Mathematicians are chronically lost and confused (2014) • Hacker News Board

Re: Mathematicians are chronically lost and confused (2014)

#111

Post by agentultra » Fri, Jun 10, 2016, 8:26 PM UTC

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…

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.

Re: Mathematicians are chronically lost and confused (2014)

#112

Post by agentultra » Fri, Jun 10, 2016, 8:33 PM UTC

Nimitz14 wrote: post #51

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…

Yup. 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.

No, 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.

Re: Mathematicians are chronically lost and confused (2014)

#113

Post by j2kun » Fri, Jun 10, 2016, 8:42 PM UTC

justifier wrote: post #78

justifier wrote: post #66

Earlier quoted context omitted.

for 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…

shame.. i am passionate about discussing this topic but it is hard to 'engage' with unaccompanied downvotes

I 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.

Re: Mathematicians are chronically lost and confused (2014)

#114

Post by seanalltogether » Fri, Jun 10, 2016, 8:48 PM UTC

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…

I think this is why I enjoyed physics classes more then math classes. The formulas we were taught had a visible effect. I could watch the values transform to something I could physically confirm at each step. As a result the formulas became more obvious and therefore more memorable.

Re: Mathematicians are chronically lost and confused (2014)

#115

Post by vinceguidry » Fri, Jun 10, 2016, 9:04 PM UTC

throwawaysocks wrote: post #110

vinceguidry wrote: post #77

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…

> ...it doesn't matter how much formal education / training you get, you're still going to have to do a massive amount of self-learning before you can hope to achieve excellence. So I'm a self-taught programmer, and this attitude annoys the hell out of me. 1. EVERYTHING requires self-learning to be more than mediocre. In fact, the more I learn about other fields -- engineering, medicine, law -- the more I realize tho…

> Just because programming is simple enough that you can learn how to do enough to get a well-paying job before hitting 16 doesn't mean that people who go through a college degree aren't also doing a ton of self-learning alongside lectures.

If you read my statements carefully, I said exactly the same thing.

Re: Mathematicians are chronically lost and confused (2014)

#116

Post by jinfiesto » Fri, Jun 10, 2016, 9:21 PM UTC

yequalsx wrote: post #62

whynotqat wrote: post #58

Earlier quoted context omitted.

Certainly some that were active in the last 50 years, though it's hard to think of any that were trained in that time-frame: Gelfand and Ian MacDonald are the first pair that come to mind, though Gelfand had some great mentors and Macdonald did an undergraduate degree.

I did not know that about MacDonald. Thanks for pointing it out. Do you agree, though, that such examples are rare? The original premise is that in math it appears self taught is not really a viable route for all but a very small few.

If I'm not mistaken, Paul Lockhart was also self-taught. If I recall correctly, he met Ernst Strauss at some point, who introduced him to Erdos who then somehow managed to get him admitted to the graduate program at UCLA (he dropped out of undergrad). He had published before being accepted to graduate school.

Re: Mathematicians are chronically lost and confused (2014)

#117

Post by trentmb » Fri, Jun 10, 2016, 9:23 PM UTC

chris11 wrote: post #99

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…

How do you get the feedback necessary to check your learning? With programming you have techniques to check your work at some level. But that's not the case with math.

This is an issue I'm having- eventually there are no solutions manuals, and the people that can (or are willing) to answer my questions become few and far between on math.stackexchange.com

Re: Mathematicians are chronically lost and confused (2014)

#118

Post by justifier » Fri, Jun 10, 2016, 9:49 PM UTC

j2kun wrote: post #113

justifier wrote: post #78

Earlier quoted context omitted.

shame.. i am passionate about discussing this topic but it is hard to 'engage' with unaccompanied downvotes

I 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 att…

my desire to respond was instigated by this quote from the gp:

> 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.

my views:

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

Re: Mathematicians are chronically lost and confused (2014)

#119

Post by throwawaysocks » Fri, Jun 10, 2016, 10:23 PM UTC

vinceguidry wrote: post #115

throwawaysocks wrote: post #110

Earlier quoted context omitted.

> ...it doesn't matter how much formal education / training you get, you're still going to have to do a massive amount of self-learning before you can hope to achieve excellence. So I'm a self-taught programmer, and this attitude annoys the hell out of me. 1. EVERYTHING requires self-learning to be more than mediocre. In fact, the more I learn about other fields -- engineering, medicine, law -- the more I realize tho…

> Just because programming is simple enough that you can learn how to do enough to get a well-paying job before hitting 16 doesn't mean that people who go through a college degree aren't also doing a ton of self-learning alongside lectures. If you read my statements carefully, I said exactly the same thing.

You stated ...No good mathematicians (currently) are [self-taught]

The main thrust of my post was that all good Xs are self-taught, for all values of X.

That's the primary point of disagreement between us.

Lots of self-teaching happens within the confines of formal education. And almost all learning that happens outside of formal education is done via some form of instruction or another (books, tutorials, video lectures, etc.)

Re: Mathematicians are chronically lost and confused (2014)

#120

Post by agentultra » Fri, Jun 10, 2016, 10:29 PM UTC

mindcrime wrote: post #101

yequalsx wrote: post #82

Earlier quoted context omitted.

I have programmed professionally but that was a long time ago. In my limited experience I believe one advantage programming has over mathematics in terms of self learning is that in programming one is more likely to know that a program works/doesn't work versus knowing whether your conception of an abstract definition or theorem is correct. It seems overall easier to believe a false notion in math than in programming…

In my limited experience I believe one advantage programming has over mathematics in terms of self learning is that in programming one is more likely to know that a program works/doesn't work versus knowing whether your conception of an abstract definition or theorem is correct. I've often wondered if automated theorem provers (Coq and the like) could be useful for this. Sure, it requires learning Coq (or Agda or ACL…

Insanely useful. I believe it should be state of the art. Even model checkers are vastly more useful than nothing.