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Mathematicians are chronically lost and confused (2014)

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Re: Mathematicians are chronically lost and confused (2014)

#121

Post by naasking »

jondubois wrote: post #43

My favourite quote about Mathematics is from John von Neumann: "In mathematics you don't understand things. You just get used to them." - This quote highlights precisely why I ended up choosing software engineering over maths. I'm just not very good at applying processes/methodologies which I don't fully understand. For example, I wasn't very good with linear algebra until I was able to visualize the equations in my…

> "In mathematics you don't understand things. You just get used to them." - This quote highlights precisely why I ended up choosing software engineering over maths.

Haha probably the most unintentionally funny and ironic comment I've read in awhile. Given more than 50% of software projects fail, which is worse than chance, I think it's safe to say the no one really understands software engineering either. Like math, they just get used to doing some things that seem to work better than others.

Re: Mathematicians are chronically lost and confused (2014)

#122

Post by Retra »

agentultra wrote: post #111
yequalsx wrote: post #42

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'm not making any claims that I'm a self-taught prodigy. I know what I know and what my limitations are. I can sit through ONAG for fun, have worked my way through Concrete Mathematics and delve into TAOCP when I come across interesting topics, and work out the proof to (\Ax |: P => Q) === {x | P} \subset {x | Q} I'm not kidding myself that I can stand with the best of them and work on bleeding edge problems. The sp…

The point here is that people who do what you say very very rarely contribute to the field of mathematics in a meaningful way. You can "learn something" all day long every day for the rest of your life. Mathematics is vast. But that doesn't mean you're learning something that is both useful and not already known.

If your argument is "you can have fun pretending to know maths all by yourself" then fine. But that's not valuable to anybody.

Re: Mathematicians are chronically lost and confused (2014)

#123

Post by Retra »

stepvhen wrote: post #74
Koshkin wrote: post #59

Earlier quoted context omitted.

Actually, 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 . 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.

Ha, well then my class/texts have failed to mention these practical uses.

Sub-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.

Re: Mathematicians are chronically lost and confused (2014)

#124

Post by Retra »

IndianAstronaut wrote: post #22
vecter wrote: post #16

I have a great personal story that highlights how long the journey of understanding mathematics is. I took linear algebra my freshman year of college. It was the non-math major course, so it didn't require proofs. I got an A+ in the class. Not just an A, an A+. I was able to obtain such a high grade by taking tons of practice tests, and since the actual tests were basically mildly veiled calculations, I just had to m…

Math programs in general suck at telling you why a particular technique is useful in the real world, or more importantly, how to model. Lots of ways to solve an existing model, but very few touch the much harder task of building a model in the first place.

Students and parents are demanding that their education fees generate employable graduates, not creative or intelligent ones. This trend will probably continue as long as education keeps getting more expensive.

Re: Mathematicians are chronically lost and confused (2014)

#125

Post by petegrif »

yequalsx wrote: post #42
agentultra wrote: post #30

Earlier quoted context omitted.

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…

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…

Srinivasa Ramanujan

Re: Mathematicians are chronically lost and confused (2014)

#126

Post by akeck »

otoburb wrote: post #94
akeck wrote: post #83

Earlier quoted context omitted.

> 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).

Out 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.

Undergrad, 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. ;-)

Re: Mathematicians are chronically lost and confused (2014)

#127

Post by sn9 »

petegrif wrote: post #125
yequalsx wrote: post #42

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…

Srinivasa Ramanujan

50 years? No.

Re: Mathematicians are chronically lost and confused (2014)

#128

Post by agentultra »

Retra wrote: post #122
agentultra wrote: post #111

Earlier quoted context omitted.

I'm not making any claims that I'm a self-taught prodigy. I know what I know and what my limitations are. I can sit through ONAG for fun, have worked my way through Concrete Mathematics and delve into TAOCP when I come across interesting topics, and work out the proof to (\Ax |: P => Q) === {x | P} \subset {x | Q} I'm not kidding myself that I can stand with the best of them and work on bleeding edge problems. The sp…

The point here is that people who do what you say very very rarely contribute to the field of mathematics in a meaningful way. You can "learn something" all day long every day for the rest of your life. Mathematics is vast. But that doesn't mean you're learning something that is both useful and not already known. If your argument is "you can have fun pretending to know maths all by yourself" then fine. But that's not…

Am I to understand that "engaging with mathematics" is to mean that the only useful contribution anyone can make is furthering the state of the art? If that's the case then yes I can see why it's so rare.

However if we broaden the scope of contribution we can see people finding applications for theory in industry as useful. It is useful to revisit pedagogy in order to bring more people into mathematics. Even people who take the role of Martin Gardner and bringing mathematics to laypersons is a good contribution -- it gets people excited about the developments of mathematics!

What I have learned has improved my life and made my work better. I think that's useful.

update

I have an inkling as to how vast mathematics is. I realize I'm not going to be publishing any papers and most people who are self-taught will not either. It's not a goal of mine besides.

However I'll still take a stab at the Erdos-Sekeres conjecture of the convex n-gon from time to time. I realize someone else will solve it but what's the worst that can happen? It's fun and enjoyable and sometimes I wish there were more people who found mathematics as enjoyable as I do. And that it was more accessible.

Re: Mathematicians are chronically lost and confused (2014)

#129

Post by sn9 »

Retra wrote: post #123
stepvhen wrote: post #74

Earlier quoted context omitted.

Ha, well then my class/texts have failed to mention these practical uses.

Sub-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.

Number theory was a major field for centuries before people discovered there was a practical use for it.

Re: Mathematicians are chronically lost and confused (2014)

#130

Post by mrkgnao »

pixl97 wrote: post #44
jondubois wrote: post #43

My favourite quote about Mathematics is from John von Neumann: "In mathematics you don't understand things. You just get used to them." - This quote highlights precisely why I ended up choosing software engineering over maths. I'm just not very good at applying processes/methodologies which I don't fully understand. For example, I wasn't very good with linear algebra until I was able to visualize the equations in my…

>Any uncertainty can be quickly resolved by simply running some code. Until you have to interact with a black box of someone else's code. You can only be certain that the data you sent that particular time works, not that all possibilities of valid data work.

So etale cohomology? :P
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