
Lessons from My Math Degree That Have Nothing to Do with Math - ginnungagap
https://medium.com/s/story/6-life-lessons-from-my-math-degree-that-have-nothing-to-do-with-math-d38aba90edfe
======
wwweston
I had a bit more fun with my math degree than the author did, but the
curriculum taught me similar things.

I'd add one more: I think it helped me be a better writer. All of college and
the closing out of adolescent cognitive development probably contributed some
of that too, but I noticed that by the time I'd made my way through analysis
classes that I was getting better responses to my written communication and
that I could detect a tightness in some of it that was familiar. I think it
came from spending so much time trying to clearly articulate details of
abstract concepts that I was struggling to come to grips with. A proof is
arguably a (very specialized) form of a persuasive essay designed first to
illuminate and convince oneself.

Perhaps it contributed to the author becoming a better writer too.

~~~
yomritoyj
Analysis has had the opposite effect on my writing. After having my head
buried in measure theory for a semester I wrote in a report for my student
organization: "The set of inactive members of the Executive Committee is a
non-negligible one." I was asked to rewrite that.

~~~
matthewrudy
"non-negligible" doesn't sound very precise.

You mean "non-empty but finite"?

"There exists a member of the Committee that is not active"

~~~
semigroupoid
In the context of measure theory, a "non-negligible" set is a set with measure
greater than zero.

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vinayms
Oddly, I can relate to all the points (mentioned below) as a software
engineer, except that I love what I do too much to even imagine giving up like
the author seems to have. In fact, I had exactly the opposite experience. I
hated computer science and programming in the beginning but ended up doing it
for fun and profit.

> 1\. I expect to not get the answer on the first try

> 2\. I can tolerate ungodly amounts of frustration

> 3\. I attack problems from multiple angles

> 4\. I check my goddamn work

> 5\. I practice persistence

I happen to be one of those engineers/persons who thrives working alone,
values quality over quantity, and tries to be as self sufficient as possible,
so I can really relate to the above points very much.

~~~
tenaciousDaniel
Number 1 was the biggest for me, coming into programming from an entirely
different profession. I never learned how to code until I was about 28. I
didn't realize that I brought what I call the "consumer attitude" towards
electronics into my programming practice in the beginning. The consumer
attitude is that machines _work_. If they don't work, something went terribly
wrong.

So when I made a mistake, I'd just crush myself with doubt and anxiety. It
literally would hurt my brain and give me the sinking feeling that I'd never
be able to do this because I can't code anything without screwing up
somewhere.

But now, after about 6 years of doing it, I've developed an entirely different
attitude. The correct attitude towards machines is that they _do not work_.
They are broken by _default_. So if they work, something went terribly
_right_.

Now, when I write a line of code, and it breaks, it's just business as usual.

~~~
vinayms
I can feel what you mean. In college at times when my 101 code wouldn't
compile I was convinced that Borland C++ had a bug.

For me its the point 2 that is most relatable. Every time I have to use a
library, even C++ STL beyond the oft used portions, or learn a new framework
or language, my heart sinks a little anticipating the impending path of
thorns. I have had so many encounters where it is literally a pain in the neck
from all the peering into the screen trying to see just what the heck is not
working, or eye burn from staring into the monitor squinting at the debugger
window with small fonts, or both of this along with sore and sweaty fingers
out of frantic googling that I shudder just writing about it. I call this
"wrestling with the API". Its an occupational hazard for us to deal with all
the man made pieces of software that are as different as their creators, and I
have made my peace with it.

It usually turns out that I missed a fine detail in the documentation.
Sometimes its my fault where I wouldn't have read the docs properly or have
made uncalled for assumptions, and other times its squarely the
documentation's fault for being unhelpful. When its my fault, I feel really
disappointed with myself for having been so careless despite being an
experienced dev. That adds to the frustration. Almost every time,
stackoverflow has bailed me out, and invariably it would be an old post. (At
times when I find a solution to something seemingly insurmountable, I have
even mused about donating some money to them.) I take solace in the fact that
someone had faced similar problem long before me and I need not be so harsh on
myself. That until it happens again.

~~~
meko
Haha! I was in the process of spinning up my little blog, and I had a similar
experience trying to get dns configured, had I merely checked my provider's
knowledgebase instead of going through github's more generalized procedures I
would have accomplished what I was trying to do within an hour instead of the
5 I spent scouring every bit of github's docs I could find. Urp.

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joe_the_user
Hmm,

I'd be slightly leery about taking advice from someone who admits they
actually didn't do well learning math. Looking at the points, most of the
advice sounds good but a couple seem a bit off.

Especially: "I can tolerate ungodly amounts of frustration".

Math isn't always easy but my hunch is that if it _feels_ hard, you're on the
wrong track. The best moments in math for me are the "it's obvious" times,
points where everything just flows from first principles.

I've always "found math easy" and occasionally tutored people who had trouble
with it. It always seemed like those who got stuck would make the mistake of
thinking math was a grind, that if they pushed through enough frustration
they'd get there. I think that attitude might help some fieds but I don't
think it helps math.

This isn't to say math really is easy. Rather, I think the appropriate
approach is to spend a lot of time and approach from multiple angles _until_
it _feels_ easy (and fun and creative). Work really "hard" to attain a state
of productive laziness. But that work shouldn't be a continuous grind either,
rather a careful survey of all the ways one can approach the topic.

And certainly being able to tolerate frustration is certainly useful in many
fields, programming among them. But I'd say that intellectual problems that
benefit from overt are problems where a person has all the knowledge necessary
for the solution and merely has to engage in a long, frustrating process of
putting them together - like a large but not hugely sophisticated, computer
program.

~~~
j7ake
If Terence Tao admits that doing mathematics is hard, then I am extremely
leery of anyone who thinks otherwise.

~~~
Barrin92
Five years of university math here and I can only mirror the author's
experience. If having the feeling that math is hard ought to disqualify you
then everybody will probably be disqualified.

Maths is hard for everybody, including the people who excel at it. I've never
met anybody who has spent serious time on a math education suggest anything
else.

If you get a sadistic pleasure out of torturing your mind with numbing puzzles
and like the reward of finally figuring something out that you had to ponder
for days (or longer) then you have a good chance of doing maths at the
university level. But it never really comes naturally to anybody, it's not the
kind of thing we're build for.

------
romwell
As someone who just went through graduate school in mathematics, I can say
this:

This person _has not been doing math_. What he was doing - that's not _what
mathematics is_.

To understand why I say this, read Lockhart's Lament[1].

In short: the true joy of doing mathematics is asking interesting questions
and exploring. It's telling a good story. It's being the only person in the
entire world who knows a spoiler or two for the upcoming series (even if it's
anticipated by only a handful). It's about noticing something simple which
makes a hard thing easy. It's about that a-ha moment, and about being
surprised - sometimes by what you say.

All the tedium, frustration, being stuck, etc _are not the end goal_ , they
just _sometimes_ happen on the way there.

The poor sap never got to do math. He's got to eat the crust off a pizza - and
never got to the delicious part.

And he never got to learn how _social_ math is - because, as an advisor of
mine once said: mathematics, like food, is beat shared.

[1][https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

~~~
jdtang13
Nice gatekeeping, friend. I've also personally never heard my math graduate
student friends talk like this.

~~~
haskellandchill
Some of their language is unfortunate but they pulled through with the sharing
part. It is quite hard to share maths with others however. How can I share
that feeling inside my brain algebraically closed fields give me?

~~~
ginnungagap
>How can I share that feeling inside my brain algebraically closed fields give
me?

That's kinda like returning home after a long day, because algebraically
closed fields are about the nicest structure you can hope to find yourself
working in!

~~~
rocqua
The algebraic numbers aren't complete. So you cannot measure the circumference
of circles in them, nor does a series like sum(1/k!) converge.

Personally I'd posit finitely generated abelian groups as the nicest
structures. Perhaps there is also something to be said for finite
algebraically closed fields.

~~~
ginnungagap
There are no finite algebraically closed fields, but I see your point, it
depends on what you have to do really, if you want to do any kind of analysis
completeness is great, but being more on the logic/model theory side I like
all algebraically closed fields!

~~~
haskellandchill
Ya'll rock.

------
rdl
I think how math is taught at the early stages (rote, focus on finding a
simple answer which is already clearly known, focus on mechanical arithmetic
and calculation) filters out many of those who would enjoy the more advanced
stuff. There are some clear filters (basic arithmetic probably is 80-90 IQ,
algebra 95, probability and statistics 100, calculus 100-105, differential
equations, analysis, and linear algebra maybe 110, algebraic topology a bit
higher), but those are really lower bounds for raw intelligence required.

I’d rather have basic arithmetic treated as a separate subject, and then some
form of “problem solving math” which can incorporate concepts from calculus,
algebra, and especially probability and statistics. The best three math
classes I’ve ever taken were a combination of physics and calculus in a small
group taught by two teachers who worked closely together, a weird MIT ESG
seminar with a postdoc and 3 students covering the broad expanse of everything
post 18.03, and number theory and crypto at the same time (a grad class I
snuck into without prereqs and spent the first month essentially 30h/wk
catching up on those.). What was consistent with two of these was having a
clear problem to solve; with the third it was just high interactivity with an
expert for an extended period.

Providing students with exposure to the problem space addressed by a certain
form of math, then letting them discover some of the truths and techniques on
their own in the same way they were originally discovered, is going to take
more time and far more skilled instructors than just repeating facts, but will
be more engaging and produce better understanding.

------
waynecochran
Yes, I was a math major as an undergrad, and it is these exact traits that
carried over to computer science / engineering. I see a lot of programmers
that are cavalier, don't check (unit test) their solutions, unwilling to
wrestle with frustrating problems, and are quick to reach for the "framework
of the day" to solve what should be trivial problems.

I also add to the list a deep appreciation for elegant solutions
(Mathematicians do not like kludges).

------
abnry
Solving a problem gives you a rush. When I majored in math, I think this was
the biggest motivating factor in continuing on. It helps I was good at it,
even though it wasn't always smooth sailing.

------
xstartup
Most people told me that I am good at math.

But I was like an addict solving every question I could find. I got a kick
from solving it before anyone else, completing the whole book before others
opened the first chapter.

I was looking at my wristwatch all time and solving it like my life would
simply end if I stopped or wasted even a moment.

I was never burned out, never felt tired.

~~~
haskellandchill
That's how I feel. The deep love, and it took me a while to get there. Math
can be like the OP described with a workman's mindset, but the untouchable
beauty of cracking a problem set and building understanding of the subject
through that... I'm not sure what turns on that switch.

------
joker3
It's not really clear that the author got anything out of doing a math degree
that he wouldn't have gotten out of doing most other degrees. I was expecting
a bit more from this.

(That said, it would be very interesting to see the same article written by
someone with a PhD in math. That's a completely different animal, and might be
much more interesting to discuss.)

~~~
MadSudaca
This post might somewhat answer your question:

[https://www.quora.com/What-is-it-like-to-understand-
advanced...](https://www.quora.com/What-is-it-like-to-understand-advanced-
mathematics-Does-it-feel-analogous-to-having-mastery-of-another-language-like-
in-programming-or-linguistics/answers/873950?share=1)

~~~
graycat
At least from my academic degrees through Ph.D. and peer-reviewed published
papers, I qualify as a mathematician. So, I'm interested in the OP and your
link to quora.

I've read a lot of high level descriptions of math including some from some
famous mathematicians that I regard as total BS. In strong contrast, the quora
link was pretty good. Some of the best parts in that quora link I had to
discover for myself, and the quora link is the first explanation I've seen by
others.

For the OP, naw, I can't go along with much of that. In strong contrast, I
loved learning, using, creating, publishing, teaching math and still do. Most
of what I learned was from what I studied from outside a formal academic
course; I studied the material because I wanted to understand it and did like
learning it. The work was great fun, not frustrating or unpleasant in any
sense. Even in courses, mostly I just wanted to learn the material and often
ignored the class and teacher, concentrated on one or a few books, studied
alone, and learned the material, generally for the course standards, quite
well.

Sorry the OP had a tough time multiplying matrices and understanding eigen
values -- I had no such problems. To me, matrix multiplication is glorious
because it is an associative operation and from what we can see from that --
amazing when think about it a little. For eigen values and eigen vectors,
those are astounding, the keys to the polar decomposition which IMHO is the
crown jewel of linear algebra and one of the more amazing results in all of
math.

The most difficult material studied was just from writing that didn't explain
very well. One example was most of the explanations I read for the simplex
algorithm of linear programming. Really, a super nice way to approach the
subject is that it's just a nice, nearly obvious, tweak of Gauss elimination.

~~~
MadSudaca
I don't have much training in mathematics, but from what little I have, I can
say that coming up with conjectures is not easy and having your conjectures be
false can sometimes be disappointing. Thus most time spent in a problem is
usually in a state of disappointment. Due to this I can relate a bit to OP.

------
Kagerjay
I didn't really enjoy any of my math courses at University. mostly because it
was forced on me and it felt like learning a boring rote process. I didn't see
the value in it besides applying it to basic physics and engineering courses I
took.

Now, as I program more, I'm starting to appreciate what math has to offer.
Especially when I dig through a library or framework and break down what its
doing on a step by step process.

I find the people I look up to most, whether its in engineering, programming
,etc - are also great mathmaticians.

Math for me has helped me in the following ways

1\. Its helped me write better. Math is like writing. Its all about expressing
the most amount of "oompf" in the fewest syntax possible.

2\. It has helped me program better. Learning discrete math helps me draw
parallels on what an array foundationally is (set theory), and why low level
logic works the way it does.

3\. It helps me write better notes. I used to use thousands of annotated
images for taking notes. Then I realize how poorly that turned out. Over the
years I've learned to take better notes by writing more in fewer words.
Eventually, this led me to math. Math is the simplest way of expressing
complex logic.

4\. It has helped my understanding of 3D and 2D processing. Learning linear
algebra from 3blue1brown has made it much easier to understand why and how 3D
rendering / imaging programs work at the most basic level. How a box is
shaded, how a 3D item is modeled when you apply a fillet to it.

I intend to learn ML / AI , so knowing statistics comes in handy, which at its
core is still math.

Just learning and knowing math makes everything so much easier to pick up
after.

~~~
internetman55
Sounds like you were confused. For example, I know people like stuff like the
3blue1brown movies, but my intro linear algebra textbook from undergrad covers
literally all the materials and movations he did if you bothered to read it.

~~~
ebullientocelot
Yes, this. Not all textbooks are worth anything, to be sure, but decent
"boring" math texts generally have all of the "easily digestible" stuff that
youtube videos do, sans animation. Math really took off for me when I started
going passed the required problem sets and doing the interesting ones that
weren't assigned. Really digging into them and drawing pictures, etc. Math is
a contact sport.

------
czardoz
I had the same overall experience. Math helped me think very abstractly about
problems, but most of the proofs and theorems and constructs I learned are not
directly applicable daily. Sometimes though, they help me come up with
surprisingly elegant solutions for certain problems.

------
paulpauper
Writing is hard..having to not just come up with ideas but articulating them
into words in a way that is grammatically correct and appealing to the reader.
I think much of writers block is not due to a lack of ideas but the difficulty
of articulating them.

~~~
resource0x
Same applies to programming IMO.

~~~
HiroshiSan
Same applies to drawing.

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daenz
>I can tolerate ungodly amounts of frustration

A trait probably shared with most proficient software developers. The diamond
of high skill must be formed by the stresses and pressures of persistent
frustration and failure.

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bluecomp
Most of the points that the author has highlighted will hold true for a person
who has a Ph.D. in any of the STEM disciplines other than math.

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mar77i
When I quit schools at a level that should have prepared me for "work", I left
a place that had me running at full speed and flailing. Ever since I took hold
in my career on my own terms, I knew that is probably the very elephant in any
room I do not want to be in.

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tgb
So the author both learned persistence and the toleration of frustration _but_
also admits to turning in half-done homeworks (if at all), half-assing
midterms and generally not trying hard. Or maybe this is just-so story without
much merit.

------
MadSudaca
Great article.

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quasimodem
Everything has to do with math.

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marsrover
I got these same benefits from a Computer Science degree.

------
baby
Persistence is key.

