I kinda took that to the extreme when I was young. Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived haha.
I was the other way around. Only when I found utility in something could I finally grasp the subject properly.
I remember how I was taught derivatives and integrals in HS, I knew how to do them but I was confused as hell. I asked the professor and once explained some uses it all clicked into place.
> I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles.
I still find it easier to understand something if I understand it from the ground up instead of in an ad-hoc way. For example, I found it easier to reason about probability once I had seen a rigorous definition for what a probability distribution is. I guess the reason is that it gives me a way to sanity check my intuition.
I still struggle with the fact that in software development, you get hundreds of technologies thrown at you and you barely have any time to understand them all fully. It makes me sometimes feel not very confident in what I do. I feel that I could understand e.g. Kubernetes better, if I had real in-depth (not just superficial) knowledge about networking. A lot of the time I'm just missing crucial information like "what problem are we trying to solve?", "why does this technology work the way it works?", etc. Something like Kafka is another example.
> I would also have a hard time processing/registering something if I'm not able to derive it analytically from first principles.
This really resonates with me. I always had a really hard time with anything where I just had to memorize formulas, but I didn't have any issues if I could derive it myself. For this reason I actually struggled a lot more with algebra in HS than I did with calculus in college. I don't know if it's just the teachers I had growing up or if it's a more broad issue with how the curriculum is structured, but I didn't even realize you could derive things from first principles until I took calculus in college.
...Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived...
Hello, 'undergraduate me'.
"haha" indeed. The universe is still experiencing California-splitting [1], planet-slapping [2] spasms of laughter at my ... stupidity [3] (speaking only for myself, here, of course).
Exactly my experience! Can tell you how often I was on the brink of failing school/college because I wanted to derive as much as I could from first principles - under time pressure in an exam! I did myself no favors.
I now find I learn better by being the opposite - finding a problem to solve and using math as a tool.
I enjoy his 3B1B videos, but this talk did not resonate with me at all. I was good at math as a kid, but no part of my motivation came from "a desire to be seen as being good at it." If anything, many people looked at me kind of funny for being good at math, so I learned to play down my ability when necessary. Maybe it's just because I grew up in an earlier era, but being nerdy was definitely not cool when I was young.
The video resonated with me. Looking back I think that I studied pure math in further education because I thought that others perceived it as the hardest subject you could study and therefore would think highly of me for studying it. I think that motivated me much longer than Sanderson too, as I think it's the main reason I started my PhD in a topic that probably wasn't the most interesting to me. Along the way I developed an appreciation for the innate beauty of the subject but these days I find it much more rewarding to work on something that's useful to someone else no matter whether it's particularly easy or hard.
The sad thing about wasting your youth trying to be seen as smart or successful is that later in life you'll probably have much less freedom of choice in what to work on.
I grew up in the eighties when being nerdy wasn't cool, but math was something that people recognized as real, not a nerdy invention, even if it was weird and nerdy to enjoy it. Other nerdy pursuits like D&D or fantasy (or, at the time, computers) were seen as escapes for people who couldn't face the difficulties of the real world and had to invent easier worlds to live in where they could pretend not to be lame. By contrast, math was real and hard. Every kid in school had moments when they wished they were better at math. I was a weirdo and an outcast, but I was a weirdo and an outcast who had an ability that people recognized.
Being better at math to make up for being socially useless in every other way didn't take me very far, though. Once I got to a top ten PhD program and was surrounded by people who were just as smart, some of them much smarter, and I faced the likely reality of ending up at minor university cranking out trivial results to get tenure, permanently outed as a mediocrity, making minor contributions that did nothing to advance the real work done by brilliant people, I couldn't face years of hard work for that outcome. Now as a programmer I have zero prestige and negative social cachet, but I get to do useful work on educational software used in primary school classrooms.
I also grew up as a nerdy kid long before being nerdy was cool. All the nerdy kids I knew took a lot of pride in being smarter than the cool kids. Being good at math was just an extension of that. I actually didn't know playing down how smart you were was a thing until much later when some of the popular kids who I had just assumed weren't that bright went on to become engineers, or doctors, or one who went on to get a PhD in biochemistry. I know a few of them still and they all talk about playing down that side of themselves in order to blend in. It makes me feel pretty silly about how smug I was about my intelligence back then.
Being open about your motivations to yourself and others and identifying how that can help or hinder you is the real takeaway here, not the particular motivation discussed.
I personally appreciate the candor and his own story of growth in this subject.
I opened the video in the background and immediately recognized the person: the author behind the 3Blue1Brown YouTube channel. It has a long series of video regarding various mathematical topics which are rather accessible.
My favorite by far is a "proposal" for an alternate notation which makes much more sense and, if adopted, would make mathematics way less intimidating (Triangle of Power (2016), 3Blue1Brown - https://www.youtube.com/watch?v=sULa9Lc4pck ).
I'd give him a Fields medal (or at least an honorary mention of some sort) :-]
Note that the alternate notation was suggested by someone named "2'5 9'2" on the Mathematics Stack Exchange [1], and not by 3Blue1Brown.
Obviously, this should not take away from the amazing educational work that 3Blue1Brown has achieved, but the honorary mention would probably suffice :)
I'm a math professor with about a decade of teaching math. On the list of things that make math intimidating, for undergrads at least, the notation for powers, roots, and log, is very low. The "proposal" also ignores that
1. The kth root of x is often denoted x^(1/k);
2. We have convenient shortcuts for the square root and the natural logarithm;
3. Parentheses become a mess;
4. The notation for squares, cubes, etc. is deeply entrenched; does anyone really think that write "x triangle 2 above" (yup, it's a mess to write in ASCII) instead of x² or x^2 would make mathematics less intimidating to everyday people?
5. Having symbols, subscripts, prescripts, and superscripts above the symbol all strewn together is much more intimidating to anyone.
6. How do you nest them? Try to write down log_a(log_a(x)) to see what I mean.
I enjoy 3B1B's videos in general, but this one really only makes sense if you don't think too much about it.
I think his key point applies to many other fields. I'll summarize it as "evaluate the work you do, at least in part, on its utility to others".
I've heard of devs who were asked to solve simple problems, but went out to choose exotic and complex approaches because that tech is the latest new hotness (though not well tested). I'm sure there are other examples.
On the other hand, seeking prestige at the expense of personal satisfaction, say, by conducting research in an "interesting" or "important" area, may be seen as an altruistic means of furthering progress in that field, and seeking personal fulfillment through the knowledge that one is helping others may be seen as a form of self-indulgence.
That’s the beauty of helping others! It’s a form of self-indulgence which is entirely ethical. Normally “self-indulgence” carries with it a negative connotation. In the case of altruistic behaviors, it’s actually a positive thing
I have an incredible feeling that this quite short commencement speech is quite complete in its treatment of the subject of one’s relationship to career choices.
Utility, originality and personal appreciation of tasks are key parameters in order to find a fulfilling job.
Historically, mathematics that initially seemed to have little imaginable practical application later become core to various fields of physics and engineering - non-Euclidean geometry as developed by Gauss-Bolyai-Lobachevsky amd Riemann became the foundation of Einstein's general relativity, number theory became the basis of cryptography (to the likely dismay of GH Hardy), etc.
So keep plowing away, mathematicians, at whatever you want to, and don't be surprised if some applied science type picks up the results and uses them for something in the so-called real world (but don't expect many of us to check your proofs, no thanks, taking it all on faith is the norm).
This reminded me in part of the work of Francis Su on math and the virtues: math and human flourishing https://youtu.be/FTXhj-puDgw
Mathematical practice can be a means of achieving the various virtues, and ‘show up’ (or make us more sensitive to) our vices. Meaning that there is something inherently good in the learning and practice of math, for it to lead to more good and to manifest to us what is bad.
There's a small number of people I know who say in social contexts "I love math" but they come up blank when asked what fields they find beautiful. I find this correlated with narcissism and it makes me believe these people don't actually find math beautiful, but just like the idea of others thinking they do and want to assert that they're the smart person in the group.
Devil's advocate: they liked the little bits of math they were exposed to.
I don't know if there's a field i like. But there's something intoxicating in math. Sometimes it's very strong.
I listened to a CS lecture now and normally I find CS a bit boring but as he kept describing aspects of the problem he was facing (finding points in intersecting disks) and as the problem got more complicated I got the itch lol.
Sitting in a logic class is more exciting than a roller coaster. It's a bit scary because I don't understand why.
To me the perfect example of people who claim to "love math" but actually don't are people who wax endlessly about something like Category Theory (or non-classical logic), but they can't even define what a group is.
No disrespect towards any serious scholar of Category Theory or Constructivism.
I think you're being a bit harsh. I can barely do simple algebra right now but I like math. I liked my math classes in high school and college because it felt satisfying to both learn and solve problems. It felt challenging in a unique way that my brain had never been forced to do before. It felt good that I was above average at it and it felt good to understand something something that started off looking like gibberish.
You can love paintings without knowing anything about how to paint.
[+] [-] yantrams|2 years ago|reply
I kinda took that to the extreme when I was young. Used to loathe anything practical - experiments, programming, applied math etc cuz you know they weren't "pure" and engaging enough. I would also have a hardtime processing/registering something if I'm not able to derive it analytically from first principles. It felt like cheating if I have to use a formula without fully understanding how it was derived haha.
[+] [-] grugagag|2 years ago|reply
[+] [-] Tainnor|2 years ago|reply
I still find it easier to understand something if I understand it from the ground up instead of in an ad-hoc way. For example, I found it easier to reason about probability once I had seen a rigorous definition for what a probability distribution is. I guess the reason is that it gives me a way to sanity check my intuition.
I still struggle with the fact that in software development, you get hundreds of technologies thrown at you and you barely have any time to understand them all fully. It makes me sometimes feel not very confident in what I do. I feel that I could understand e.g. Kubernetes better, if I had real in-depth (not just superficial) knowledge about networking. A lot of the time I'm just missing crucial information like "what problem are we trying to solve?", "why does this technology work the way it works?", etc. Something like Kafka is another example.
[+] [-] importantbrian|2 years ago|reply
This really resonates with me. I always had a really hard time with anything where I just had to memorize formulas, but I didn't have any issues if I could derive it myself. For this reason I actually struggled a lot more with algebra in HS than I did with calculus in college. I don't know if it's just the teachers I had growing up or if it's a more broad issue with how the curriculum is structured, but I didn't even realize you could derive things from first principles until I took calculus in college.
[+] [-] agumonkey|2 years ago|reply
I'm still like that, albeit with some plasticity to avoid dying on my lonely rock.
[+] [-] tiffanyg|2 years ago|reply
Hello, 'undergraduate me'.
"haha" indeed. The universe is still experiencing California-splitting [1], planet-slapping [2] spasms of laughter at my ... stupidity [3] (speaking only for myself, here, of course).
[1] https://www.bbc.com/news/world-us-canada-48921915
[2] https://en.wikipedia.org/wiki/Tunguska_event
[3] https://archive.org/details/novicetomasteron0000mori_w1f1
[+] [-] freetinker|2 years ago|reply
I now find I learn better by being the opposite - finding a problem to solve and using math as a tool.
[+] [-] inimino|2 years ago|reply
[+] [-] munchler|2 years ago|reply
[+] [-] jebarker|2 years ago|reply
The sad thing about wasting your youth trying to be seen as smart or successful is that later in life you'll probably have much less freedom of choice in what to work on.
[+] [-] dkarl|2 years ago|reply
Being better at math to make up for being socially useless in every other way didn't take me very far, though. Once I got to a top ten PhD program and was surrounded by people who were just as smart, some of them much smarter, and I faced the likely reality of ending up at minor university cranking out trivial results to get tenure, permanently outed as a mediocrity, making minor contributions that did nothing to advance the real work done by brilliant people, I couldn't face years of hard work for that outcome. Now as a programmer I have zero prestige and negative social cachet, but I get to do useful work on educational software used in primary school classrooms.
[+] [-] importantbrian|2 years ago|reply
[+] [-] AnotherGoodName|2 years ago|reply
I personally appreciate the candor and his own story of growth in this subject.
[+] [-] hashar|2 years ago|reply
My favorite by far is a "proposal" for an alternate notation which makes much more sense and, if adopted, would make mathematics way less intimidating (Triangle of Power (2016), 3Blue1Brown - https://www.youtube.com/watch?v=sULa9Lc4pck ).
I'd give him a Fields medal (or at least an honorary mention of some sort) :-]
[+] [-] smokel|2 years ago|reply
Obviously, this should not take away from the amazing educational work that 3Blue1Brown has achieved, but the honorary mention would probably suffice :)
[1] https://math.stackexchange.com/questions/30046/alternative-n...
[+] [-] hfkwer|2 years ago|reply
1. The kth root of x is often denoted x^(1/k);
2. We have convenient shortcuts for the square root and the natural logarithm;
3. Parentheses become a mess;
4. The notation for squares, cubes, etc. is deeply entrenched; does anyone really think that write "x triangle 2 above" (yup, it's a mess to write in ASCII) instead of x² or x^2 would make mathematics less intimidating to everyday people?
5. Having symbols, subscripts, prescripts, and superscripts above the symbol all strewn together is much more intimidating to anyone.
6. How do you nest them? Try to write down log_a(log_a(x)) to see what I mean.
I enjoy 3B1B's videos in general, but this one really only makes sense if you don't think too much about it.
[+] [-] Turneyboy|2 years ago|reply
[+] [-] raverbashing|2 years ago|reply
Yes, that is noted by the 3B1B in the title
But yeah the asymmetry of operators in math is exhausting.
[+] [-] dwheeler|2 years ago|reply
I've heard of devs who were asked to solve simple problems, but went out to choose exotic and complex approaches because that tech is the latest new hotness (though not well tested). I'm sure there are other examples.
[+] [-] rahimnathwani|2 years ago|reply
[+] [-] 93po|2 years ago|reply
[+] [-] prvc|2 years ago|reply
[+] [-] zarathustreal|2 years ago|reply
[+] [-] 0wis|2 years ago|reply
[+] [-] photochemsyn|2 years ago|reply
So keep plowing away, mathematicians, at whatever you want to, and don't be surprised if some applied science type picks up the results and uses them for something in the so-called real world (but don't expect many of us to check your proofs, no thanks, taking it all on faith is the norm).
[+] [-] k__|2 years ago|reply
It's crazy what these two fields produce, but once I a while something useful comes out.
[+] [-] spicyusername|2 years ago|reply
His videos on mathematics are amazing.
[+] [-] seanc|2 years ago|reply
[+] [-] kurosawa|2 years ago|reply
Mathematical practice can be a means of achieving the various virtues, and ‘show up’ (or make us more sensitive to) our vices. Meaning that there is something inherently good in the learning and practice of math, for it to lead to more good and to manifest to us what is bad.
[+] [-] unknown|2 years ago|reply
[deleted]
[+] [-] jdeaton|2 years ago|reply
[+] [-] kandel|2 years ago|reply
I don't know if there's a field i like. But there's something intoxicating in math. Sometimes it's very strong. I listened to a CS lecture now and normally I find CS a bit boring but as he kept describing aspects of the problem he was facing (finding points in intersecting disks) and as the problem got more complicated I got the itch lol. Sitting in a logic class is more exciting than a roller coaster. It's a bit scary because I don't understand why.
[+] [-] Tainnor|2 years ago|reply
No disrespect towards any serious scholar of Category Theory or Constructivism.
[+] [-] 93po|2 years ago|reply
You can love paintings without knowing anything about how to paint.
[+] [-] jfbaro|2 years ago|reply
[+] [-] desertvrt|2 years ago|reply
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[+] [-] minionnn|2 years ago|reply
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