Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Why Mathematics is Boring (2007) [pdf]

math.ucr.edu

Post reply on HN
Print view View original

81–90 of 129 posts

Re: Why Mathematics is Boring (2007) [pdf]

#81

Post by 085335977350 »

enriquto wrote: post #25
taneq wrote: post #20

Earlier quoted context omitted.

As a non-mathematician this seems to be lacking a little something. Would you not want your paper to provide some indication of what you're attempting to communicate and why? Or is that information (as the joke goes) possible, and therefore trivial, to infer?

A great deal of maths is that you get to use theorems for purposes that they were not intended for. Presenting the theorem in a "pure" form thus allows to approach it without pre-conceptions. I love the analogy with cooking recipes in another comment. Math papers are like recipe books, deliberately devoid of their social context. The same recipe may mean different things to different cooks, even contradictory! Having…

@

Re: Why Mathematics is Boring (2007) [pdf]

#82

Post by hasmanean »

Jensson wrote: post #69
bedobi wrote: post #67

I always struggled (and still struggle) with math. A couple of years ago, randomly browsing YouTube, I came across this home made video asking how they figured out the distance to the moon before modern technology. The host starts out small scale showing he can calculate the distance to things in his back yard using trigonometry and then scales it up to the moon. My mind was blown, because no one ever told me that. I…

Most math textbooks contextualize it like that, so I guess yours did too. Just that in school kids almost never care about that, they just want to pass the tests and therefore ignore all contextualization and just remember the minimum possible amount required to solve test questions. So likely you already saw those things many times before and forgot since you didn't find it important back then. That is the main stru…

There was a book called “Calculus the EZ way” https://vpl.bibliocommons.com/v2/record/S38C1299093 that I discovered in the summer before Uni. It was so much fun to read I learned it again just for the sheer pleasure of it. Even though they used medieval characters in a magical kingdom to explain calculus that was not the innovation there. The real thing was that they explained the problems they encountered with existing methods before they introduced a new method.

That was novel. That is how research is done…you start with a problem and figure out a way forward.

That is not how textbooks are written. It’s like, why waste our valuable paper to print the wrong way to do something even if it helps people learn? They only print the right way to do it. The student loses the ability to participate in the discovery process and just becomes a dumb initiate who is forced to believe whatever is written down. It’s more like a degenerate religion you’re forced to memorize without the inspiring examples of all the saints and martyrs who showed others the way before you.

Re: Why Mathematics is Boring (2007) [pdf]

#83

Post by krisoft »

enriquto wrote: post #8
abdullahkhalids wrote: post #3

If you read any science papers, they start with a clear introduction with the aims, claims, importance and novelty of the work. A lot of math papers (but not all) just start off with a dry statement of what the theorems being proved are, and jump right into the proofs. I always wonder why editors don't understand the importance of these things and don't enforce them.

I for one welcome the "dryness" of mathematical writing. It feels clean, like reading a story without distracting ads. A beautiful advice that I received as a student was to write mathematics as a series of definitions, propositions and proofs. No text is allowed to exist outside of these three. In practice it is difficult to enforce, but it is helpful to keep this as an aim.

> A beautiful advice …

Oh my goodness! So there are actual people who prefer that? I had to chew my way a fair share of books like that and I can’t stand them. Clearly the person who thought of these definitons, propositions and proofs had some reason to think of them. Sometimes they were trying to solve a problem, sometimes they were combining ideas, sometimes they were looking for structures with certain aesthetic properties. There was always a why behind why they thought about this and not something else. Sometimes there are multiple possible such reasons, that is fine. In that case the author can select whichever they fancy the most. Every time i had the misfortune to read a book like what you describe it felt like I was eating powdered milk without reconstituting it. There was a clear chain of thought between ideas and they choose to just hide it.

I understand that math requires work. One needs to get a paper and a pencil and work out examples, check proofs, play with definitions. But why wouldn’t the author write down what made them care about the next item?

> it is helpful to keep this as an aim.

Why?

Re: Why Mathematics is Boring (2007) [pdf]

#84

Post by umvi »

whatshisface wrote: post #66
umvi wrote: post #19

Earlier quoted context omitted.

I think it would be better to just get away from ultra terseness. It's crazy to me how terse mathematics is compared to CS. def velocity(time_ms): return ... vs. v(t) = ... Like nearly every operation and variable is one character or symbol long (with the puzzling exception of trig where you get a whopping 3 characters - sin/cos/tan/etc.)

I really don't want to write a complete word hundreds of times when I am solving an equation on paper.

Use short hand with pencil and paper. But make it less terse inside textbooks, inside computers, etc

Re: Why Mathematics is Boring (2007) [pdf]

#86

Post by whatshisface »

Jtsummers wrote: post #74
whatshisface wrote: post #66

Earlier quoted context omitted.

I really don't want to write a complete word hundreds of times when I am solving an equation on paper.

At least that idea is better than the other way some people want to "improve" math notation: drop it and write everything in "plain English". Like anyone who does even basic algebra would really benefit from that. "The position of a particle at some point in time is its original position added to the product of its initial velocity and the time added to half the acceleration times the square of the time. Now, if I te…

That's actually quite close to how Newton's Principa was written. If you want a real challenge, go try and read it... and if you really want a challenge, try to read it without already understanding mechanics!

Re: Why Mathematics is Boring (2007) [pdf]

#87

Post by civilized »

chmaynard wrote: post #79
canada_dry wrote: post #33

An aside: his UC Riverside page is full of interesting stuff: https://math.ucr.edu/home//baez/README.html

Dr. Baez is a brilliant mathematical physicist, but web design and publishing is not his strong suit.

I think the page looks and is great. One column of plain text and pictures. Minimal, loads quickly, easy to understand and navigate.

It doesn't have any of the pointless bloat of most "modern" web design, and is all the better for it.

Re: Why Mathematics is Boring (2007) [pdf]

#89

Post by bedobi »

Jensson wrote: post #69
bedobi wrote: post #67

I always struggled (and still struggle) with math. A couple of years ago, randomly browsing YouTube, I came across this home made video asking how they figured out the distance to the moon before modern technology. The host starts out small scale showing he can calculate the distance to things in his back yard using trigonometry and then scales it up to the moon. My mind was blown, because no one ever told me that. I…

Most math textbooks contextualize it like that, so I guess yours did too. Just that in school kids almost never care about that, they just want to pass the tests and therefore ignore all contextualization and just remember the minimum possible amount required to solve test questions. So likely you already saw those things many times before and forgot since you didn't find it important back then. That is the main stru…

> Most math textbooks contextualize it like that

I'm all but certain mine didn't. For sure there was the odd contextualization and examples of real world applications here and there but definitely not enough and definitely not interesting or fascinating ones.

Eg if there was one for trigonometry it would have been something lame like "Alice is standing in the field some distance from Bob and Billy. Calculate the distance based on "

Hardly riveting stuff :P

Re: Why Mathematics is Boring (2007) [pdf]

#90

Post by newbie2020 »

Jensson wrote: post #69
bedobi wrote: post #67

I always struggled (and still struggle) with math. A couple of years ago, randomly browsing YouTube, I came across this home made video asking how they figured out the distance to the moon before modern technology. The host starts out small scale showing he can calculate the distance to things in his back yard using trigonometry and then scales it up to the moon. My mind was blown, because no one ever told me that. I…

Most math textbooks contextualize it like that, so I guess yours did too. Just that in school kids almost never care about that, they just want to pass the tests and therefore ignore all contextualization and just remember the minimum possible amount required to solve test questions. So likely you already saw those things many times before and forgot since you didn't find it important back then. That is the main stru…

Yeah, my run of the mill textbooks tried to invent fun scenarios like that. But alas, we just made of Adam for carrying a hundred apples back home for dinner.
Post reply on HN