Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

What is it like to be a mathematician?

slate.com

Post reply on HN
Print view View original

21–30 of 53 posts

Re: What is it like to be a mathematician?

#21

Post by nephorider »

ska wrote: post #16
adrianlmm wrote: post #7

Same as to be a biologist, or a programmer or a doctor.

Not in my experience. I've worked both as a research mathematician and as a programmer working on production software. Even applied to the "same" types of problems, I've found them to be very different in day to day activities, goals, incentives ... really they are quite far apart.

Certainly not the same, but I do believe that when a computer model is having some kind of math root, it gets its own coherency and can be developed further. By math root it does not imply a math model. but the idea of creating a set of object with given rules and behaviors like for example a vectorial space. Very often it starts with real "computer tries" but the best part are always when there is an underlying model. I tend even to believe that the level of math knowledge in modern programming has grown up in regards to 15 years ago.

Re: What is it like to be a mathematician?

#23

Post by fvirexi »

joe_the_user wrote: post #18
logicallee wrote: post #5

When you're a mathematician, everything is black or white, but you get to define what those two words mean.

I think that's another misunderstood thing about math. By the time you get into higher mathematics, you get to a place where nearly everything is unknown. I remember reaching the level of ordinary differential equations and realizing that "most" non-linear equations had no exact solution at all. In ways, math and programming have this in common - as the size of the systems being studied increases, a randomly chosen e…

I read logicalee's comment as a reference to the way most (all?) branches of mathematics may be built using sets and their axioms. Set theory boils down to "in the set" and "not in the set", ie. black and white.

Re: What is it like to be a mathematician?

#24

Post by joe_the_user »

fvirexi wrote: post #23
joe_the_user wrote: post #18

Earlier quoted context omitted.

I think that's another misunderstood thing about math. By the time you get into higher mathematics, you get to a place where nearly everything is unknown. I remember reaching the level of ordinary differential equations and realizing that "most" non-linear equations had no exact solution at all. In ways, math and programming have this in common - as the size of the systems being studied increases, a randomly chosen e…

I read logicalee's comment as a reference to the way most (all?) branches of mathematics may be built using sets and their axioms. Set theory boils down to "in the set" and "not in the set", ie. black and white.

Ah but the real story is that like sophisticated math systems, in relation to any fixed axiomization, set theory involves provably, provably false and unprovable/independent statements. And in relation to any fixed model, set theory involves true and provable, true but unprovable, false but un-disprovable and false and disprovable.

And when you're math as a human endeavor, you can also add "provable but not yet proven" and "proven independent"

So, learn some stuff, see how far from black and white higher math can be.

Re: What is it like to be a mathematician?

#25

Post by thearn4 »

ska wrote: post #16
adrianlmm wrote: post #7

Same as to be a biologist, or a programmer or a doctor.

Not in my experience. I've worked both as a research mathematician and as a programmer working on production software. Even applied to the "same" types of problems, I've found them to be very different in day to day activities, goals, incentives ... really they are quite far apart.

I'd have to concur. I highly value both kinds of experience, for this diversity actually.

Re: What is it like to be a mathematician?

#26

Post by icecreampain »

The article mentions how most of us are introducted to math and the reaction most of us have to math in later life: "Oh no, I don't want to hear about this, I was so bad at math." The article continues about how wonderful math is and what not.

The article is wasting our time.

Those of us who were force-fed useless mathematics since 1st grade have already closed our minds completely to any attempts at beautifying something that we normal people, after +-/, see as completely fucking useless, boring and hate-inducing. At least I feel that way, but I assume I'm not alone.

I was force fed not only simple +-/ but several university level courses. Why? Because I wanted to get myself a programming degree and for that one, somehow, needed a whole bunch of weird-ass algebra and shit. I could see no reason for learning that at 15, when I was writing Pascal and PCBoard PPEs, no reason for learning that at 20 when I was writing C/C++ shit and no reason now at 30+ when I'm writing webapps in PHP/js/html5/etc. But time and time again I was told that without that complicated mathematics I wouldn't become shit.

Well, now I'm making a living programming, without a degree, and without being able to derive x2 from god-knows-what. My mind has PROVEN to me that I don't need complicated math and therefore cemented my previously belief that advanced math is necessary to program.

Not once during all my years of school and university was I ever shown a use for that advanced math, even though I _begged_ for at least some connection to reality, some proof that the math is going to be useful for anything else other than passing an exam. Do my SQL queries speed up if I use cosine? Will my code autoindent properly if the square root of x^y is used? No. Instead I was told to just learn it because I'd use it "some day".

My brain is now completely, 100% closed to advanced math. So what this Edward guy in the article should do is not try to change our minds, or even change the minds of the kids of today that are being force-fed math. Instead he should concentrate his efforts on bringing the teachers (and curriculum) down to earth. Change the way math is taught. Bring in real-world examples of why derivations are somehow important. After that is done then the NEXT generation won't fucking hate math, and mathematicians, as much as use older folk do.

Fuck I hate math.

Re: What is it like to be a mathematician?

#27

Post by jfthiigsegbje »

icecreampain wrote: post #26

The article mentions how most of us are introducted to math and the reaction most of us have to math in later life: "Oh no, I don't want to hear about this, I was so bad at math." The article continues about how wonderful math is and what not. The article is wasting our time. Those of us who were force-fed useless mathematics since 1st grade have already closed our minds completely to any attempts at beautifying some…

You've got a list of stores, and a person's location. Which store is closest?

You are buying ads online, and want to maximize your ROI.

You have 6 types of EC2 nodes you can use, and you want to pick the most efficient set for your mildly parallel work.

Re: What is it like to be a mathematician?

#28

Post by Perseids »

fvirexi wrote: post #23
joe_the_user wrote: post #18

Earlier quoted context omitted.

I think that's another misunderstood thing about math. By the time you get into higher mathematics, you get to a place where nearly everything is unknown. I remember reaching the level of ordinary differential equations and realizing that "most" non-linear equations had no exact solution at all. In ways, math and programming have this in common - as the size of the systems being studied increases, a randomly chosen e…

I read logicalee's comment as a reference to the way most (all?) branches of mathematics may be built using sets and their axioms. Set theory boils down to "in the set" and "not in the set", ie. black and white.

Quite interestingly, the axioms mathematics is build upon do not let you decide every question that you might come up with. As such in mathematics not everything is black or white. For example, the continuum hypothesis is independent of the most commonly used axiom system ZFC. To explain what that means imagine ZFC would be describing an apple. Out of the definition of "apple" you can get theorems that tell you "if you start on any point of the apple and dig down in a straight line, at some future point in time you will reach the 'other side' of the apple" or some statements you can disprove "if you walk on the surface of the apple in a straight you will never come back to point where you started". What you will not get is the colour of the apple. Everything you know about the apple is consistent with it being green. But all that is also consistent with it being red. The colour of the apple is independent of everything that you are interested in in an apple. Therefore there is no reasonable answer to the question "which colour does the apple have", except maybe: It should not matter. The same is true of the continuum hypothesis. I remember reading that if you need the CH to prove something, then you should definitely reconsider the statement you are trying to prove :).

Re: What is it like to be a mathematician?

#29

Post by billforsternz »

icecreampain wrote: post #26

The article mentions how most of us are introducted to math and the reaction most of us have to math in later life: "Oh no, I don't want to hear about this, I was so bad at math." The article continues about how wonderful math is and what not. The article is wasting our time. Those of us who were force-fed useless mathematics since 1st grade have already closed our minds completely to any attempts at beautifying some…

That's pretty sad. Programming and mathematics are normally things that go together, like burgers and beer. I can't imagine loving one and not the other. I do sympathise with the wish to see a practical application. I have a distinct recollection of an ah-ha moment for me, at about 15 years of age. We were being taught basic calculus. The idea was introduced that a function f(x) could be used to represent the yield of some industrial process. You put in x, you get out y = f(x). So far, so obvious, so boring right? But then came the cute part; If you can calculate the derivative of f(x), you get another function f'(x) which is the slope of f(x) for any value of x. Then to find the maximum yield you seek the value of x where f'(x) = 0, because the slope of f(x) will be zero 'at the top of the hill'.

I guess it's a personal thing, but for me this fired my enthusiasm for both learning the various techniques for differentiation, and for equation solving. Then integration followed as simply reverse differentiation [amazing - one is the area under the graph - one is the slope of the graph - why should they be opposite ? Because maths is beautiful is the short answer - a universe of discovery is the long answer]. Around this point maths became fun, the work part evaporated. Later I got interested in computation because you can't always differentiate or solve equations analytically (with pure math), but you can do it numerically, to any desired degree of accuracy with a computer.

Re: What is it like to be a mathematician?

#30

Post by Strilanc »

michael_nielsen wrote: post #13

On a related note, there's a good in-depth answer to the question "What is it like to understand advanced mathematics?" here: http://www.quora.com/Mathematics/What-is-it-like-to-understa... I'm not a mathematician, but was a theoretical physicist for more than a decade, and the Quora article accords well with my experience in understanding mathematics. (Fairly) readable examples of some of the points made in the abov…

That is definitely good and in-depth.

(I had to use the web dev inspector to remove the overlay trying to force me to enable scripts and sign in, but it was worth it.)

Post reply on HN