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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?

#41

Post by ttflee »

thearn4 wrote: post #8

I'm an applied mathematician (PhD) working partially in software development, partially in research mathematics and statistics proper. 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 pos…

> it's also unlikely that the few folks who can judge your work are in any position to fire you

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.

Re: What is it like to be a mathematician?

#42

Post by codezero »

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.)

You can also add ?share=1 to the end of any Quora URL to remove the overlay.

Re: What is it like to be a mathematician?

#43

Post by axitanull »

pmtarantino wrote: post #2

I did three years of Maths in University. Then, I swap to Computer Science because it was always 'my thing'. When I read this kind of posts I really miss Maths. It is beautiful. If you never tried, if your only experience is high school, go for it. Learn some Math. You will be happier.

Where can I start learning math on my own? I always thought math books are arcane in the sense that perquisites math knowledge for one book are so vast that I couldn't wrap my head around one.

Re: What is it like to be a mathematician?

#44

Post by cgag »

axitanull wrote: post #43
pmtarantino wrote: post #2

I did three years of Maths in University. Then, I swap to Computer Science because it was always 'my thing'. When I read this kind of posts I really miss Maths. It is beautiful. If you never tried, if your only experience is high school, go for it. Learn some Math. You will be happier.

Where can I start learning math on my own? I always thought math books are arcane in the sense that perquisites math knowledge for one book are so vast that I couldn't wrap my head around one.

What math do you know, what math do you want to know?

Re: What is it like to be a mathematician?

#45

Post by ivansavz »

> When, later on in life, the subject of mathematics comes up, most people wave their hands and say, "Oh no, I don't want to hear about this, I was so bad at math."

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
Because of this reasoning, "math haters" start to feel bad about themselves and thus prefer to avoid this subject of conversation. I guess we could call this a math complex.

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...

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!

Re: What is it like to be a mathematician?

#46

Post by trobertson »

axitanull wrote: post #43
pmtarantino wrote: post #2

I did three years of Maths in University. Then, I swap to Computer Science because it was always 'my thing'. When I read this kind of posts I really miss Maths. It is beautiful. If you never tried, if your only experience is high school, go for it. Learn some Math. You will be happier.

Where can I start learning math on my own? I always thought math books are arcane in the sense that perquisites math knowledge for one book are so vast that I couldn't wrap my head around one.

I would recommend 'Concepts of Modern Mathematics' [1], by Ian Stewart. It has some very nice illustrations and humor, and reminds me of 'Learn You A Haskell For Great Good' (though I believe CoMM came out before LYaH). It's a wonderful preview of a variety of topics, and is intended to introduce someone with a poor math background to some of the different fields of math.

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.

---

[1]: http://www.amazon.com/Concepts-Modern-Mathematics-Dover-Book...

Re: What is it like to be a mathematician?

#47

Post by joe_the_user »

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…

Ah,

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.

Re: What is it like to be a mathematician?

#48

Post by wellboy »

pmtarantino wrote: post #2

I did three years of Maths in University. Then, I swap to Computer Science because it was always 'my thing'. When I read this kind of posts I really miss Maths. It is beautiful. If you never tried, if your only experience is high school, go for it. Learn some Math. You will be happier.

Math is somehow what intrigued me most during university. After my startup endeavours, I want to make my mark in Physics and Maths, because I think once you have mastered earth and humans(with a startup), it is time to take on the universe (Maths & Physics)

Re: What is it like to be a mathematician?

#49

Post by axitanull »

cgag wrote: post #44
axitanull wrote: post #43

Earlier quoted context omitted.

Where can I start learning math on my own? I always thought math books are arcane in the sense that perquisites math knowledge for one book are so vast that I couldn't wrap my head around one.

What math do you know, what math do you want to know?

When I did Project Euler, I couldn't come up with elegant solution that was derived from high enough abstraction using math, leaving me using brute force method that was not really efficient.

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.

Re: What is it like to be a mathematician?

#50

Post by Perseids »

ced wrote: post #34
Perseids wrote: post #31

Earlier quoted context omitted.

> 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?

I just stated the definition of having one and only one solution, yes :). That was kind of the point I was making.

I originally intended to write a statement specific to ODE, but was then to lazy to look the specifics up ^^.

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