What is it like to be a mathematician?
slate.com
slate.com
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 above article may be found in Terry Tao and Scott Aaronson's comments about how to think intuitively in high dimensions:
http://mathoverflow.net/questions/25983/intuitive-crutches-f...
(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.)
A mathematician is someone who works on things that honestly very few folks can understand completely (not due to complexity per se, just depth and lack of general familiarity). Publication peer-review aside, it's also unlikely that the few folks who can judge your work are in any position to fire you. It's a rewarding and pretty secure gig.
But I still think that the most interesting work is very multidisciplinary in nature, so a CS, engineering or physical sciences background really does enhance the work you can do. Like in any other career, don't let yourself become a one-trick pony.
But in the other hand, it means those who can judge your work are not in the same position to hire you, and it is not ruled out that people in position to fire you has to understand your work in order to do so.
If you never tried, if your only experience is high school, go for it. Learn some Math. You will be happier.
To each his/her preference. I like both.
From the Amazon description:
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and other subjects. No advanced mathematical background is needed to follow thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, and more. 200 illustrations.
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[1]: http://www.amazon.com/Concepts-Modern-Mathematics-Dover-Book...
I was fascinated by how people come up with elegant math solution for the challenges in Project Euler. I am not sure how I can achieve such elegance, proving my math is insufficient for what can be done.
I've noticed this happening a lot. It is interesting that nobody says that about the other two Rs: reading and writing. Have you ever heard anyone say "I don't like books and reading in general"?
As far as I can tell this is the reasoning used by most "math haters"
Kids who are smart are good at math
I was not good at math
Therefore I am not smart
The first fault with this reasoning is the premise---there are plenty of smart kids who are simply not drawn to math, especially since math is often presented as memorization and not understanding. So whether you liked math in high school or not has almost no bearing on how good you are at math. Chill.
The other fault with the reasoning is that of time-invariance. Math was "tough" for me when I was 8 years old, so it will still be tough for me even though I am an adult now. It takes some level of humbleness to go back to learning something that "kids should know," but it is totally worth doing. Whether you are a coder, an english major, or a designer, learning a bit of math will give you a lot of extra power to do whatever you do already, and other stuff. For example, learning math will suddenly make half a million more wikipedia pages accessible to you (all the ones with lots of equation blocks). That is a lot of knowledge, and knowledge is power...
<plug>What if there was a high school math textbook written for adults? A textbook with no BS, which gets directly to the power part right away. What if learning high school math opened the door for you to learn differential calculus (lim,ƒ'(x),max), and integral calculus (∫ƒdx,∑a_i) in the same sitting. Then knowing calculus, you would be able to pick up mechanics (F=ma, a(t)=x''(t), p=mv, ∑Ei=∑Ef, Acos(ωt+ϕ)) quite easily too. All of this in just 383 pages that you can read four weeks if properly caffeinated!</plug>
Well, I have heard engineery types saying they don't see the point of reading fiction ("it's just made up stories"), and more frequently have heard them disparaging subjects like philosophy and history. Maybe that's the equivalent response?
http://www.newcriterion.com/articles.cfm/The-Fifth-problem--...
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 example becomes harder and harder to deal and thus the "art" consists in choosing important and tractable examples out of a world of huge but intractable systems.
She of course responded that we couldn't be more wrong.
Annoyed the hell out of me until I came across Godel and began to understand maths from a different perspective.
Wish I'd had chance to study under that professor.
This may be a bit theoretical for most readers, but every ODE that has one and only one solution has an exact solution. That the best definition for that function is "the solution to that ODE" does not mean that the function is any less exact than something you can construct out of exp, sin, cos, etc. In fact it would be completely reasonable to define exp as a solution to a differential equation and then to prove afterwards, that exp is equivalent to the usual power series and accidentally also has some other nice properties :).
I spoke too loosely. I should have written "closed-form symbolic solution" rather than "exact solution" (though "exact" is used colloquially to mean this, it's not clear). Yes, all solutions to an ode would be "exact solutions" in the literal sense.
It is worth noting also that an ode having a solution around a point doesn't imply that it can be extended indefinitely - you can hit "singularities" that make extension impossible.
Upvoted, but - is that a particular theorem, or are you just basically stating the definition of "having a solution"? Wouldn't your statement be true of any system of differential equations, not just ODEs?
I originally intended to write a statement specific to ODE, but was then to lazy to look the specifics up ^^.
This is not entirely true. There are many proofs that begin by assuming CH. There are also two ways of interpreting "need CH to prove". One way is that the thing you are trying to prove is equivalent to CH, which is an interesting/useful result. Another way to interpret it is that you can not come up with another way of proving it. In the latter case, the CH based proof justifies that your proposition is not inconsistent, and may even lead you (or others) to proof that it is true regardless of CH. If I recall correctly some statements have been proved by proving the statement when CH is true, and also when CH is false.
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.
On one tangents....
I think we mathematicians are a little bit behind the curve. We are not fully aware of the Frankenstein that we may have already created or could create. I think that's another aspect of this responsibility of mathematicians to take a more public role—to educate the public by giving them access to the beauty and power of mathematics.
Interesting tie in to the importance of ethics for mathematics. It's not just a bunch of folks writing proofs about numbers in journals.
In research it was usual to go for a few months without any relevant feelings of success (and not just me, many of my colleagues felt the same). In programming I usually get some positive feedback a few times a day, at the very least every few days.
That's a huge difference.
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.
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.
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.
indeed. here's a better link:
http://en.wikipedia.org/wiki/Langlands_program
> Fuck I hate math.
this is the only other sentence of your post i had time for, and all i have time to say in response is that i don't.
Something else I remember was a computer graphics professor saying that the fast fourier transform was the greatest invention after the wheel.
Generally speaking you can find programming jobs where you need basically no understanding of mathematics. But computational engineering science is so much more than programming. Conversely often enough the abstract thinking that is the core of mathematics can greatly help you to tackle the more complex problems you can encounter in programming.
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.