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What is it like to be a mathematician?

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Re: What is it like to be a mathematician?

#31

Post by Perseids »

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 remember reaching the level of ordinary differential equations and realizing that "most" non-linear equations had no exact solution at all.

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 :).

Re: What is it like to be a mathematician?

#32

Post by anonymous »

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…

See that https in your browser bar right now? You can thank math for that.

Re: What is it like to be a mathematician?

#33

Post by Perseids »

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…

As a more advanced examples take a look at perfect hashing. Without some randomization an attacker can produce collisions for any fast hash functions and thus degrade your hash table to the worst case possible. This was a real DoS attack vector in real web applications (see for example https://mail.python.org/pipermail/python-dev/2011-December/1... ). With a little advanced math this matter is trivial to solve.

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.

Re: What is it like to be a mathematician?

#34

Post by ced »

Perseids wrote: post #31
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 remember reaching the level of ordinary differential equations and realizing that "most" non-linear equations had no exact solution at all. 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…

every ODE that has one and only one solution has an exact solution

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?

Re: What is it like to be a mathematician?

#35

Post by DoublePlusWill »

Strilanc wrote: post #30
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.)

There's a link on that overlay to "close and continue reading" if you get out your microscope. ;)

Re: What is it like to be a mathematician?

#36

Post by pbhjpbhj »

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…

When I was 17, high school, and really enjoying maths a maths professor came to our school to speak to a few of us about continuing maths at University. She really annoyed me. She asked what about maths we liked and a friend and I answered that it was the certainty - that things were right or wrong and you could most often tell plainly which they were.

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.

Re: What is it like to be a mathematician?

#37

Post by slurry »

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…

From the examples in your post, it seems like you only got to calculus. Which is not really advanced math.

Re: What is it like to be a mathematician?

#38

Post by auvrw »

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…

> The article is wasting our time.

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.

Re: What is it like to be a mathematician?

#39

Post by gizmo686 »

Perseids wrote: post #28
fvirexi wrote: post #23

Earlier quoted context omitted.

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…

> I remember reading that if you need the CH to prove something, then you should definitely reconsider the statement you are trying to prove

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.

Re: What is it like to be a mathematician?

#40

Post by rjdagost »

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…

Software is a very broad field and you are painting with a very broad brush. It is true that for many branches of software you do not need much in the way of advanced mathematics. But EVERY graphics programmer I have ever met has told me he wishes he had paid more attention in higher level math courses. The same holds true for folks doing signal and image processing, computer vision, artificial intelligence, and on and on...
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