Mathematicians are chronically lost and confused (2014)

Re:Mathematicians are chronically lost and confused (2014) by agentultra on Friday June 10, 2016 @04:26PM (#11879727)

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 sphere packing problem sounds really cool but it would probably take me quite a while to work my way up to really understanding it. But I believe it's possible if I don't fall into the trap of self-deception and work out the requisite material before digging into it. "Convince yourself," and all. That's what is so amazing for me.

It's important to not be afraid to admit you do not understand something. It's an opportunity to learn after all! And there are some of us who are voracious learners.

The point I was making is that mathematical literature is rich enough that it's possible for people with no formal training to engage with a topic and learn something from it. Maybe they could take cracks at interesting proofs. There's nothing in the field that says you cannot practice mathematics without a degree or license.

What I do disagree with is that the power of mathematics is the sole domain of the priesthood. I believe that anyone motivated enough can work their way through the material. Formal training would benefit those people, for sure, but it's not a prerequisite for enjoying, using, and engaging with mathematics.

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Re:Mathematicians are chronically lost and confused (2014) by Retra on Friday June 10, 2016 @08:34PM (#11881303)

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.

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Re:Mathematicians are chronically lost and confused (2014) by agentultra on Friday June 10, 2016 @10:29PM (#11881700)

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.

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