I no longer understand my PhD dissertation • Hacker News Board

Re: I no longer understand my PhD dissertation

#151

Post by datashaman » Mon, Feb 15, 2016, 7:11 AM UTC

closure wrote: post #11

This does not surprise me in the least. Math was always extremely easy for me growing up. Up through my first differential equations class I found almost everything trivial to learn (the one exception is that I always found proving things difficult). I made the mistake of minoring in math and that slowly killed my enjoyment of it. Once I got to differential geometry and advanced matrix theory it all just became too a…

The same is true of creative writing in general. I've found pieces from my years as a student, which seem to have been written by an alien.

Re: I no longer understand my PhD dissertation

#152

Post by rafekett » Mon, Feb 15, 2016, 7:14 AM UTC

nanis wrote: post #9

First, I am not sure Functional Analysis is as obscure as some other areas. But, second, this just shows, once again, that one ought never to use "clearly," "obviously" etc in proofs. It is the same principle as writing programs so they are easier for the next programmer to read. That person may be you.

it also leads to proof by intimidation which often masks errors.

Re: I no longer understand my PhD dissertation

#153

Post by jackmaney » Mon, Feb 15, 2016, 7:15 AM UTC

danieltillett wrote: post #150

This post inspired me to re-read my thesis (well browse through it). Although it has been 16 years since I last looked at it, I didn’t have any problem understanding it and I didn’t even really cringe reading it. I guess it depends on your field how bad this effect is.

I was about to write much the same thing... Last year, I found a hard copy of my dissertation (which I defended in 2004). I skimmed through it and had absolutely no problem whatsoever understanding what I had written 11 years prior. And I've been out of academia since 2008.

Re: I no longer understand my PhD dissertation

#154

Post by rekado » Mon, Feb 15, 2016, 7:20 AM UTC

phamilton wrote: post #76

jacobolus wrote: post #35

Earlier quoted context omitted.

V.I. Arnold: “Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of characters.”

I've always loved the idea that the academic disciplines form a cycle. Arts -> Social Sciences -> Life Sciences -> Physical Sciences -> Mathematics -> Arts Mathematics was/is a very creative process for me.

I very much like the related point Paul Lockhart makes in "A Mathematician's Lament"[1]: that mathematics is an art form and ought to be taught like one.

[1]: http://mysite.science.uottawa.ca/mnewman/LockhartsLament.pdf

Re: I no longer understand my PhD dissertation

#155

Post by sdenton4 » Mon, Feb 15, 2016, 7:40 AM UTC

JScarry wrote: post #91

vinceguidry wrote: post #52

Earlier quoted context omitted.

I started taking readability very seriously once I started going back to extend old code and finding I couldn't immediately understand what it was doing. Now, if I have that problem, it's now two problems. The original problem, and the readability problem. The readability problem is solved first, and the original problem can only be solved afterward. I don't see comments helping me, I could spend the time better by m…

I'm fixing someone else’s code right now and a few single line comments would have saved my client thousands of dollars. Today I put in a log statement to see why the code deletes data from the database if there is no new temperature data for the time period. The cron job has been running all day and so far every time it attempts to delete the data, there is no data to delete. Another line runs a different script if…

Deleting from any empty database could just be a sanity check. If it's logically supposed to be empty at a given time, it's a perfect time to clean up database errors...

Re: I no longer understand my PhD dissertation

#156

Post by peterbraden » Mon, Feb 15, 2016, 7:52 AM UTC

Could part of it just be because Mathematical notation is just so bad? It's more of a shorthand than an actual tool of conveying meaning. So much context goes into establishing what a notated equation means - and that context is now gone.

Re: I no longer understand my PhD dissertation

#157

Post by sdenton4 » Mon, Feb 15, 2016, 7:55 AM UTC

markus2012 wrote: post #93

marcosdumay wrote: post #41

Earlier quoted context omitted.

I've recently taken a calculus problem (multidimensional real optimization) I guess for the first time since I was an student. While your description has some merit, there's a huge amount of trivia in the format of "I can do X, I just have to do Y first", "X has no known solution, try something else", and "operation X is very useful, try it". That goes away, and everything gets way harder.

I've always felt that if I had done all of my calculus with Mathematica I would have left college with an excellent grasp on how to use higher level functions provided by Mathematica that would have largely abstracted away all of this. Of course, the higher level functions might get covered in cobwebs - but I suspect not the same way; I would have kept these higher level skills up to date because: - I recently went t…

Yeah, you should always, always code what you're thinking about, IMHO. I once turned in a take home differential geometry final in the form of an ipython notebook because I found computing curvature coefficients so tedious. Debugging the thing to pass all my unit tests (not to mention solving the test question) probably have me the best understanding of anyone in the class.

Re: I no longer understand my PhD dissertation

#158

Post by akie » Mon, Feb 15, 2016, 8:11 AM UTC

wfo wrote: post #141

csense wrote: post #14

TLDR: The author independently re-discovered what you may know as Old Code Syndrome. I think that's because mathematical papers place too much value on terseness and abstraction over exposition and intuition. This guy's basically in the position of a fairly new developer who's just been asked to do non-trivial update of his own code for the first time. All those clever one-liners he put into his code made him feel sm…

It would be really nice if all it took to understand difficult mathematics were some easy programming tricks. The problem with looking at old code is you forget what is going on or what the purpose of different components are. The problem with looking at old mathematics is that it is genuinely very difficult to understand. You work very hard to be an expert in a field and get to a level where you can read a cutting-e…

> Do you think perhaps there's a reason why a simple and easy trick like commenting and renaming lemmas has been discovered and solidified as standard practice in programming, but hasn't been adopted in mathematics? Are mathematicians really just SO dumb?

No, they aren't, but the example in question would have been easier to understand if he had tried to explain what was going on, instead of just saying "it is trivial that this or that follows". I think the comparison with "old code syndrome" is pretty much spot on, to be honest.

Re: I no longer understand my PhD dissertation

#159

Post by bambax » Mon, Feb 15, 2016, 8:14 AM UTC

> what is the purpose of studying maths? Mathematics is an excellent proxy for problem-solving / Mathematics embeds character in students / Mathematics is fun

Those may be reasons to study maths (although, studying anything seriously probably yields comparable benefits) but doing a PhD and writing a thesis is not only about yourself: it's supposed to advance the field. It's something you do for the general community.

Re: I no longer understand my PhD dissertation

#160

Post by z3t4 » Mon, Feb 15, 2016, 8:27 AM UTC

I've also forgotten basically all high level math from school. And have to re-learn when the occasion comes to use some of it. But one thing that occurred to me is that in school I just learned how to make the calculations, so I never got a deep understanding on how things worked anyway. And that's fine.