
What is it like to be a mathematician? - ColinWright
http://www.slate.com/articles/health_and_science/new_scientist/2013/10/edward_frenkel_on_love_and_math_what_is_it_like_to_be_a_mathematician.html
======
michael_nielsen
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...](http://www.quora.com/Mathematics/What-is-it-like-to-understand-
advanced-mathematics/answers/873950)

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...](http://mathoverflow.net/questions/25983/intuitive-crutches-for-
higher-dimensional-thinking)

~~~
Strilanc
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.)

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

~~~
broken_symlink
For me that only shows the top answer.

------
thearn4
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 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.

~~~
pmiller2
My advisor in grad school put it this way: being a mathematician basically
amounts to being the world's leading expert on something only about 5 people
give a shit about.

------
pmtarantino
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.

~~~
axitanull
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.

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

~~~
axitanull
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.

------
ivan_ah
> 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...

<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>

~~~
benpbenp
> Have you ever heard anyone say "I don't like books and reading in general"?

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?

------
revelation
From Edward Frankel also comes this wonderful excerpt on antisemitism in
Russian higher education (that doesn't sound exciting now, but you'll like the
article):

[http://www.newcriterion.com/articles.cfm/The-Fifth-
problem--...](http://www.newcriterion.com/articles.cfm/The-Fifth-problem--math
---anti-Semitism-in-the-Soviet-Union-7446)

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

~~~
joe_the_user
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 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.

~~~
Perseids
> 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 :).

~~~
ced
_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?

~~~
Perseids
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 ^^.

------
mathattack
Great article. I think we lose the forrest and trees in math. Similar in
computer science. Many times we get hung up on language syntax to miss the
beauty underneath. (For example: Godel's incompleteness theorum or the
implications of Turing machines)

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.

------
mrcactu5
Ed Frenkel made a film to convey the beauty of math - some nudity.
[http://www.imdb.com/title/tt1530994/](http://www.imdb.com/title/tt1530994/)

~~~
dominotw
I am big fan of Ed Frenkel's lectures on youtube but this movie was one of the
worst movies I've ever watched.

------
pmiller2
I'd like to add a little to the puzzle analogy. Not only is doing research
like putting together a puzzle without an idea what the picture is, but the
puzzle is irregularly shaped.

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

~~~
ska
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.

~~~
nephorider
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.

------
joshlegs
i'm pretty sure that title should be "mathemagician", cuz that shit is freakin
mysterious

------
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.

~~~
billforsternz
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.

