, formatted instructions. This, of course, takes a while to get used to for anyone. I find that most mathematicians don't have a problem developing algorithms, but with actually implementing them with finicky programming languages. The problem is not with fundamental "mental blocks", but with practice.

The kind of computer problem is also significant here. Mathematicians will probably find it much simpler to devise an elegant, recursive solution to some computer science problem, than to create a software system. That is, computer science is much closer to it's mathematical roots than software engineering.

[d2312564]

Not sure if it's true or not, but add me to the list of programmers that are terrible at math.

[dELtaluca]

Given that I'm on a straight to masters course in joint mathematics and computer science at a top uni, I can't say I agree too much :P

I also don't have time, but i certainly don't agree with you alphabit in saying programmers don't need any intuition :P Proper programmers anyway, script kiddies using code snipped around to build a drag and drop game (extreme example) certainly don't lol.

[henke37]

Given how bad I seem to be at practical math, I have to agree with the theory, but I am not sure about the explanation.

[CronoMan]

I think programming requires a different method of abstract thought

[GustTheASGuy]

Expanding on what Cinjection said, software engineering and computer science are different disciplines. The latter is close to mathematics, both academia.
The other is all coffee drinkers that punch their computers until shit kind of works, and then it's marketed. Those might not necessarily be good at math then.

[Cinjection]

At 11/13/09 02:12 AM, Peaceblossom wrote: Math seems much more linear, where programming can be done in pieces, inside out, backwards, etc and still get the correct result. I find that I'm terrible at math but I'm fully able to implement the problem solving required in programming.

I definitely don't think math can be considered linear. Almost all advanced mathematics involves thinking out of the box. For example, consider Graph Theory and Combinatorics (I mention them only because I have a midterm in a couple days on that subject :S). The proofs we do in these subjects are far from linear and require a lot of creativity to solve.

I think it helps to mention that even software engineering has a math core as well. After all, software engineers are computer scientists too. For instance, consider time-complexity analysis. O notation is a fundamentally mathematical idea, and understanding it certainly helps analyze complicated code. Unfortunately, I think a lot of programmers forget this and just remember things like O(n) is better than O(n^2).

[Super-Yombario]

How ironic; I had this conversation with my dad yesterday. I'm not very good at math, but as far as programming I can do almost exactly what I do in my math class, just with a different approach.

[Benny-Creations]

Sounds pretty accurate to me. I very nearly failed maths at A levels, yet I scored top marks in Computing and other IT related subjects. Truth be told it's not hard for me to pick up a new language and get a basic understanding of it within a few days - but mathematical functions have just never made sense to me...

B_C

[RyanPridgeon]

I disagree. Straight A's in Maths and Computing.

I know many others who are good at both too.

[DanielZ]

Add me to the very long list of people who suck both at math and at programming.

[Cinjection]

Another such exert:
"MATH 137 Calculus 1 for Honours Mathematics
MATH 138 Calculus 2 for Honours Mathematics
MATH 135 Algebra for Honours Mathematics
MATH 136 Linear Algebra 1 for Honours Mathematics
MATH 239 Introduction to Combinatorics
STAT 230 Probability
STAT 231 Statistics"

These are the math requirements for a B.CS from the University of Waterloo.
source.

[ZJ]

Well, that's a relief to me. I've never been much of a math man.

[Alphabit]

At 11/13/09 03:00 AM, dELtaluca wrote: Given that I'm on a straight to masters course in joint mathematics and computer science at a top uni, I can't say I agree too much :P

Yeah but you're a freak of nature ;p

I also don't have time, but i certainly don't agree with you alphabit in saying programmers don't need any intuition :P Proper programmers anyway, script kiddies using code snipped around to build a drag and drop game (extreme example) certainly don't lol.

I guess I do need intuition for some aspects of programming (especially on the architectural side) but it feels really different from mathematical intuition... It's strange but with math; the less I think about what I'm doing (in the immediate sense / small picture), the better the outcome - while doing proof by induction, I find that if I try to think about the process too much, I tend to lose track of the purpose of what I'm doing and I mess everything up.

I think that my worst math blunder was in an exam one time I had to find a solution to an equation involving complex numbers and I ended up proving that 361 = 36i (which is obviously both wrong and off-topic; I actually giggled out loud when it happened; people probably thought I was a complete math freak). Also, if I don't get enough sleep, that messes me up big time.

[Alphabit]

At 11/13/09 06:51 AM, GustTheASGuy wrote: Expanding on what Cinjection said, software engineering and computer science are different disciplines. The latter is close to mathematics, both academia.
The other is all coffee drinkers that punch their computers until shit kind of works, and then it's marketed. Those might not necessarily be good at math then.

I agree that computer science is closer to mathematics. At my university, computer science has a lot more math, but software engineering is more focused on software architecture and 'planning'. The way I see it; computer scientists are better when it comes to making efficient algorithms, but software engineers are better when it comes to producing large-scale programs that are functional and maintainable (they are good at putting the little pieces together).

[kiwi-kiwi]

I think it has to do with your area of interest. Personally I tend to believe that if you don't really need math in your activity, then you're probably gonna suck at it.

However I also think that it's important for programmers to have some mathematical knowledge, stuff like trigonometry, integrals and derivatives, basic geometry (Pythagoras theorem, polar coordinates, stuff like that), maybe some linear algebra too if you have to work with matrices.
That's because some problems have a simple mathematical solution that is usually easier and sometimes better than a more intuitive algorithm (The only thing that comes to mind right now is population dynamics)

[daniel-mcl]

This is total nonsense. ALL the guys who developed computers in the first place -- Turing, von Neumann, Aiken, Knuth, Hopper, Church, Ackermann, etc. were mathematicians and/or mathematical physicists by training, mainly employed as math professors, and all of them published significant mathematical work unrelated to their work with computers.

If your idea of a computer programmer is some guy who sits around and writes little utilities or whatever, then sure, maybe they're not great at math. But I guarantee you that there's nobody working for Google who'd have any trouble at all earning a Ph.D. in math (if they haven't got one already).

Your problem might be that you think math is closely related to the sorts of things that are done in e.g. your high school calculus classes, where you are given an algorithm to solve a particular type of problem and you are expected to memorize it. That's kind of like saying that the best surgeon is the guy who memorized the list of body parts the fastest in fifth grade -- there's really minimal correlation.

Mathematics is the study of problems where we know all the ground rules, as opposed to, say, science, where we're trying to figure out what the rules are. As a result, all computer problems are essentially mathematical in nature (or at least they should be, though it seems like professional programmers spend a lot of time trying to figure out why all the undocumented components don't work the way they expect.)

[FireSickle]

you guys make some awesome points

In my opinion math and programming are both logical in their roots. They both require a separate set of unique knowledge, and in some ways "syntax".

I am both good at math and programming. I only took up to Calc 2 in college, but I breezed through it. I haven't really applied my math knowledge since college, but I've been programming daily for several years now. I consider myself good at math, but I always have to take a 10 minute brush up with cheat sheets first if I'm doing something beyond simple math.

Being good at math, and being good at programming are about learning rules that build on top of each other, but they are different rules... just because you like one doesn't make you like the other, i happened to like math first ;)

[Rucklo]

At 11/13/09 05:02 AM, CronoMan wrote: I think programming requires a different method of abstract thought

that it does, but i would like to suggest that one of the biggest differences between maths and programming is the language itself.
what i mean is that there are tons of notations and terms in both maths and programming that have very distinct meanings. knowing one doesn't mean you know the other.

however, when it comes to the actual "thinking", they're both abstract in different ways, like you say.
I'm personally not very good at either one. when i was younger my abstract thinking was alot better overall, was pretty good at maths at school, and the very little programming i tried out seemed perfectley clear and logic to me. most got lost after school, pretty weird how the brain seemed to just crumble and fade away like that... as i'm in school now i try to pick both things up, but it's a slow process, and im not very good at studying at home.

a friend and old classmate of mine is a programmer since birth (more or less), and very good at maths too. so if the OP made a survey of some sort, he's another exception :=)

dunno if anyone here ever used matlab? that's the playground where maths and programming meet and duke it out. ^____^

[kiwi-kiwi]

At 11/23/09 11:24 AM, Rucklo wrote:

dunno if anyone here ever used matlab? that's the playground where maths and programming meet and duke it out. ^____^

I did, matlab is fun :D.
Also algorithm analysis