[HN Gopher] An Infinitely Large Napkin [pdf] (2019)
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An Infinitely Large Napkin [pdf] (2019)
Author : Qision
Score : 162 points
Date : 2025-02-10 11:51 UTC (3 days ago)
(HTM) web link (venhance.github.io)
(TXT) w3m dump (venhance.github.io)
| perihelions wrote:
| https://news.ycombinator.com/item?id=20168936 (2019, 33 comments)
|
| https://news.ycombinator.com/item?id=30302291 (2022, 18 comments)
| gcr wrote:
| Is there a version of this with narrower margins? I can't see
| well and need larger fonts
| dlazaro wrote:
| TeX source is available if you want to modify the styling
| yourself: https://github.com/vEnhance/napkin/
| fbn79 wrote:
| How many of you upvote this pretenting to find some day the time
| and spirit to read and learn from it, but perfectly knowing that
| will never happen. I'm one of them unfortunally, gosh!
| Komte wrote:
| I feel attacked
| bheadmaster wrote:
| No. Nuh-uh. Not me. I'll _definitely_ find some time to read
| and work through this. As soon as I finish a few of these
| things I still have on my TODO list... Just a few more days...
| gorlilla wrote:
| You said that a few days ago.... And a few before that... And
| a few....
| JadeNB wrote:
| > You said that a few days ago.... And a few before that...
| And a few....
|
| Aha, so already they're studying induction.
| cwillu wrote:
| <clicks download, notices the filename is Napkin (1).pdf>
|
| Last time was Feb 11 2022 :D
| Vox_Leone wrote:
| Glad to know it is not only me. The things is we got to have
| some kind of discipline, and this one deserves my commitment.
|
| ps. That diagram is just fantastic.
| Mithriil wrote:
| I'm reading it while waiting for the compiler.
| Out_of_Characte wrote:
| This quite literally points out a thousand things I havent fully
| understood about mathematics in a concise manner.
| jcmontx wrote:
| I'm too dumb for this, and how popular it is here gives me
| anxiety
| BobBagwill wrote:
| It's math about math. FTFW. You're welcome! :-;
| kira0x1 wrote:
| me and you both
| tanseydavid wrote:
| careful with the grammar there </sarc>
| Vaslo wrote:
| That first equation(statement? not sure what to call it?) in
| part 6 was enough to close it and say it's not for me. This is
| written for a very small group of people to understand and
| enjoy.
|
| So to those who do enjoy it, have fun!
| reikonomusha wrote:
| This document reminds me of the kinds of things I wrote at a
| smaller scale when I'd self-teach math. The usual pattern was:
|
| Step 1. I don't know how X works.
|
| Step 2. I collect several sources about X and try to understand
| it.
|
| Step 3. I put in a lot of effort to understand X by reading all
| these sources repeatedly. I try to do exercises, do calculations,
| etc. I'm desperately seeking the moment it "clicks".
|
| Step 4. I finally kinda sorta "get" X.
|
| Step 5. I feel, "why didn't anybody simply explain X in _this_
| way? " / "why was everybody so overly formal?" / "why was
| everybody so overly informal?"
|
| Step 6. I'm motivated to write a short note about X that makes it
| (allegedly) easier to understand X.
|
| Step 7. I write it, and I realize it's actually hard to weave
| together a narrative that doesn't over- or under-assume
| prerequisites, that captures nuance, that has good examples, etc.
|
| Step 8. "There are 15 competing standards."
|
| Step 9. Find the next topic X and go back to Step 1.
|
| The Infinitely Large Napkin is a really cool consolidation of a
| ton of undergrad/early grad pure math topics. It's so incredibly
| expansive in its scope and, if it were in book form, I'd have
| been ecstatic to have it as a 16 year old.
|
| But paging through it, I find that they're very much in the style
| of quasi-formal lecture notes. A lot of topics are mentioned by
| their formal definition, and it's followed by a very anemic (if
| any) discussion, sometimes preceded by a very informal (sometimes
| humorous) introduction. Often such definitions are immediately
| followed up by a relatively technical exercise that presumes a
| fully synthesized understanding of material preceding. This can
| make it very difficult to learn from as a primary/sole source. It
| does make it fun to flip through, though, when you already have
| familiarity with the topics.
|
| In my view, this isn't the kind of book you work through. It's
| not "math distilled". Instead, it can serve as a great diving-off
| point for a new subject, or an inspiration to know where to look
| further on a given subject, or even a useful document to find a
| topic that piques your interest. Other books like this are those
| of yore that were encyclopedic in nature, such as:
|
| - VNR Concise Encyclopedia of Mathematics (1975-1989) edited by
| Gellert et al. The math here doesn't get terribly advanced
| (complex and numerical analysis), but it's a good, expansive
| treatment to dive into.
|
| - Mathematics From the Birth of Numbers (1997) by Jan Gullberg:
| This is another grand tour of math, albeit "only" to differential
| equations. It's refreshingly written by somebody who was a
| surgeon/anesthesiologist and amateur mathematician.
|
| - The Princeton Companion to Mathematics (2008) edited by Timothy
| Gowers. This is a massive book that covers just about everything,
| up to and including some of the latest problems in mathematics.
| It's 1000 dense pages. (There's also the Princeton Companion to
| Applied Mathematics edited by Nicholas Higham.)
|
| - The CRC Encyclopedia of Mathematics (1999) by Eric Weisstein.
| This is an anti-digitization of the Wolfram MathWorld into book
| form. Expansive, and also famous for some of the drama around its
| copyright. :)
| JadeNB wrote:
| In theoretical CS, I've seen Steps 4-8 called "the monad
| tutorial fallacy."
|
| https://byorgey.wordpress.com/2009/01/12/abstraction-intuiti...
| kazinator wrote:
| Delimited continuations are just a green fork; it's
| childishly simple!
| quietbritishjim wrote:
| This reminds me of All the Mathematics You Missed (But Need to
| Know for Graduate School), which is a nice brief introduction to
| various undergrad maths topics
|
| https://www.amazon.co.uk/All-Mathematics-You-Missed-Graduate...
| mclau156 wrote:
| Is Github becoming the best place to host pdfs nowadays?
| trevithick wrote:
| > The _Infinitely Large Napkin_ is a light but mostly self-
| contained introduction to a large amount of higher math.
|
| > light
|
| 1,044 pages.
| r0uv3n wrote:
| This is a fantastic resource, and I used it heavily in 2018
| before starting my BSc in Math while still in school to learn the
| stuff that interested me a bit in advance (and to some extent as
| a familiar reference for a few years afterwards).
|
| I can only recommend this as a good starting point for anyone
| without the time for a full scale education, or in preparation
| for such, especially if you have some experience with math
| olympiads (as mentioned also in the introduction).
|
| I only wished I had spent some more time with stuff like category
| theory before starting my studies, and had had the guts to take
| more advanced courses directly in my first semester.
|
| With just a bit of prep from these notes I'm pretty convinced
| that it's possible to directly take e.g. Algebraic Topology,
| Differential Geometry, Category Theory, or Algebra during the
| first semester (don't know about number or measure theory, or
| anything requiring lots of functional analysis, have not engaged
| enough with those topics to know how good these notes would be as
| prep).
| skrebbel wrote:
| > With just a bit of prep from these notes I'm pretty convinced
| that it's possible to directly take e.g. Algebraic Topology,
| Differential Geometry, Category Theory, or Algebra during the
| first semester
|
| Why is it important/useful to take advanced classes so early
| on?
| mauvehaus wrote:
| Technically, napkin is a diminutive of "nape" with the suffix
| "kin" meaning small[0]. So really the title probably ought to be
| "An Infinitely Large Nape". Unless the author is going for an
| oxymoronic use of napkin like "jumbo shrimp".
|
| [0] https://www.etymonline.com/word/napkin
| redherring22 wrote:
| We do not speak Middle English.
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