[andrepd]

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor.

* 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overexcited exclamation marks).

[sorry if I am being blunt, but it's how I feel]

* Imprecise definitions. This defeats the purpose of learning mathematics. Like Leslie Lamport says, rigour in mathematics is not a hurdle or a chore one must endure, it's the whole point of learning the damn thing. You give imprecise definitions, and then obscure it even further with neverending paragraphs of confusing explanations. This to me kills the whole pedagogical value the book might have. Here is a rule of thumb that in my experience applies well to almost everything in mathematics: the simpler your explanation is, the better. Your goal is to explain a concept as succintly and beautifully as possible. This exposes the idea behind it. A long and meandering explanation only serves to obscure the idea behind. Less is more.

* Attempting to shoe-horn programming "lingo" into mathematics. Sometimes, the best way to explain something, even to programmers themselves, is not to force an awkward analogy with Java programming. EDIT: 5 pages later: "The best way to think about this is like testing software." oh boy...

* The graph in e.g. page 8 (20 of the pdf) is terribly typeset. The axes text is way too small to read and in a font that doesn't match the rest of the content.

[adrianmonk]

Regarding the first point, if you are the type of person who just wants it to get to the equations with a minimum of talk, you're probably not the intended audience of this book.

The culture of mathematics (including its lingo) has always been a big barrier for me. Thus far, I've only skimmed it, but that part looks promising to me.

It seems reasonable to guess that if someone has learned a good bit about programming but managed to avoid learning about math, reasons like culture, terminology, accessibility, and motivation might be a big part of why. So including that sort of material in this book makes sense to me.

[andrepd]

Regarding the first point, if you are the type of person who just wants it to get to the equations with a minimum of talk

I don't want "no talk" and "just equations, I want the "minimum of talk possible" that communicates the ideas and nothing more. I find the more stuff you write the more there is to confuse people. The best way is to strip everything that is superfluous. You are left with the essential, in the clearest form there can be.

[sn9]

Math books already exist for that audience.

Indeed, most of the canonical texts for undergrads would likely fit the bill.

[westoncb]

There is a common category of misguided book review that the parent comment falls under: the reviewer has some particular things they are looking for from a book and fails to see that there are more uses for it than their own; so they generalize, reading the book's failures to meet their personal criteria as a failure intrinsic in the book's content, and mistakenly lambaste the work.

> 19 pages of droning before you start with something concrete.

One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things. I can offer another perspective that what the author wrote on polynomials within the first 19 pages there is in fact pretty unique and interesting.

> Imprecise definitions. This defeats the purpose of learning mathematics.

The commenter is again taking a minority viewpoint and baselessly extending it. There is a special kind of paranoia that often manifests in discussions of mathematical pedagogy that any departure from perfect rigor will weaken the minds of students. This is a blatantly shallow and one-sided view of things: the fact that rigor has value does not imply that the most effective method of teaching—which is a matter of both mathematics and human psychology—is to offer nothing but the most rigorous presentation possible.

This particular book is explicitly targeted at helping to transition programmers into mathematics. Given that goal, do you really think the pedagogically superior approach would be to offer a more rigorous definition of polynomial than:

"A single variable polynomial with real coefficients is a function f that takes a real number as input, produces a real number as output, and has the form: f(x) = a0 + a1x + a2x^2 + ... + anx^n"

—in the introductory chapter of the book?

I would urge potential readers to take the parent comment with a grain of salt. And also, if you're among this book's target audience and trying to teach yourself mathematics, be aware of such personalities preaching this particular dogma of mathematical instruction: it's fairly common on the internet. But it basically represents the same corner of the mathematics world as that of the programming world where folks insist on using nothing but VI/Emacs on Linux with C++ and/or Haskell, and are all too ready to belittle any alternatives perceived as softer/weaker. These aren't necessarily the most impressive programmers—they just project the most intimidating auras. Don't let their counterparts in mathematics scare you off.

[andrepd]

>One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things.

You are absolutely correct in that regard. I've talked to many people who hated the textbooks I most liked, and preferred ones that I found unreadable. Just goes to show that what works for you may not work for me.

You are very wrong on the other point: none of what I said is borne out of a view that mathematics should be difficult and "hard" an impenetrable (rather than soft and approachable). Indeed I view this sort of overlong prose as impenetrable and confusing, and the succinct style of e.g. Landau textbooks much clearer (see my other comment).

>The commenter is again taking a minority viewpoint and baselessly extending it.

This is not a minority viewpoint. I'd daresay is the majority opinion among mathematicians. It is also the opinion of prominent computer scientists: Dijkstra, Leslie Lamport, Donald Knuth, to name a few off the top of my head.

It is also plainly true: mathematics is about rigour. It is not an obstacle, nor is it an end in itself, but it is a fundamental part of mathematical study and reasoning. If you aren't being rigorous, you're not doing mathematics, it's just a waste of time. I'll let Michael Spivak speak for me:

"In addition to developing the students’ intuition [...], it is important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions."

>be aware of such personalities preaching this particular dogma of mathematical instruction: it's fairly common on the internet. But it basically represents the same corner of the mathematics world as that of the programming world where folks insist on using nothing but VI/Emacs on Linux with C++ and/or Haskell

Completely nonsensical comparison (C++ and Haskell?? two languages who could not be further apart), and again, not in the least bit what I mean with my criticism.

[westoncb]

> I'd daresay is the majority opinion among mathematicians. It is also the opinion of prominent computer scientists: Dijkstra, Leslie Lamport, Donald Knuth, to name a few off the top of my head.

There are reasons partly historical and partly due to the subject matter of CS that mathematicians closer to it tend to place relatively higher value on formality.

> It is also plainly true: mathematics is about rigour.

This is taking taking it too far and you're placing yourself in the formalist camp, which is a minority viewpoint. You gave a nice quote from Spivak where he characterizes rigor, "...the natural medium in which to formulate and think about mathematical questions."

Labelling it a 'medium' is very informative. Computer programs likewise depend totally on the formality of the medium; it's in intrinsic part of how they are able to operate. Same with the magic of formality + inference in mathematics.

That said, the psychological questions of pedagogy involve much more than the intrinsic features of some subject. In learning to write completely formal computer programs, one benefits immensely from instruction which departs from total formality. I'm assuming this would be obvious to the readership here so I won't go into more detail.

> Completely nonsensical comparison (C++ and Haskell?? two languages who could not be further apart)

I was referring to the social standing of the languages (which is all that matters for the points I was making), not their intrinsic features.

[sn9]

I'm sure the author would have liked for you to enjoy his book, but if you've already read Spivak and Landau, then you are most definitely not his intended audience.

Your criticism is like that of a professional mathematician complaining of the elementary results presented in some high school math book.

[mlevental]

wtf is wrong with hn.

>[sorry if I am being blunt, but it's how I feel]

you should learn to keep your feelings to yourself when the only function they serve is to denigrate others and derive cruel satisfaction for yourself.

>Here is a rule of thumb that in my experience applies well to almost everything in mathematics

this is aspirational pretension - everyone claims to appreciate formal purity /after/ they've learned something but when you're /learning/ none of that matters because you're just trying to develop intuition. to be one of those people that understands after their own stumblings/ruminations and then begrudge the next person the same is despicable. shame on you and i hope you're never in a position where someone depends on you to teach them absolutely anything.

>Imprecise definitions. This defeats the purpose of learning mathematics. Like Leslie Lamport says, rigour in mathematics is not a hurdle or a chore one must endure,

but that's just like your opinion man (or leslie lamport's). there are shelves and shelves of books for people like you - go read bourbaki or rudin or mochizuki or whomever you'd like. this book is not for /you/ - it's stated purpose is to excite and entice people that don't have formal mathematical training to learn mathematics and those sorts of people decidedly don't enjoy austere definitions and succinct theorems and terse proofs.

hence the only purpose your comment serves is to hurt the author's feelings, an author whom i might add has done infinitely more for the math community than you have with your pedantry and vitriol by maintaining a blog https://jeremykun.com/ with literally reams of interesting mathematical content that is simultaneously exciting /and/ rigorous. and furthermore iirc jeremy was originally a math ed phd student so i trust his opinion of the right way to teach math infinitely more than i do yours mr random internet physics guy.

next time think twice before posting this kind of lowbrow mean shit.

[tptacek]

This was close to being a great, meaty comment, but personalizing your criticism kind of ruined it. Which is too bad! I’m inclined to agree with the substance of what you’re saying.

[hyperpallium]

https://news.ycombinator.com/newsguidelines.html ("Guidelines" link at bottom of every page)

> In Comments

> Be civil. Don't say things you wouldn't say face-to-face. Don't be snarky. Comments should get more civil and substantive, not less, as a topic gets more divisive.

> When disagreeing, please reply to the argument instead of calling names. "That is idiotic; 1 + 1 is 2, not 3" can be shortened to "1 + 1 is 2, not 3."

[hyeomans]

I'm grateful for OP opinion and your opinion. I agree with you except in "next time think twice...", I think that opinion trigger your response which was great!

Enjoy your weekend, both of you!

[j2kun]

It's funny, because I discuss Lamport's view in the book as well in a later chapter. I think some folks are annoyed that the first chapter is slow, but I promise it ramps up :)

[krick]

As far as I can tell, you are what's wrong with HN. His post is a well-justified opinion, with reasoning provided, whether you chose to agree or disagree with that. Somebody may (or may not) take it into consideration. Yours are simply "how dare you!"-post, adding absolutely no value to the discussion. Also, learn capitals, it's hard to read you like that.

[mlevental]

there is zero justification in the post I responded to outside argument from authority and prescription so i have no idea what you're talking about

[andrepd]

I have not one single time invoked any kind of authority to make the points I'm making. It was only below, after you've (ironically) invoked the writer's credentials and insultingly proclaimed I never should be allowed to ever teach anything, that I let you know my qualifications.

[twtw]

Erm...

> Like Leslie Lamport says

Pretty clear appeal to authority, IMO.

[andrepd]

20 lines of reasoning and one quote that I think conveys what I mean. I think if you can't honestly engage with that besides accusing me of "appeal to authority" there is nothing to be gained from continuing a discussion.

Btw it's actually Lamport quoting Spivak.

[theoh]

"wtf is wrong with hn"

One thing that's wrong with HN is that perceived "negativity" often gets condemned in exactly the way you have done here.

It seems as if a significant number of HN readers have never really participated in a spirited discussion with arguments made from multiple different perspectives. Maybe any kind of apparent conflict scares them, maybe they project their own aggression onto a comment that seems to go against the grain of the discussion. It will never change.

[axiometry]

There are many easy ways to rephrase OP's comment into one that isn't so direct and denigrating. The only thing "apparent" here is that OP has trouble with empathy.

[posterboy]

What's the problem, too much empathy? I mean, if the opposite of empathy is appathy, then I don't see that in the OP.

[fmoralesc]

The opposite of empathy is antipathy.

[andredz]

The opposite of antipathy is sympathy.

[andrepd]

"Direct", yes. "Denigrating", how?? I'm genuinely asking so I can fix that in the future, unless you think criticising is offending.

>The only thing "apparent" here is that OP has trouble with empathy.

Again, I can do without the online pretend-therapy. Amazing how perceptive some people are that they deduce the most profound things from a dozen lines of text!

[hyperpallium]

I wanted to say I found your original comment critical, but not offensive. But I found the reply made to you offensive, because personal and aggressive. Which I think is how you see it too.

However, it seems several people took the side of the replier.

So I reviewed your original comment, and I think I've found the problem: it exaggerated and labelled, e.g. droning, talk talk talk, talking about nothing, neverending paragraphs.

Many of these aren't literally true ("nothing", "neverending"). Others are emotionally loaded ("drone"). It's probably almost always better to speak directly, without exaggeration or emotion... but this is particularly important when criticizing.

I didn't notice these at first because I tend to filter out decoration, and just hear the content (i.e the literal meaning) - though this is much easier to do when I'm not personally involved!

I think, "to be blunt", to speak plainly, to get to the point, really mean to be factual and accurate - without emotional language, exaggeration or labeling.

Anyway, I notice dang asked to not continue this thread, but I was troubled by it, and reviewing it helped me - maybe it will help you too.

[mlevental]

Maybe you should take a hint huh? If many people are telling you something about yourself (a subject you're inexorably biased on) you think maybe you should reconsider your position?

[andrepd]

>wtf is wrong with hn.

I believe you must have mistaken me for someone else. My name is andrepd. Is this "hn" a friend of yours?

>you should learn to keep your feelings to yourself when the only function they serve is to denigrate others and derive cruel satisfaction for yourself.

It never ceases to amaze me how some people are so perceptive that they can confidently deduce the intentions and personality of a person half a world away by reading a short text online. Are you available for therapy sessions? I could use your valuable insights.

Also, I was under the impression that I was making constructive criticism. I made concrete points and showed examples of books that in my opinion did those things right (see my other comment). I regret the "very very poor" phrase at the start though. I've changed it to just "poor".

>everyone claims to appreciate formal purity /after/ they've learned something but when you're /learning/ none of that matters because you're just trying to develop intuition

Oh, I see you know more about how I felt learning stuff than I do myself! Lovely.

I can tell you that I found it was almost always reading the most succinct treatments that I truly understood the greatest insights. Although from your tone I suspect that none of this will make a difference about how you feel. I won't repeat myself. You can (re)read my other comments if you're interested (and if you find I didn't explain myself well I'd be happy to discuss it more), and also check the examples I've mentioned.

>shame on you and i hope you're never in a position where someone depends on you to teach them absolutely anything

>an author whom i might add has done infinitely more for the math community than you have with your pedantry and vitriol

>jeremy was originally a math ed phd student so i trust his opinion of the right way to teach math infinitely more than i do yours mr random internet physics guy.

I am doing a maths PhD and (woe is you) I teach undergraduate classes AND I've been tutoring students of physics, maths and computer science for over 4 years now, online and in person. I can say with no false modesty that I've been repeatedly complimented by students on my ability to teach and explain concepts.

What Nobel prizes have you got, since that seems to be so important to you?

[mcguire]

Is there any way we can keep this somewhat civil?

[andrepd]

You're totally right. Apologies for my part. I should know better than to engage with

"next time think twice before posting this kind of lowbrow mean shit".

It was meant to attack and irritate and I fell for it.

[mlevental]

on the internet everyone is a dog and has read all of the volumes and TAOCP and all of the volumes of landau lifshitz (and also peskin and shroeder and read baby rudin at 5). no one cares about /you/ man - it's a public forum so the point is to give advice that is generally relatable.

[andrepd]

*>on the internet everyone is a dog and has read all of the volumes and TAOCP and all of the volumes of landau lifshitz (and also peskin and shroeder and read baby rudin at 5). no one cares about /you/ man - it's a public forum so the point is to give advice that is generally relatable.

I am again very sorry to disappoint I've not read TAOCP or Landau or even Peskin from cover to cover. I'm however curious if you can let me know where you got that idea from, cause I scoured my comments and can't for the life of me find anywhere I indicated so.

Seriously though, I have no idea what your point is supposed to be. I shouldn't give my opinion because... it might not be relevant to someone else, is that it? Someone might not agree? If it interests you I've met many people in the past few years who share my view (and also many personalities, again, Lamport, Dijkstra, Knuth, in the field of computer science). I've also met many who don't agree! And that's fine, what works for some might not work for others. Clearly this concept does not sit well with you.

This is being an uninteresting conversation which is only serving to irritate me (and you, it seems). I will stop replying now.

[Brakenshire]

I personally think this is exactly wrong. Most people struggle with Maths because they don’t have the implicit understanding that books like you’re talking about rely on. It’s like telling a novice programmer to read the documentation. I’m not sure how successful this book is but it seems a worthy attempt.

[andrepd]

That's not at all the point I was trying to make. Indeed, if you check my other comment, both the books I give as an example have precisely the feature of being self-contained. Landau's Mechanics starts with the basic concept of a particle. Cohen-Tannoudji's Quantum Mechanics starts with the simplest possible description of the double-slit experiment. Again, they assume no prior knowledge about what they are trying to teach (wouldn't be much of a textbook about the subject if it did require previous knowledge about the subject, now would it? :))

[pcein]

The counterparts of these books in the mathematical domain may be self-contained with respect to the subject matter, but you fail to consider the fact that most of them require a high degree of mathematical sophistication and are really targeted at people who have already acquired the required level of intuition. The "self-contained" nature of these books is deceptive - they might start with some innocent looking stuff about counting, integers etc and very soon drill deep into abstract stuff through complex chains of reasoning which a beginner will find extremely dry, bewildering and unfathomable. When you are a total beginner and trying to learn a subject through self-study, you are more likely to appreciate a book in which the author tries to recreate the experience of sitting in a classroom and listening to a professor holding your hand and showing you stuff from various angles.

[marktangotango]

Attempting to shoe-horn programming "lingo" into mathematics.

This statement is particularly amusing and highlights to me the fact that mathematics are a natural language, and not a programming language. Sussman had a really great presentation on this point; anyone who’d argue this please watch!

https://www.infoq.com/presentations/Expression-of-Ideas

[throwawaymath]

Do you mind summarizing Sussman's presentation? I can't view it on the link you provided without making an account. I can't tell from your comment whether you agree or disagree with the parent's point.

[espeed]

Here's a YouTube link of the presentation...

https://youtu.be/iqlxsSrd-M4

NB: The slides aren't visible in the video, but here's the corresponding AI Memo by Gerald Jay Sussman and Jack Wisdom from November 2012...

AI Memo 2002-018: The Role of Programming in the Formulation of Ideas (November 2012) [pdf] https://dspace.mit.edu/bitstream/handle/1721.1/6707/AIM-2002...

[andrepd]

That was very interesting! Certainly a different perspective.

[ReidZB]

I'd recommend reading Tao's blog post "There’s more to mathematics than rigour and proofs":

https://terrytao.wordpress.com/career-advice/theres-more-to-...

[jbasrai]

I enjoyed reading this opinion, do you have any recommendations for math textbooks that reach the standards you've described?

[andrepd]

Not exactly math, but physics, since that was my background. Perhaps my favourite textbooks are Landau and Lifschitz[1]. They pretty much exemplify what I mean. They are concise, lucid, entirely self-contained. All the relevant information is there and not one bit more. The material is reduced to its key ideas, therefore making their exposition as clear as it can possibly be. Many people I've spoken to, however, don't like it precisely for being "too terse", so there you have it as well: ymmv.

Another book that fits this is Cohen-Tannoudji's Quantum Mechanics[2]. The first two chapters explain quantum mechanics from absolute scratch. It starts as all physics does: with an experiment. Then everything else follows from looking carefully at the consequences of that observation, and the concepts are truly explained for what they are, because they are presented in the simplest way possible. "Idea" is more understandable than "Idea+Cruft". This is remarkable to me: much fuss is made about how quantum mechanics is strange and confusing and difficult to grasp, and it is indeed so. In that first chapter, however, I've found the most illuminating explanation of quantum mechanics I've ever read.

[1] https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics

[2] https://en.wikipedia.org/wiki/Claude_Cohen-Tannoudji#Selecte...

EDIT: I just opened Landau's Mechanics Vol I, and here's what his colleague had to say about his writing and teaching style: "[These are] all the features of his characteristic scientific style: clarity and lucidity of physical statement of problems, the shortest and most elegant path towards their solution, no superfluities.". Indeed.

[physicsguy2]

I find this a bit funny. You are comparing books that are used by advanced undergraduates or graduate students to a book written essentially for the subset of programmers with almost no math background. There are beautiful mathematics books by Springer (Undergraduate Texts in Mathematics), Carus Mathematical Monographs and Dover that provide both intuition and rigor at an introductory level. The main problem for a beginner though is knowing where to start and getting a survey of the arena they are entering. They might think linear algebra is adding vectors together with a vector being just a list of numbers.

This book hopefully fills that gap. There are other introductory books like Mathematics: Its Content, Methods & Meaning by Aleksandrov and Kolmogorov but that requires a serious investment of time.

Lastly, I apologize but I am going to rant about this physicist phenomenon. I am a physicist myself (high-energy theory) that entered quantitative finance after my PhD (a heavily disliked field on HN). I found a lot of physicists outside academia who tend to be aggressive and condescending and often haven't actually gone through the rigors of a PhD program themselves. Maybe it makes one feel smarter to tell other people that they are reading easy books or can't jump straight to Landau or Bourbaki (those two couldn't be more different but you get the point) and there are no other physicists around to correct the notion that there are multiple ways to gain knowledge and build intuition.

It doesn't matter who says what about which book. Sample some books, find what you like as long as its not junk science/mathematics, do plenty of exercises, and try to derive things yourself and don't fool yourself that you understand something deeply by studying it for a year.

[diffeomorphism]

Landau-Lifschitz as a reference is also very polarizing. There are people that really like the style (myself included), but I have also met many people that really dislike it, think it is too hard, too brief, too dry, too little description of intuition... . Similarly, the Feynman lectures are loved by some and disliked by others.

[dustycat]

I am curious how many people the author has taught mathematics to.

It doesn't seem a good idea to jump into writing a textbook teaching mathematics unless one has experience of teaching mathematics.

But the author makes the very point about early failures of programming, due to lack of experience, so perhaps he can supply information about what his pedagogical experience consists of.

Teaching other people is a craft, similar to programming or mathematics, with its own necessities.

[j2kun]

It's a good question, and sort of hard to balance. I don't have any formal training as a teacher, or really a _pedagogy_ per se. I did teach five years of discussion sections among calculus, python programming, and differential equations. I do guest lectures for high school math classes, volunteered with groups like Black Girls Code and Hour of Code. I also did years of tutoring-center style tutoring, which meant I worked with students from the entire math curriculum. One time I even did an impromptu linear algebra course for a group of co-interns when I worked at MIT Lincoln Lab.

So in terms of number of people face to face, somewhere in the low thousands seems right. In terms of writing, my blog has on the order of millions of all-time page views.

I think it's a stretch to call the book a textbook. I think of it as an O'Reilly-type general technical book, but for math. If someone uses it to teach a course, that would be pretty wild, and I'd feel honored.

Hope you enjoy it :)

[jacobolus]

Apparently he was a TA as a math PhD student at UIC. Now is a programmer working at Google. He wrote a bunch of posts on his website over the years, https://jeremykun.com/main-content/

[mcguire]

His blog has appeared here before and I've found it well written.