[HN Gopher] Mathematicians Transcend Geometric Theory of Motion
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Mathematicians Transcend Geometric Theory of Motion
Author : theafh
Score : 93 points
Date : 2021-12-09 15:28 UTC (7 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| echopurity wrote:
| It's unfortunate that they omit Floer's suicide. Nobody wants to
| talk about the negative effects of a career in mathematics.
| sabellito wrote:
| You're saying that an article about "Mathematicians Transcend
| Geometric Theory of Motion" should also be about "the negative
| effects of a career in mathematics"?
| kevinventullo wrote:
| Are mathematicians statistically more likely to commit suicide?
| pizza wrote:
| Genius and dead at 34 - if you read between the lines, it said
| it all.
| moelf wrote:
| >Arnold predicted that every phase space of a certain type
| contains a minimum number of configurations in which the system
| it describes returns to where it started.
|
| is this article talking about Ergodicity without mentioning
| Ergodicity? https://en.wikipedia.org/wiki/Ergodicity
| ABeeSea wrote:
| All dynamical systems have a phase space and ones with the
| return property don't necessarily have to be ergodic.
| [deleted]
| revskill wrote:
| What if mathematical theorems are described by executable code
| instead of just symbols then ? Currently it seems impossible for
| reader to verify all theorems in a math paper.
| joppy wrote:
| This question seems to always come up on Hacker News - figuring
| out how to even formulate the statement of theorems in theorem
| provers such as Lean is a massive research undertaking in
| itself, requiring much creativity and novel work. Let alone
| figuring out how to formulate the proofs. I'd recommend you
| have a look at some of the talks that Buzzard has given on this
| to understand the complications (both technical and social) and
| progress that has been made so far.
| eigenket wrote:
| Currently transforming a new piece of maths from its "standard"
| form (i.e. what working mathematicians actually use) to
| something a computer can understand is a big task that usually
| takes a team of experts something of the order of years.
|
| Maths is really hard and proofs require a tonne of steps. For
| this reason mathematicians have to be comfortable jumping over
| the standard pedestrian intermediate steps in proofs and just
| focusing on the important stuff. This is necessary because
| including all the details would obscure the important stuff
| (imagine directions for driving somewhere with steps like "now
| walk up to the car", "now click the opener", "now open the car
| door", "now sit down in the drivers seat").
|
| Computers (currently) are way too dumb to skip these steps so
| you have to walk them through it.
| r-zip wrote:
| There are efforts in that direction:
| https://leanprover.github.io/theorem_proving_in_lean4/
| ABeeSea wrote:
| A major advancement happened this year where a recent paper
| from a fields medalist on an incredibly abstract topic was
| formally proved in Lean. The theorem was that Scholze's new
| condensed mathematics was logically consistent with real
| functional analysis.
|
| https://www.quantamagazine.org/lean-computer-program-confirm...
| del_operator wrote:
| Well, this is how I learned Manolescu left UCLA and is now at
| Stanford
| del_operator wrote:
| Also, yet another article that makes me rethink my choice to
| take Homological Algebra with no real algebraic topology
| coursework. Merkurjev was teaching so at least I have all his
| notes. It kind of forced me to give up any concrete basis and
| just handle abstract tools.
| ABeeSea wrote:
| If you already understand homological algebra, Peter May's AT
| book might get you where you want to be quickly. It's free on
| his website.
| mathematicaster wrote:
| good advice
| spekcular wrote:
| I urge you to read Hatcher's book (or better, tom Dieck's
| book published by EMS) immediately. I can't even imagine
| learning homological algebra without a bunch of concrete
| topological examples to compute with. That sounds confusing.
| xyzzyz wrote:
| Homological algebra without algebraic topology or geometry
| sounds like the driest possible exercise in pointlessness.
| wrycoder wrote:
| Tell them what you're going to tell them.
|
| Tell them.
|
| Tell them what you told them.
|
| The first and last parts are missing from this article. You have
| to take a gestalt approach and scan the whole thing to get an
| idea of what it's about.
| munificent wrote:
| I despise this structure and the kind of writing and
| presentations it tends to produce. The absolute worst, which I
| see all too often in presentations, is its fractal form:
| 1. Tell them that you are going to: 1. Tell them
| what you are going to tell them. 2. Tell them.
| 3. Tell you what you told them. 1. Tell them what you
| are going to tell them. 2. Tell them that now you will
| tell them what you will tell them. 3. Tell them.
| 4. Tell them that you are done telling them what you will tell
| them. 5. Tell them that you will tell them what you
| told them. 6. Tell them what you told them. 7.
| Tell them that you are done telling them what you told them.
|
| A structure I like much better which permits the above
| structure but allows other variations is:
|
| 1. Explain how to tell if this is worth their time.
|
| 2. Tell them.
|
| 3. If there was a lot, suggest what's worth remembering.
|
| The focus here is on _how it benefits the audience_ and not on
| some arbitrary structural form.
| blablabla123 wrote:
| It's also a trade-off between length of presentation or
| article in that case and amount of interesting content. Also
| I think Dynamical Systems are quite a mixture of theory and
| practical applications, so it makes sense to mix that.
| enobrev wrote:
| It seems you're suggesting the same strategy, and just don't
| like when it's done poorly.
| munificent wrote:
| Not at all. There are many ways to let an audience decide
| whether the rest of the material is worth their time.
| Summarizing to give them a preview is only one (and often
| the least interesting one).
|
| Other ways:
|
| * Describe a problem that the audience also has, so that
| they understand that you are aligned with them.
|
| * Tell an engaging anecdote so that they expect it will be
| a rewarding experience. (The idea that a piece of writing
| should entertain, inform, or persuade and that those are
| mutually exclusive is another canard that I find to be
| completely toxic and antithetical to good writing. Good
| writing should entertain, inform, _and_ persuade.)
|
| * Telegraph that the time investment will be smaller by
| getting started and making the overall thing shorter.
|
| * Describe previous failures to solve a problem.
|
| * Give them an interesting insight right off the bat, which
| implies there may be more to come.
|
| * Tell them something personal which conveys whether you
| are likely to be a person with interesting things to say.
|
| * Throw out a detailed, hard to acquire fact, which implies
| that you have other hard-won knowledge.
|
| Note that what all of these have in common is that the
| intro material _is unique_ and is not simply a pre-
| statement of information they will encounter lately.
|
| Also, the fact that I made step 3 optional is significant.
| Most writing and presentations don't need a summary and a
| summary will often detract. If you want to stick in the
| audience's memory, what you really need is a _climax_ , and
| "here's what I just said, said again" is about the most
| anti-climactic ending you can imagine.
| [deleted]
| crispyambulance wrote:
| It's an article and not a power-point slide. There's nothing
| wrong with the format.
|
| The outline you gave is more appropriate for slide-deck talks
| where the audience is captive and they're apt to be unconscious
| during the middle.
| adrianmonk wrote:
| The reason I'd like part 1 (tell them what you're going to
| tell them) is it helps me answer the question, "Is this
| relevant and interesting enough to me to spend the time
| reading it?"
|
| In a sense, I need part 1 _because_ I 'm not a captive
| audience. If this were (say) a lecture in a college class,
| then it's a foregone conclusion that I'm using the time, so I
| might as well pay attention.
|
| But since it's a web article, I have the choice to keep
| reading or close the browser tab. I'd prefer to be able to
| make an informed choice.
| canjobear wrote:
| It's also the standard for scientific papers.
| wisty wrote:
| I think science has the abstract (tell em what you'll tell
| em) then the body and a discussion which is more "OK, now
| that I got you're attention, here is what I actually think
| but can't prove".
| crispyambulance wrote:
| Right, but it's also not a scientific paper.
| eigenket wrote:
| That depends on the field, especially in areas of pure
| maths I see this "slide-deck" style way less.
| hprotagonist wrote:
| there isn't a universal standard for scientific papers.
|
| more's the pity.
| Ar-Curunir wrote:
| Science is a very broad term, and writing style varies
| between research groups, let alone between fields.
| rbanffy wrote:
| Sometimes the journey is its own destination.
| ABeeSea wrote:
| I like the way quanta writes their math articles and I hope
| they never go towards a stilted formulaic approach to writing.
| :shrug:
| smitty1e wrote:
| > The planet's position and momentum can be described by six
| numbers, three for each property. If you represent each of the
| different configurations of the planet's position and momentum as
| a point with six coordinates, you'll create the phase space of
| the system. In this case, it has the shape of flat six-
| dimensional space. The motion of a single planet can be
| represented as a line weaving through this space.
|
| Sounds like ephemeris?
|
| https://en.m.wikipedia.org/wiki/Ephemeris
| paulpauper wrote:
| I think the gulf between research math and teaching math is so
| wide that it may as well be a different subject altogether. The
| vast majority of mathematicians are teachers, not researchers. If
| all mathematicians have at the very minimum PHDs, then is the
| difference in ability so great?
| spekcular wrote:
| It's not so hard to get a PhD in math, in the sense that if
| you're willing to attend a low-ranked program and have at least
| a moderate affinity for mathematics, you could probably do it.
| It takes a lot of time to learn all the prerequisites, but
| that's why the undergrad degree is 4 years and the PhD
| typically 5+. Then you just find a suitable advisor, ask to be
| handed a dissertation problem and some ideas for the solution,
| write down that solution, and graduate. Anyone who's been doing
| math research for a few years has a collection of problems they
| know how to solve but haven't written up for various reasons,
| which they can give for this purpose. (Usually: the question is
| too boring or simple, no one cares, and there are bigger impact
| things to do instead).
|
| Doing research that meaningfully advances mathematics, as
| opposed to being make-work in service of getting a degree? Much
| harder.
| vecter wrote:
| I wouldn't consider someone a mathematician unless they were a
| researcher. Otherwise what does a mathematician do? Many people
| have undergraduate or advanced degrees in math, but most of
| them don't "do math" for a living (i.e. research).
| [deleted]
| physicsguy wrote:
| Same for most science - physics, chemistry, etc... I have a
| Physics PhD and I still wouldn't consider myself a physicist
| as applying the physics skills is not what I do day to day.
| bckr wrote:
| with a bachelor's in Biochem, in my head I say I'm formally
| trained in biochemistry. But iut loud I just say "my
| bachelor's was in biochem"
| mathematicaster wrote:
| often as large as a draft prospect and nba player with years of
| experience
| syki wrote:
| I was ABD in math at a top 25 program when I went to a talk
| given by a graduate student from Berkeley. He was in my area
| and we had the same length of them spent on the subject. As
| close to equals in terms of experience and area of study as one
| can get. He was far better than me and I knew that I'd never
| understand the subject as well as him. Shortly after I quit the
| Ph.D. program. I realized I would never do anything worthwhile
| in the field. There is a large variation in talent within the
| community of professional mathematicians. Outliers amongst
| outliers.
|
| In trained in MMA for a number of years and sparred against
| some local fighters. They were better than me but I could get
| some hits in. I could cause them to expend some effort. Once I
| sparred with a low level UFC fighter. He thoroughly destroyed
| me. It was like I was 5 years old. Outliers amongst outliers.
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