91–100 of 147 posts
What are you supposed to do if you like math and the idea of grokking it, but you also have a job and a family and can't afford to spend six months contemplating each room in the mansion?
> Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark... What are you supposed to do if you like math and the idea of grokking it, but you also have a job and a family and can't afford to spend six months contemplating each room in the mansion?
Learn to come to grips with the idea that the universe isn't always going to support your mutually exclusive preferences?
Earlier quoted context omitted.
Not 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…
> 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. This is an interesting contrast with my experience with learning programming, where, it doesn't matter how much formal education / training you get, you're still going to have to do a massive amount of self-lea…
I think that may be because, in mathematics, it's hard to "follow the thread". For example, while programming, you can take a program (or a technique) and start reading the code, following links on Wikipedia, and you will eventually catch on. That is, you can do a top-down approach without many problems.
However, doing that in mathematics is way harder. It's not easy to take a paper, read it and start searching for concepts you don't know in Wikipedia: they usually require other base concepts and ideas which are not easy to understan. Sometimes those concepts are not even mentioned becauase the author just expects every mathematician in the field to know them, but to the layman it just looks like magic.
So in maths you need a bottom-up approach, and that's hard to do alone. You need someone to tell you what to study next and why, teaching you the applications and the related fields. Doing it alone is way harder than in the university.
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 w…
> 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).
> Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark... What are you supposed to do if you like math and the idea of grokking it, but you also have a job and a family and can't afford to spend six months contemplating each room in the mansion?
> What are you supposed to do if you like math and the idea of grokking it, but you also have a job and a family and can't afford to spend six months contemplating each room in the mansion? Learn to come to grips with the idea that the universe isn't always going to support your mutually exclusive preferences?
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 w…
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.
A mathematician was walking home from campus one day, and as he walked he was pondering a particularly thorny problem. At one point, he snapped out of his reverie and looked around and realized that he had no idea where he was. He saw a young boy playing with a ball in a yard, and figured maybe the boy could tell him the way home. So he says to the boy, "young man, do you know where Prof. So-and-so lives?" The boy lo…
This story is usually told about Norbert Wiener and his daughter.
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 w…
I 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 mathem…
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 w…
I 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 mathem…
Earlier quoted context omitted.
> 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. This is an interesting contrast with my experience with learning programming, where, it doesn't matter how much formal education / training you get, you're still going to have to do a massive amount of self-lea…
Simple profit incentives. You can't really make a living off of being a self-taught mathematician, whereas you can by knowing how to program, and run your own business. The only way to make a living as a mathematician is to into academia, so that why you see all mathematician in academics. Basically it isn't that academia produces mathematician, although it helps, but that it attracts mathematicians. Just as, say, Y-…
I would guess the more applied math you care about / the closer to software your math is, the better you can do as a self-taught. I actually know of one guy who transitioned from an engineering ph.d. to teaching applied math doing self-taught / working on fluid dynamics in aerospace, but I expect the examples of someone doing this in more abstract / pure areas are extremely few.