
How to Learn Advanced Mathematics Without Heading to University – Part 3 - shogunmike
https://www.quantstart.com/articles/How-to-Learn-Advanced-Mathematics-Without-Heading-to-University-Part-3
======
lumberjack
This is stupid. The hard part about a Math degree is the number of hours you
have to put in. If you cannot go to university full time, go part time. If you
cannot go part time, you don't have enough time to actually learn any of these
topics on your own.

I've done these classes. It's typically 150 hours per class and it's not
something you do after coming exhausted home from work either. After those 150
hours you'll get a basic understanding of the topic. You won't be an expert by
any means. That will require more exposure, more time.

The lectures themselves are not that useful, I find. The lecturers are mostly
useful in guiding you along, telling you which aspects of the theory to focus
on and weeding through the study material to deliver you the best bits. The
problem sets are indispensable. Exams make sure you actually know the basics
in depth instead of just knowing about them.

My advice: enrol part-time, take one class at a time, catch up on the lectures
and do the problem sets and the homework over the weekend.

~~~
svanderbleek
I hope it is not stupid. I won't fit inside the university system at this
point. They would make me take courses on subjects I already know which is a
waste. I have about 20 hours on the weekend I can use towards accomplishing a
class and I will have minimal waste since my curriculum is tailored directly
for me. Of course it is only because I already wasted a decade learning math
poorly that I know what I want to know and what I need to know to know it ;)

~~~
whorleater
Prerequisites for classes are oftentimes a suggestion, you can easily get into
a class you don't meet the prerequisites for by simply signing up for the
class (most class registration systems don't bar this), or by emailing the
professor and getting an override. Furthermore, if you're a non-degree seeking
student, the university cares very little about you, so you can skate by with
a lot more freedom with classes.

~~~
Roodgorf
> most class registration systems don't bar this

Interesting, anecdotally, I went to three different universities and they all
barred this from happening without an explicit override from a professor or
occasionally an adviser. Just curious what experience you have that makes you
say this?

~~~
whorleater
Huh, I've attended classes at two universities: one for my undergraduate and
one while I was in HS, and neither had a system in place to explicitly bar you
from registering for a class whose pre-reqs you didn't fulfill. At best you'd
get a scary message confirmation message telling asking you "You don't meet
the pre-reqs, you may be dropped from the class, are you sure?".

Also, at least when I was an undergrad, the Banner student system (from
ellucian company) had no system in place for barring you from registering from
classes. This was frequently the point of discussion between the professors
that I TA'd for.

------
yodsanklai
> How to Learn Advanced Mathematics Without Heading to University

I wonder if it's even possible. Learning maths requires much work, time and
dedication. Doing so alone must be very difficult.

There are several things universities provide that are hard to replicate
alone: a degree, which gives you access to a job, motivation, learning
environment, and "peace of mind".

What I mean by peace of mind is that, when you're a student, your job is to
study, that's what you're expected to do and normally your degree will give
you access to a job (esp. if your university is reputable).

Now suppose someone learns advanced maths on their own. There's a huge
opportunity cost. Not only it takes a lot of time, and the few lucrative jobs
that make use of maths are in finance. I suspect financial institutions are
very conservative and rarely recruit someone without a proper academic
background.

An other thing when learning things alone, is that your job is twofold. You
must be teacher and student at the same time. You need to find the material,
impose yourself some pacing, decide when it's ok to move on etc... It may be
ok when you want to learn a new technique in a field you already know, but
something as broad as "learning advanced mathematics" seems impossible.

~~~
mungoid
I really hope this doesn't come across as brash. I don't mean it to, but I
must disagree with your assertions (In my case at least). Learning advanced
mathematics without university is completely possible. Because it is at your
own learning pace. Not one of a University.

I graduated several years ago with a BS in Computer Science, with a Focus on
Networking. And during that time, I held 3 part time jobs while also being a
math tutor. Almost none of the math I use today as a physics developer was
learned from schools. I also never had that piece of mind you mentioned,
because I was constantly juggling several things at once while going to
school. My knowledge of advanced mathematics at the time of my graduation was
pretty non existent. I think the most advanced math I had was Algebra 2 or
something like that, and the Professors just basically read verbatim from the
book.

A few years after Uni, I started teaching myself Calc, Trig, Vector maths,
Diff Eq and Physics strictly from what I have found on various sites, software
and books. Because of that, I ended up getting a physics simulation developer
position at a software company. Because in my companies view, being able to
teach yourself all that math is much more impressive than being taught from a
University.

I hated math during High School and College, but since then, I have found that
I absolutely love math, and I will never stop trying to learn or do new
things. My degree was two small lines on my CV, while about 50% of what I had
on my CV was all learned on my free time, by myself.

So learning math without a College or University is totally possible, and in
my situation, worked way better. Sites like Khan Academy, Wolfram, Youtube,
etc. all give you the resources and leave it up to you to progress at your own
pace, for free.

~~~
sixo
I don't mean to be rude by saying this, but the truly-difficult advanced math
- the stuff that's really hard to build an understanding of by yourself,
because it's fairly distantly separated from any obvious applications or
anything you'd readily have experience with, and heavily obfuscated (to
newcomers) by the notation and pedantic proof-focused thoroughness
(appropriate for academic math, less so for applications) - starts a few
courses _after_ Diff eq.

~~~
tprice7
If you don't consider the topics mungoid mentioned to be advanced math,
perhaps you'll still consider this to be:
[http://arxiv.org/abs/1509.05797](http://arxiv.org/abs/1509.05797) It was
accepted to Algebraic Geometry in May, (the Foundation Compositio Mathematica
journal, not JAG), so it will probably appear online sometime around December.
So far I've received three invitations to visit two different universities as
a result of this paper. (search for "Price" on these pages:
[http://www2.math.binghamton.edu/p/seminars/arit](http://www2.math.binghamton.edu/p/seminars/arit)
[http://www2.math.binghamton.edu/p/seminars/arit/spring2016](http://www2.math.binghamton.edu/p/seminars/arit/spring2016)
, I will also be travelling to a German university in October but
unfortunately I have no evidence to show for this currently). I say this as
someone who left undergrad after four terms and is mostly self-taught, from
such resources as books, online papers, and wikipedia.

~~~
gone35
Impressive. Congratulations on your achievement!

------
fantispug
Learning advanced mathematics without going to university would take an
extreme amount of dedication, focus, and effort, but it's certainly possible.
It's much easier with the resources available on the internet, and being able
to connect with people through forums and stack exchange.

John Baez's recommendations:
[http://math.ucr.edu/home/baez/books.html](http://math.ucr.edu/home/baez/books.html)

For theoretical physics 't Hooft's recommendations:
[http://www.staff.science.uu.nl/~gadda001/goodtheorist/](http://www.staff.science.uu.nl/~gadda001/goodtheorist/)

~~~
jwdunne
Those are some awesome recommendations. Half way through a bookmarking so
paused to give a big thank you.

I don't care if I need 2 lifetimes to learn advanced mathematics. I might not
even scratch it. It's the journey that counts to me - if I can learn one new
tool, one new perspective of looking at problems and the world, I'm a very
happy man.

The only person who loses out is my poor wife who must listen to my excitement
and then has to go lie down for a bit because it's too much to digest.

------
bitchy
These books will kick your teeth in if you're not prepared. You either get a
teacher who'll hold your hand or you need to gear up for fight(develop math
maturity and learn all the tricks and tips). To the latter end, you can check
out the Book of Proof by Richard Hammack[0] and Discrete Math by Susanna
Epp[1].

[0]
[http://www.people.vcu.edu/~rhammack/BookOfProof/](http://www.people.vcu.edu/~rhammack/BookOfProof/)

[1] [https://www.amazon.com/Discrete-Mathematics-Applications-
Sus...](https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-
Epp/dp/0495391328/ref=sr_1_1?ie=UTF8&qid=1473084498&sr=8-1&keywords=susanna+epp)

------
biofox
I have found the Chicago undergraduate mathematics bibliography useful for
directing self-study:

[https://www.ocf.berkeley.edu/~abhishek/chicmath.htm](https://www.ocf.berkeley.edu/~abhishek/chicmath.htm)

Previously discussed on HN:

[https://news.ycombinator.com/item?id=9927909](https://news.ycombinator.com/item?id=9927909)

~~~
tgb
As a math grad student, I can say that this Chicago list has primarily books
that mathematicians know. The one posted here has primarily books that I am
unfamiliar with. If one were to follow that one, other people trained in math
would have a hard to judging what you've done (it's common to say things like
"I've learned algebra at the level of Dummit and Foote" but this only works if
people know the book you're referring to).

On the other hand, books written for mainstream math majors and graduate
students are not necessarily the ones best suited for an autodidact. Perhaps
the author of this post has selected those that are more appropriate, but I
can't judge. Also, Springer is a great name in math books and you generally
don't go too far wrong by sticking with them, but I've never seen their
undergraduate series before. Perhaps they're more common in the UK than the
US?

~~~
ryanmonroe
An added benefit to learning from a book that's more popular is that if you
hit a wall and have a specific question about the material as it's presented
in your book, you're more likely to find your question answered online. You
might even be able to find course material that follows the book, whether from
an official online course or just because the professor at some university
didn't bother to make the course page blocked off from non-students.

~~~
mafribe

       book that's more popular 
    

Yet another benefit of popular books is that they won't be first edition, so a
lot of mistakes that make it into the first edition will have been ironed out.

Don't underestimate how much a strategically placed typo can confuse a
learner.

Rule of thumb: avoid first edition maths books.

~~~
_asummers
I once had an analysis book that began the chapter "There exists epsilon < 0",
which I found very amusing.

------
saretired
What bothers me about this article is the hook: if you can learn this stuff
you can get a quant job on Wall St. Realistically, very very few people can
(truly) learn this amount of material on their own, and even so, you will be
competing with top people with advanced math degrees, so if you're not the
second coming of Gelfand, the goal of getting this kind of job is completely
unrealistic.

On the other hand, if you have the time (and ability) to learn some of this
material on your own, for a purpose other than competing for a highly paid job
as a mathematician, great.

------
mathgenius
This stuff is brutally difficult to learn from books. Sigh. Maybe in the years
since I studied this as an undergraduate things have changed with youtube and
so-on. But there is nothing quite like talking to a real mathematician. One
minute you are asking a question about some little thing you are stuck on, and
the next minute the master is levitating and bending spoons! That's when you
start to feel the real depth behind the concepts. It doesn't come from books.

~~~
Chris2048
You want an amazing, 21st century math tutorial?

I was astounded by this: [https://acko.net/blog/how-to-fold-a-julia-
fractal/](https://acko.net/blog/how-to-fold-a-julia-fractal/)

Amazing intro to complex numbers.

~~~
iorrus
Thanks that was incredible.

~~~
Chris2048
I actually emailed the author, asking if they had a tip jar since I was so
impressed.

They replied "I'd be equally happy if you made a charitable donation this
holiday to someone or some organisation that can use it more."

:-)

------
ziedaniel1
To get the key ideas behind many of these topics, you could try reading Evan
Chen's Infinitely Large Napkin:
[http://www.mit.edu/~evanchen/napkin.html](http://www.mit.edu/~evanchen/napkin.html)

~~~
jacobolus
Concept: undergraduate with no teaching or writing experience who was an
International Math Olympiad gold medalist writes a draft book explaining all
of undergraduate mathematics (or rather, most of the topics from his
coursework in random-ish order) to slightly younger IMO participants.

It’s great that he’s making the effort, but I’m not sure this is the most
useful resource for a typical autodidact.

------
lordnacho
Seems pretty comprehensive to me. As a career quant trader I'd say it's a
matter of doing the advanced stuff so that you understand the simple stuff.
Especially in statistics, there are a number of simple principles, but they
need to be learned by incorporating them into some complicated lessons.

There's also programming. That's a whole can of worms in itself. There's both
theory and practice, where I'd say the practice is far more important than it
seems. You really have to have bashed your head against a wall (of your own
making) to appreciate how to code in a sensible, maintainable way.

~~~
Chris2048
I'm aiming to become a quant dev.

I'm already a dev, but trying to catch up wrt the math at the moment :-O

I'm finding there are a whole bunch of skills unrealted to most dev concerns.
looking at this: [http://quantjob.blogspot.com/2011/12/how-to-avoid-
quantdevel...](http://quantjob.blogspot.com/2011/12/how-to-avoid-
quantdeveloper-black-hole.html) I think a lot of dev skills _are_
"housekeeping" \- VC, commenting, testing, agile, automation, standards etc.

The quant dev stuff seems to be a lot more concerned with performance,
correctness and accuracy, and the last two in particular are somewhat
specialist dev skills I think - I've found code derived from mathematical
equations be be a little different to other code.

~~~
lordnacho
But housekeeping is important! I've seen supposed quants who didn't know how
version control worked. It caused productivity to plummet when people just did
what they thought quants do.

If anything it's knowing the plumbing that makes you productive as a dev, of
any kind. You just can't get around understanding how branching works, or
having some unit tests.

Very little of the work ends up being the bit you think you're there for. I
suspect it's the same in many industries. My parents ran a restaurant, and
there's a lot of cooking, but there's also a lot of driving to the wholesaler,
picking out vegetables, cleaning surfaces before and after a day, doing the
plates, accounts, and so forth.

~~~
Chris2048
> it's knowing the plumbing that makes you productive as a dev, of any kind

Is this true of quant devs? Seems the focus is different - regular devs aren't
as rare, so maybe the most important thing is producing a viable POC?

As for quants not knowing VC - did they come from a dev background?

~~~
lordnacho
> As for quants not knowing VC - did they come from a dev background?

No, and that was the problem. The more you venture into this field, the more
you realise how much of it is coding. New idea about how price series X
relates to Y? No use unless you can pull the data, do the transformations
yourself.

Another critical problem is that when you're unproductive, you make
contortions to make your results "real". You make rationalizations that don't
hold up, because OMG it's a lot of work to test some more ideas.

~~~
Chris2048
I think the last point is very important. Can a failing Quant easily bluff.
Yikes.

------
ronald_raygun
My two cents - I got a BS in math and an MS in stats. A ton of this stuff is
really hard and takes a lot of time to understand, and it really does help to
have a bunch of time to dedicate to it, a professor to guide you, and friends
to try problems with. It also really helps to be exposed to a good order to
learn stuff (for example I'd suggest tons of functional analysis, then prob,
then stats, then finally ML)

But once this stuff clicks it becomes very easy to teach yourself. I've been
learning stuff like quantum algorithm, network analysis, etc.

------
kikishortler
On the face of it this looks more like studying than learning. The distinction
is not meaningless. I _studied_ French for six years and passed an exam at the
end. However despite all this activity I have never been able to converse in
French. By a variant of Gell-Mann Amnesia effect, I conclude that I cannot do
mathematics either.

------
Tycho
What do people think of this idea. Let's say you want to casually improve your
maths knowledge in your spare time. Let's say you find it frustrating how you
generally can't just google concepts as you come across them, because the
material is usually presented so obtusely and you need to be able to ask
questions and have things explained in different ways. Let's say you live in a
university town. Let's say you pay a graduate student to just spend a couple
hours per week answering your questions, on whatever concepts you're having
difficulty with.

Do you think this would work well? Obviously it costs money but I'm guessing
the rate wouldn't need to be too high to make it worth their time. They
wouldn't need to do any preparation, just have a good grounding in the
language of maths.

~~~
ctchocula
That was the idea with this business [1].

[1]
[https://news.ycombinator.com/item?id=12268362](https://news.ycombinator.com/item?id=12268362)

------
ekm2
There is another guide online: "
[http://hbpms.blogspot.com/2008/05/stage-1-elementary-
stuff.h...](http://hbpms.blogspot.com/2008/05/stage-1-elementary-
stuff.html?m=1)

------
hal9000xp
As I a software developer with no degree (working since 2009 in 3 countries),
I can share my experience of attempts to learn advanced math.

In 2010, I was very interested in foundations of mathematics, an extremely
abstract math branches:

[https://en.wikipedia.org/wiki/Foundations_of_mathematics](https://en.wikipedia.org/wiki/Foundations_of_mathematics)

In particular I spent huge amount of time on:

[https://en.wikipedia.org/wiki/Nicolas_Bourbaki](https://en.wikipedia.org/wiki/Nicolas_Bourbaki)
(Set theory)

[https://en.wikipedia.org/wiki/Principia_Mathematica](https://en.wikipedia.org/wiki/Principia_Mathematica)

[https://en.wikipedia.org/wiki/The_Foundations_of_Arithmetic](https://en.wikipedia.org/wiki/The_Foundations_of_Arithmetic)

[http://www.jhtm.nl/tudelft/tw3520/Introduction_to_Mathematic...](http://www.jhtm.nl/tudelft/tw3520/Introduction_to_Mathematical_Logic.pdf)

What attracted me is that these books doesn't require any specific knowledge
of classical math. I.e. they are self-contained.

It was fun and ... the experience to delve into highly abstract view on entire
math.

The big problem is that while I read that for more than a year, I had no
experience in problem solving and just ignored exercises (thinking that
concept is everything). As a result of that, my entire knowledge is completely
evaporated and I literally can't solve any of exercises.

After that year, I dropped math till recently.

Now, I have completely different approach. I learning elementary olympiad
style math and most importantly solving problems all the time. Currently, I'm
into series of books:

[https://www.artofproblemsolving.com/store](https://www.artofproblemsolving.com/store)

These books made for math olympiad preparation. While I solving exercises, I
feel how solid my knowledge is.

So if you want to learn advanced mathematics, learn elementary olympiad-style
math first. It will give you solid background to start learning advanced math
(not just knowledge background but most importantly problem solving skills).

~~~
adrianm
I don't agree with your suggestion about olympiad math since it often has
little relationship to applying advanced mathematics, but there definitely is
merit to the idea that you might need to put theory into practice in order to
gain insight about these things.

I recommend (surprise surprise) programming. Implement fast fourier transform
in C and then Common Lisp. Write a finite difference PDE solver. Try solving
actual problems to motivate you. Signals analysis can be a fun way to exercise
your knowledge. Try analyzing your favorite songs and figuring out what makes
them sound the way they do. Maybe implement some audio filters. If that's not
your cup of tea, write physics or chemistry simulations instead. Then use
OpenGL to visualize them. Then make them interactive.

I can go on and on, but I'll just leave two book recommendations for those who
might enjoy programming advanced mathematics.

Structure and Interpretation of Classical Mechanics :
[https://mitpress.mit.edu/classical_mech](https://mitpress.mit.edu/classical_mech)

Functional Differential Geometry : [https://mitpress.mit.edu/books/functional-
differential-geome...](https://mitpress.mit.edu/books/functional-differential-
geometry)

~~~
FabHK
Several Project Euler problems require some mathematical nuggets and provide
nice motivation to dive deeper (and provide an application right there, too).

------
echelon
Would it be possible to do this for quantum mechanics, chromodynamics, etc.
(to the point where I can follow the primary literature)? I have an
undergraduate understanding of physical chemistry, but that was the closest
exposure I got to the subject. My mathematics background is petty weak, too
(only a modest background in PDE, no ODE, and a faint memory of linear
algebra).

I'd pay handsomely for a personal tutor / teacher.

------
partycoder
Unless you work on graphics, physics, signal analysis, sound, trading, data
science, computer vision, machine learning, etc... it's hard as a software
engineer to be exposed to math past the basics, meaning that you can survive
without having to go beyond arithmetic.

You might still get some exposure to discrete mathematics once in a while.
Statistics is always there to help you, some people avoid it, some others
embrace it.

~~~
kkarakk
>data science

how do you survive as a software engineer without data science?

------
naveen99
Sympy can help get over the fear of following scary looking equations or just
speed you up.

[http://minireference.com/static/tutorials/sympy_tutorial.pdf](http://minireference.com/static/tutorials/sympy_tutorial.pdf)

------
IvanK_net
The hard part of learning anything without heading to university is not
learning that subject, but persuading yourself, that you realy do need to
learn each specific area of the subject thoroughly, even if you have never
heard of it in your previous "career".

------
jimhefferon
> it is essential that we study topics such as Measure Theory and Linear
> Functional Analysis

I love this sentence. I'm not sure it is true, but it is nonetheless a great
sentence.

------
graycat
Somewhere in the OP or its links is a statement that in 1997 or so the world
of finance was really hot for _quants_.

Net: What I found was not "hot" but ice cold.

In contrast, early in my career around DC, for applied math for US national
security and NASA, in one two week period I went on seven interviews and got
five offers. In four years, my annual salary increased by a factor of 4 to six
times what a new, high end Camaro cost. That was "hot".

When I went for my Ph.D. in applied math, I'd read E. O. Thorpe who had,
basically an early but basically correct version of the Black-Scholes option
pricing model. In the back of his book, he mentioned _measure theory_. So, I
dug into Royden's _Real Analysis,_ and in grad school I got a really good
background in measure theory, probability, and stochastic processes from a
star student of E. Cinlar, long in just those topics and the mathematics of
operations research and mathematical finance at Princeton.

In more detail, about 1992 to 2000, after my Ph.D., I tried to get into
finance in NYC as a _quant_. My Ph.D. dissertation research was in stochastic
optimal control, with careful attention to measure theory and the relatively
obscure topic of _measurable selection_ and with a lot of attention to real
world modeling, algorithms, and software. I had a good background in
multivariate statistics and time series techniques, an especially good
background in advanced linear algebra and numerical linear algebra (e.g.,
numerically exact matrix inversion using only double precision machine
arithmetic and based on number theory and the Chinese remainder theorem),
double precision inner product accumulation and iterative improvement, etc.

So, I sent nicely formatted resume copies, in total 1000+.

I have held US Federal Government security clearances at least as high as
Secret; never arrested; never sued; never charged with worse than minor
traffic violations; never bankrupt; good credit; physically normal; healthy;
never used illegal drugs or used legal drugs illegally; married only once and
never divorced; etc.

Results:

(1) I got an interview at Morgan Stanley, but all they wanted was software
development on IBM mainframes (where I had a good background at the time) with
no interest in anything mathematical.

(2) I got a _lunch_ with some guy who claimed to be recruiting for Goldman
Sachs, but, except for the free lunch and what I had to pay for parking in
Manhattan, that went nowhere.

(3) I had a good background in optimization, published a nice paper in JOTA
that solved a problem stated but not solved in the famous paper in
mathematical economics by Arrow, Hurwicz, and Uzawa.

So, for mathematical finance, I got a reference to

Darrell Duffie, _Dynamic Asset Pricing Theory_ , ISBN 0-691-04302-7, Princeton
University Press, Princeton, New Jersey, 1992.

and dug in: The first chapters were heavily about the Kuhn-Tucker conditions,
that is, the topic of my JOTA paper. By the end of the chapter, I'd found
counterexamples for every significant statement in the first one or two (IIRC)
chapters. I had to conclude that Duffie was not a good reference for anything
good!

(4) Headhunters: I tried them, especially the ones claiming to be interested
in technical work, computing, etc. They were from unresponsive down to
insulting. It wasn't clear they had any recruiting requests.

(5) In those days, getting names and mailing addresses of hedge funds was not
so easy. But I did get some lists and mailed to them. Got next to nothing
back. I didn't hear about James Simons until well after year 2000.

(6) Right, there was Black-Scholes. Well, of course, that was Fisher Black at
Goldman Sachs. So I wrote him and enclosed a copy of my resume. I got a nice
letter back from him saying that he saw no roles for applied mathematics or
optimization on Wall Street.

So, I gave up on trying to be a _quant_ on Wall Street!

So that was 1992-2000, 8 years, 1000+ resume copies, and zip, zilch, and zero
results.

Curious that the OP thinks that 1997 was a "hot" year for applied math on Wall
Street.

Now I'm an entrepreneur, doing a startup based on some applied math I derived,
computing, and the Internet! To heck with Wall Street: If my startup is at all
successful, I will make much more money than I could have on Wall Street. And
I don't have to live in or near the southern tip of Manhattan and, instead,
live 70 miles north of there in the much nicer suburbs!

Lesson: Take the OP with several pounds of salt!

------
Hnrobert42
Am I missing something? This just appears to be a link to buy some guy's
ebooks.

~~~
mathgeek
There are about a half dozen ads (and a fade-in popover) above the actually
content. It's a terrible site design from the perspective of someone wanting
to read the content on mobile, but the article is there.

I also just left without reading it, due to the ads.

~~~
shogunmike
Thankyou for the necessary feedback!

I'm actually in the process of overhauling the design of the site,
particularly with regards to mobile, as the current Bootstrap-derived design
pushes all sidebar content to the top on mobile/table.

------
paulpauper
On question is: why? The examples in differential geometry can be difficult
and time-consuming , unlike simple calculus, and are best done with computer,
not by hand. A single tensor, as found in general relativity, may have dozens
of components...writing them out would be taxing. My question is, what do want
to do with this knowledge. There is value in learning complicated, abstract
math to signal intellect and thus become more popular online, and maybe get
consulting work. But in terms to practical applications, a lot of it is done
by software programmed by large teams (not just one person), although learning
the rules is always helpful. If you want to be a professional researcher who
makes original findings in pure mathematics, it will presumably require full
dedication, and one can't be both a quant trader and pure researcher at the
same time (even someone as smart as James Simmons, founder of Renaissance
Capital, was forced to choose between one or the other; he chose the former).

It seems as of late ,especially since 2013, there is huge demand for learning
complicated mathematics, coding, and trading algorithms. It's like the AP-math
class of high school, but as of 2013 expanded to include almost everyone, not
just a dozen students lol. This recent obsession with math and finance is
described in more detail in . People observe, read headlines about high-IQ
founders, venture capitalists, and coders making tons of money in Web 2.0
(Uber, Pinterest, Snaphat, Dropbox, etc.); STEM people getting tons of
prestige, status, and global notoriety for their finding (Arxiv physics and
math papers frequently go viral); and how the economy, especially as of 2008,
rewards intellectualism and STEM in terms of higher wages and surging asset
prices (like stocks (the S&P 500 has nearly tripled since the 2009 bottom),
web 2.0 valuations (Snapchat is worth $15 billion, on its way to $50 billion),
and real estate (Palo Also home prices have doubled since 2011)), and,
understandably, many people want a piece of the wealth pie. They see that
intellect - which includes STEM, finance, and also quantitative finance - is
the path to both riches and social status (as embodied by wealthy geniuses
like Musk, Thiel, Zuckerberg, Shkreli), which is why there is so much interest
in these technical, difficult subjects, unlike decades ago when only a handful
of people were interested.

But another question is: Does algorithmic trading work? I don't know for sure,
but I think a lot money is made in market making (Citadel Capital comes to
mind), which tends to full under the umbrella of algorithmic trading - the two
are closely related. And the math in involved has much less to do with
differential geometry and number theory and more to to do with statistics and
linear algebra (such as analyzing correlations between data). This involves a
lot of trading and paying constant attention to order books - it's a full time
job. I don't think it's as glamorous as many think it is, and I'm not sure if
the returns are worth the effort. There are simpler methods, based on
mathematics such as the ETF decay, that an also generate very good returns and
don't require full-time trading. Here is one
[http://greyenlightenment.com/post-2008-wealth-creation-
guide...](http://greyenlightenment.com/post-2008-wealth-creation-guide/)

~~~
zizzles
_It seems as of late ,especially since 2013, there is huge demand for learning
complicated mathematics, coding, and trading algorithms. It 's like the AP-
math class of high school, but as of 2013 expanded to include almost everyone,
not just a dozen students lol. This recent obsession with math and finance is
described in more detail....._

Obsession with Math? Where do you live where people have math obsessions?
Where I live STEM graduates are a massive minority (We had an HN article on
the front page about this very topic just yesterday) Mathematics is some sort
of taboo magic in the eyes of 99.99% of humans, not something anybody studies
to gain prestige, status or global notoriety. Your average citizen can't even
name one mathematician.

 _People observe, read headlines about high-IQ founders, venture capitalists,
and coders making tons of money in Web 2.0 (Uber, Pinterest, Snaphat, Dropbox,
etc.); STEM people getting tons of prestige, status, and global notoriety for
their finding (Arxiv physics and math papers frequently go viral); and how the
economy, especially as of 2008, rewards intellectualism and STEM in terms of
higher wages and surging asset prices (like stocks (the S &P 500 has nearly
tripled since the 2009 bottom), web 2.0 valuations (Snapchat is worth $15
billion, on its way to $50 billion), and real estate (Palo Also home prices
have doubled since 2011)), and, understandably, many people want a piece of
the wealth pie. They see that intellect - which includes STEM, finance, and
also quantitative finance - is the path to both riches and social status (as
embodied by wealthy geniuses like Musk, Thiel, Zuckerberg, Shkreli)...._

There is NOTHING genius about narcissistic photo-sharing websites or SnapChat.
These are just illusive innovations, a fools-paradise for the masses. Not only
that, but the "social status" of these founders you mention has rarely left
the confines of the tech-world anyway, if you want social status in our
society go to acting school and move to Hollywood. I mean..... this world you
mention where STEM students gain so much prestige and math papers go....
viral? Where is this world? What planet are you posting from? Which galaxy is
it located in? Is this post of yours real-life or am I dreaming?

~~~
imjustsaying
> this world you mention where STEM students gain so much prestige and math
> papers go.... viral? Where is this world? What planet are you posting from?
> Which galaxy is it located in? Is this post of yours real-life or am I
> dreaming?

[https://en.wikipedia.org/wiki/Echo_chamber_(media)](https://en.wikipedia.org/wiki/Echo_chamber_\(media\))

------
karma_vaccum123
People don't go to university to learn, they go to university to get
degrees...or to be more blunt...to buy degrees.

------
DavidWanjiru
"Why are you wanting to learn mathematics?"

The author is called Michael Halls-Moore. Why would a person called Michael
Halls-Moore write a sentence like this? I'm genuinely curious, coz I'd assume
this is a native English speaker.

