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To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to va
by laingc 10y ago
To me, this is about "mathematical maturity".
My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the way of formal education.
However, I truly believe that Mathematics is a discipline that is very hard to engage with outside of formal education - or at least nobody has really found a great model for doing so yet.
Learning Mathematics in a classical, structured way really does change the way you think. I notice a substantial difference even between those of my colleagues who entered industry straight after their Masters or even Bachelors, and those who completed Doctorates or even held postdoctoral positions.
In my opinion, it is this lack of mathematical maturity that makes the switch from general programming to scientific programming more challenging than the converse.
- okoksowhatis 10y agoThis is very well-written. The prosody of it illuminates the topic you're speaking about. Being so rare, I wonder what makes you different.
- agentultra 10y agoI disagree that mathematics itself is difficult to engage with outside of academia. There are some academic mathematicians who think mathematics has to be hard because it was difficult for them to understand. There are others for whom sharing their insights is more important than searching for new ones. I think that the set of mathematicians together have done a rather good job in the 20th century of producing mathematical literature and pedagogy that laypersons and the polymaths can understand. I skipped university when I was young due to circumstance. I still had a love for maths but couldn't pursue formal training. When I came around to programming as a career instead of odd-loner-hobby it was as you say. I was quite impressed with my ability to code circles around CS graduates who, for all their theory and training, weren't prepared for "coding in the real world." I never stopped studying mathematics. I've recently been going through temporal logics. If only more programmers were aware of the beauty of the proof of weak fairness. And its implications in system specifications. Where I can see formal training being useful is exposing you to subjects you were not aware of in short order. My experience has been more akin to the mansion metaphor. Where I encounter limitations or difficulties in my programming I look to maths for the right tool to simplify the task and ensure it is correct. So I agree about "mathematical maturity." I just don't believe it is exclusively acquired in an academic setting. I think some people have an inclination or awareness that pushes them to think this way.
- redcalx 10y ago> proof of weak fairness Interest piqued. Do you have a good link for an intro to this?
- yequalsx 10y agoNot knowing your level of mathematical insight and knowledge makes it hard to know if your belief about your mathematical talent is a self deception. I've never encountered anyone who understood typical second year graduate level mathematics without formal training. I know such people could exist. I've just never met any. I have met people who claimed to be self taught in mathematics and it was obvious that they didn't really understand the concepts though they were absolutely convinced they knew what they were talking about. Outliers exist. But have any good mathematicians been self taught in the last 50 years?
- Nimitz14 10y agoYup. He's probably just unaware of how difficult and vast math actually is. Reminds me of comments I've read from programmers talking about learning 'advanced mathematics': Linear Algebra. Lol.
- agentultra 10y agoNo, not completely unaware. I'm glad I've reminded you of something you find entertaining. I hope you discourage more people from learning something awesome.
- stepvhen 10y agoI think math is "easier" to learn while it still holds a clear practical value, up to calculus and linear algebra. Past that, when you start to enter the world of "pure" mathematical s, it can be muh more difficult. The practical value of earlier subjects allows a student or what have you to draw connections between what they already know and this new concept. Something like group theory however is more difficult to find a "use" for, outside of solving problems in your text book. There are some good texts out there for learning by yourself. I currently own 7 or so Dover Books on Mathematics, and I could understate my appreciation of them.
- throwawaysocks 10y agoMy experience was the opposite. The more practical Mathematics was too easy to hand wave through so no one ever bothers with proof. But then when something goes wrong or you're not sure whether a particularly complicated calculation makes sense, you're SOL without a real formalism to go on. I didn't really believe in calculus except on a case by case basis until after my first analysis course. I think the only reason the less formal mathematics courses seem easier is because the thing being studied is also dead simple and the calculations are easy. But that approach doesn't scale.
- Koshkin 10y agoActually, group theory is not a very good example of a theory that has no or few practical applications; see https://en.wikipedia.org/wiki/Group_theory#Physics https://en.wikipedia.org/wiki/Group_theory#Physics. In general, you would probably be surprised to learn how much of the modern mathematics (including category theory) has already made its way into theoretical physics and other sciences.
- stepvhen 10y agoHa, well then my class/texts have failed to mention these practical uses.
- Retra 10y agoSub-disciplines of mathematics don't blow up and become cornerstones of education if they don't have practical applications. Analysis, Topology, Algebra, Abstract Algebra, Linear Algebra, Statistics, Geometry... If something doesn't have a major practical use, it'll probably be named after somebody specific and studied in relative obscurity.
- tuckerman 10y ago(warning: studied Math in college, so don't know how that biases me in this discussion) I wonder if some of this is because of the number of jobs in industry for each discipline? There are a great many jobs available which nurture CS skills but I can't quite think of a job besides academia off the top of my head where that lecture in Toric Varieties I took would come in handy. Maybe its that there is a career/financial incentive to go deeper into CS but not mathematics?
- justifier 10y agofor me your comment is so sad to read mathematics is unconstrained by any desired artificial 'engagement' requirement engagement is as easy as acting on and developing an interest and i encourage everyone to engage with mathematics your attempts to create an artificial toll or make a case for one, especially in lieu of your argument being unsolicited from the contents of the linked article, is suspicious at best, and wholly detrimental at worst > very hard to engage with outside of formal education - or at least nobody has really found a great model for doing so yet this seems like contradictory logic.. you appear to be denying 'informal' students from using the same model you advocate from these 'formal' sources also i think you need to flesh out your definitions a bit.. what precisely do you mean by: formal education, outperform, general programming, scientific programming? you also seem to be setting up a logical fallacy in your attempt to define your thesis of 'mathematical maturity' > my colleagues who entered industry straight after their Masters or even Bachelors, and those who completed Doctorates or even held postdoctoral positions are you comparing a ~20 year old at their first job to a ~30 year old who spent thaer twenties in academia? have you tested your hypothesis by comparing others of similar time spent on the subject but lack receipts for the money they paid into the academic institution? are there anomalies present in your investigations? your argument seems to lack any substantial scrutiny, and this would seem to me to be the defining element of some such concept of an interest in mathematics 'maturing': devotion to rigor
- justifier 10y agoshame.. i am passionate about discussing this topic but it is hard to 'engage' with unaccompanied downvotes
- j2kun 10y agoI did not downvote your comment, but to me your comment seems to be building up a bunch of straw men, peppered with negativity. It also doesn't clearly communicate anything relevant that I can understand. The original commenter is noticing a difference of culture between the startup community and the academic mathematics community: the stereotypical attitude of startup folks is "establishment be damned," but that attitude doesn't seem to fare well when it comes to mathematics because the process of learning mathematics is so incremental. Disruption and the hackathon mentality won't help you learn math (in the author's opinion). Meanwhile you're nitpicking definitions that seem to me to already have satisfactory informal definitions with no need for that level of scrutiny. It doesn't add to the conversation in a meaningful way. What I can glean from your comment is that if you have the right attitude toward math, then none of the original commenter's points hold. And I think everyone agrees with that. It's just that the people being discussed don't have the right attitudes, so it seems mildly pointless to say "Well if only they had the right attitude!" The same statement applies to most discussions about human behavior. I sincerely hope this helps you communicate your views better in the future.
- Bahamut 10y agoHow much difference is there between those who entered industry after their masters and those who hold doctorates? I personally haven't encountered much of a difference as a masters holder (spent 4 years in graduate school though, 2 to finish the masters, and 2 in a math PhD program before leaving), but I also haven't worked with many PhD holders.
- throwawaysocks 10y agoMy experience: not all masters degree holders are created equal. There's a big difference between people who leave a funded phd program early with a masters, and people who enroll in a terminal masters program. Especially if the terminal masters program was a "professional", non-thesis program. But there's much less difference between people who leave a Ph.D. early with a masters and those who stick it out.
- akeck 10y ago> Learning Mathematics in a classical, structured way really does change the way you think Yes! I bashed my way through an Applied Math degree in night school. It hurt my head, but it rewired my thinking permanently (for the better).
- otoburb 10y agoOut of curiosity, a graduate or undergrad applied math degree? Contemplating embarking on a similar path myself in a few years after I have the requisite background courses.
- akeck 10y agoUndergrad, 10 years, one class at a time. I swore off night academics afterwards, but... now I'm feeling the itch again to do a math graduate degree. My wife isn't pleased. ;-)
- nitwit005 10y agoI've seen some examples that don't seem to agree with that. Programmers often don't need advanced math, but the ones that do, such as video game engine developers, seem to get fantastically good at it. You need a lot of time to master any skill, and few jobs provide that for mathematics. At least, not with any diversity in problems. The degree provides some years of dedicated effort.