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Lessons from My Math Degree That Have Nothing to Do with Math

268 points by ginnungagap 8y ago

vinayms 8y ago
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 8y ago
  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 8y ago
    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.
    - tenaciousDaniel 8y ago
      well said!
    - meko 8y ago
      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.
  - Terr_ 8y ago
    I feel that's related to the mentality that if something was broken, and you do not know why it's working again, then it's not really fixed. This can be difficult to inculcate in new programmers as they try to tweak their way past error messages.
- evincarofautumn 8y ago
  In the past 7–8 years I’ve come around to the realisation that programming truly is a branch of mathematics, in a deep sense—and a strange one at that. It makes sense that they would share a lot of lessons. In my experience, those who say programming isn’t mathematics are usually mistaken about what math actually is. Or at least I know I was. I used to think math was about calculation, because that’s most of what I was exposed to in school—virtually every problem, even in higher-level mathematics, was brought back around to work with concrete values, perhaps in an effort to tie the problems to something “real-world” and get kids interested in it. But it had the opposite effect on me—that’s like saying programming is about making a machine do calculations! Yes, in a literal sense, but there are much higher-level, more abstract and interesting things at work there. To me, a computer’s value is that it’s an automated proving machine. You can make useful, entertaining, or interesting things happen in the real world—just by writing a proof that you can!
abnry 8y ago
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.
MadSudaca 8y ago
Great article.
joe_the_user 8y ago
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.
- Smaug123 8y ago
  I dunno, I'm objectively fairly good at maths (I got a first in the Cambridge MMath), but the reason I learned so much from the course was because I spent almost the entire time failing miserably to get anywhere on problem after problem. Sure, eventually you make the breakthrough - but only after hours of failure. Every avenue you try that doesn't work out is a frustration - often a blank-wall kind of frustration - and there are lots and lots of them before you succeed. Further, every avenue I try feels equally fruitful at the beginning, and frequently reaching the end is highly nontrivial even when you're on the right path, so "if it feels hard, you're on the wrong track" isn't a very easy thing for me to apply.
  - joe_the_user 8y ago
    Well, the question I'd ask is whether you began approaching simpler math as being hard? Getting used to going up against brick to solve really hard problems is useful once you have a toolkit needed to solve those problems. But getting the relatively simple manipulations of the toolkit should be easy - and math undergrad work (at least at not super-advance school) is about putting together the toolkit.
wwweston 8y ago
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.
- newen 8y ago
  This is so true. I took a proofs class the second year (maybe semester idk) of my college and it was really illuminating. Before that class, language was just something I used to talk to people or to read stories. I don't think I really grasped the fact that language can be used for analysis or arguments before that class. I never read philosophy before that class so that could be it too.
- yomritoyj 8y ago
  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 8y ago
    "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 8y ago
      In the context of measure theory, a "non-negligible" set is a set with measure greater than zero.
tgb 8y ago
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.
waynecochran 8y ago
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).
Kagerjay 8y ago
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 8y ago
  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 8y ago
    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.
joker3 8y ago
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 8y ago
  This post might somewhat answer your question: 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 https://www.quora.com/What-is-it-like-to-understand-advanced...
  - graycat 8y ago
    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.
baby 8y ago
Persistence is key.
bluecomp 8y ago
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.
paulpauper 8y ago
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 8y ago
  Same applies to programming IMO.
  - HiroshiSan 8y ago
    Same applies to drawing.
xstartup 8y ago
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 8y ago
  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.
- majos 8y ago
  What do you do now?
czardoz 8y ago
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.
marsrover 8y ago
I got these same benefits from a Computer Science degree.
romwell 8y ago
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.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....
- jdtang13 8y ago
  Nice gatekeeping, friend. I've also personally never heard my math graduate student friends talk like this.
  - haskellandchill 8y ago
    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?
    - tome 8y ago
      > How can I share that feeling inside my brain algebraically closed fields give me? Poetry.
      - haskellandchill 8y ago
        it was correct by construction stretchy compactness continuity we wrote numbers in the sand watched the glass dance of entropy against tired eyes until our vision blurred remaining only feeling legs crossed in a field blade of grass simplification is hard work it's clear there is no enemy but misunderstanding
daenz 8y ago
>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.
quasimodem 8y ago
Everything has to do with math.
mar77i 8y ago
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.
rdl 8y ago
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.
- galieos_ghost 8y ago
  yeah, I hated math in school. Once I started self-learning programming and moved into machine learning and actually saw real world use cases for stuff I actually started enjoying it. Teaching for the lowest common denominator is horrible. Imagine if the US spent as much money identifying and helping high potential students as it does for special ed students. It sounds cruel but at my school there was probably a 10x better student to faculty ratio for special ed as opposed to general student population. Most of those kids will only ever work a minimum wage job, if that. Think if that was done for high potential students instead. Tremendous waste of financial resources and talent in the form of kids from poor families who could achieve so much more if put in the right environment. I know a lot of smart kids from poor families who fell by the wayside and are working dead end jobs instead of reaching their potential.

268 points by ginnungagap 8y ago

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 8y ago
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 8y ago
  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.
  - tenaciousDaniel 8y ago
    well said!
  - meko 8y ago
    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.
- Terr_ 8y ago
  I feel that's related to the mentality that if something was broken, and you do not know why it's working again, then it's not really fixed. This can be difficult to inculcate in new programmers as they try to tweak their way past error messages.
evincarofautumn 8y ago
In the past 7–8 years I’ve come around to the realisation that programming truly is a branch of mathematics, in a deep sense—and a strange one at that. It makes sense that they would share a lot of lessons. In my experience, those who say programming isn’t mathematics are usually mistaken about what math actually is. Or at least I know I was. I used to think math was about calculation, because that’s most of what I was exposed to in school—virtually every problem, even in higher-level mathematics, was brought back around to work with concrete values, perhaps in an effort to tie the problems to something “real-world” and get kids interested in it. But it had the opposite effect on me—that’s like saying programming is about making a machine do calculations! Yes, in a literal sense, but there are much higher-level, more abstract and interesting things at work there. To me, a computer’s value is that it’s an automated proving machine. You can make useful, entertaining, or interesting things happen in the real world—just by writing a proof that you can!

abnry 8y ago

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.

MadSudaca 8y ago

Great article.

joe_the_user 8y ago

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.

Smaug123 8y ago
I dunno, I'm objectively fairly good at maths (I got a first in the Cambridge MMath), but the reason I learned so much from the course was because I spent almost the entire time failing miserably to get anywhere on problem after problem. Sure, eventually you make the breakthrough - but only after hours of failure. Every avenue you try that doesn't work out is a frustration - often a blank-wall kind of frustration - and there are lots and lots of them before you succeed. Further, every avenue I try feels equally fruitful at the beginning, and frequently reaching the end is highly nontrivial even when you're on the right path, so "if it feels hard, you're on the wrong track" isn't a very easy thing for me to apply.
- joe_the_user 8y ago
  Well, the question I'd ask is whether you began approaching simpler math as being hard? Getting used to going up against brick to solve really hard problems is useful once you have a toolkit needed to solve those problems. But getting the relatively simple manipulations of the toolkit should be easy - and math undergrad work (at least at not super-advance school) is about putting together the toolkit.

wwweston 8y ago

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.

newen 8y ago
This is so true. I took a proofs class the second year (maybe semester idk) of my college and it was really illuminating. Before that class, language was just something I used to talk to people or to read stories. I don't think I really grasped the fact that language can be used for analysis or arguments before that class. I never read philosophy before that class so that could be it too.
yomritoyj 8y ago
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 8y ago
  "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 8y ago
    In the context of measure theory, a "non-negligible" set is a set with measure greater than zero.

tgb 8y ago

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.

waynecochran 8y ago

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).

Kagerjay 8y ago

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 8y ago
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 8y ago
  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.

joker3 8y ago

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 8y ago
This post might somewhat answer your question: 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 https://www.quora.com/What-is-it-like-to-understand-advanced...
- graycat 8y ago
  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.

baby 8y ago

Persistence is key.

bluecomp 8y ago

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.

paulpauper 8y ago

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 8y ago
Same applies to programming IMO.
- HiroshiSan 8y ago
  Same applies to drawing.

xstartup 8y ago

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 8y ago
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.
majos 8y ago
What do you do now?

czardoz 8y ago

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.

marsrover 8y ago

I got these same benefits from a Computer Science degree.

romwell 8y ago

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.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....

jdtang13 8y ago
Nice gatekeeping, friend. I've also personally never heard my math graduate student friends talk like this.
- haskellandchill 8y ago
  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?
  - tome 8y ago
    > How can I share that feeling inside my brain algebraically closed fields give me? Poetry.
    - haskellandchill 8y ago
      it was correct by construction stretchy compactness continuity we wrote numbers in the sand watched the glass dance of entropy against tired eyes until our vision blurred remaining only feeling legs crossed in a field blade of grass simplification is hard work it's clear there is no enemy but misunderstanding

daenz 8y ago

>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.

quasimodem 8y ago

Everything has to do with math.

mar77i 8y ago

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.

rdl 8y ago

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.

galieos_ghost 8y ago
yeah, I hated math in school. Once I started self-learning programming and moved into machine learning and actually saw real world use cases for stuff I actually started enjoying it. Teaching for the lowest common denominator is horrible. Imagine if the US spent as much money identifying and helping high potential students as it does for special ed students. It sounds cruel but at my school there was probably a 10x better student to faculty ratio for special ed as opposed to general student population. Most of those kids will only ever work a minimum wage job, if that. Think if that was done for high potential students instead. Tremendous waste of financial resources and talent in the form of kids from poor families who could achieve so much more if put in the right environment. I know a lot of smart kids from poor families who fell by the wayside and are working dead end jobs instead of reaching their potential.