Habits of highly mathematical people • Hacker News Board

Re: Habits of highly mathematical people

#21

Post by sidek » Sat, Jul 30, 2016, 3:02 PM UTC

raldu wrote: post #18

maroonblazer wrote: post #7

Couldn't this also be titled "Habits of high rational people", with mathematics simply being one application? I'm not a mathematician and was miserable at math in school, but I apply these habits in the business world every day. They help me cut through a lot of crap that comes from other people's sloppy/lazy thinking. >Anyone who has gone through an undergraduate math education has known a person (or been that perso…

Nice spot on. The described qualities would also apply to philosophers, logicians, etc. I think a broader term would be, habits of highly "analytical" people.

Philosophers? Using precise definitions? Maybe some philosophers do... But not most.

Re: Habits of highly mathematical people

#22

Post by jameshart » Sat, Jul 30, 2016, 3:12 PM UTC

geertj wrote: post #2

Only six habits, I would have hoped for a seventh one :)

7: Schematizing things into, for example, lists.

Re: Habits of highly mathematical people

#23

Post by auggierose » Sat, Jul 30, 2016, 3:15 PM UTC

Very good article. I might add that a further pitfall in being "highly mathematical" is when you assume that the person you are communicating with is also "highly mathematical" and therefore has similar habits. That's not true MOST OF THE TIME and can lead therefore to severe misunderstandings.

Re: Habits of highly mathematical people

#24

Post by marcosdumay » Sat, Jul 30, 2016, 3:19 PM UTC

coliveira wrote: post #13

vanderZwan wrote: post #11

Earlier quoted context omitted.

> I'm not a mathematician and was miserable at math in school Maths in school is not really like the maths that mathematicians do.

True, but if you're not good at school math, I believe there is little hope you can be good at the style of math that mathematicians do...

I wouldn't bet on that, they are really different.

Some of the most blatantly off-putting characteristics of school math, like mindless repetition, are antagonical to real math.

Re: Habits of highly mathematical people

#25

Post by sidusknight » Sat, Jul 30, 2016, 3:19 PM UTC

javier2 wrote: post #5

7. Being precise. The precision you hold yourself to through a rigorous approach to a problem is also very valuable and is the reason I think calculus is very important.

Calculus doesn't have any true rigour/precision. That's why it's not analysis.

Re: Habits of highly mathematical people

#26

Post by bjz_ » Sat, Jul 30, 2016, 3:20 PM UTC

mrcactu5 wrote: post #14

#6 scaling the ladder of abstraction This is one I have a tough time explaining to students who are so focused on the task at hand they don't feel there's time to sit back and reason in generality.

Came across this Dijkstra quote via https://www.youtube.com/watch?v=GqmsQeSzMdw

> The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise

By taking away all the non-essential things and leaving only on what you need, it allows you to truly understand the structures that you are studying. Definitely rings true when I work in ML/Haskell-style type systems. Easier said than done convincing the students though...

Re: Habits of highly mathematical people

#27

Post by izacus » Sat, Jul 30, 2016, 3:24 PM UTC

maroonblazer wrote: post #7

Couldn't this also be titled "Habits of high rational people", with mathematics simply being one application? I'm not a mathematician and was miserable at math in school, but I apply these habits in the business world every day. They help me cut through a lot of crap that comes from other people's sloppy/lazy thinking. >Anyone who has gone through an undergraduate math education has known a person (or been that perso…

> I don't disagree but would argue that the far more common problem is people - not just mathematicians, mind you - not considering definitions enough which ultimately leads to confusion and/or misunderstandings and consequently additional, unnecessary, cycles spent in discussion about "what do you really mean?"

It's all a difference in context and environment. When talking through the specification of a product your building and prerequirements for it, nitpicking the definitions will save you pain and money.

On the other hand, nitpicking whether someones analogy in covers exact 100% cases of the issue while ignoring the point of the conversation will just make you look like an arsehole in front of the group of people. And the latter is still painfully common on HN as well. As the article says - understanding when some detail is important for the current conversation is an important social skill.

Re: Habits of highly mathematical people

#28

Post by anaysis » Sat, Jul 30, 2016, 3:25 PM UTC

coliveira wrote: post #13

vanderZwan wrote: post #11

Earlier quoted context omitted.

> I'm not a mathematician and was miserable at math in school Maths in school is not really like the maths that mathematicians do.

True, but if you're not good at school math, I believe there is little hope you can be good at the style of math that mathematicians do...

High School math (often) is all about memorizing a few tricks from the analysis of real numbers and maybe elementary number theory/combinatorics. I think there'd be more mathematicians if people got to see what math is like in actuality. I fell in love with math when I discovered that it's an actual body of knowledge complete with definitions, concepts and proofs just like any other discipline. Compared to that high school math (loosely) could be said to be a bunch of party tricks with no rhyme or reason to them.

Re: Habits of highly mathematical people

#29

Post by catnaroek » Sat, Jul 30, 2016, 3:26 PM UTC

bjz_ wrote: post #26

mrcactu5 wrote: post #14

#6 scaling the ladder of abstraction This is one I have a tough time explaining to students who are so focused on the task at hand they don't feel there's time to sit back and reason in generality.

Came across this Dijkstra quote via https://www.youtube.com/watch?v=GqmsQeSzMdw > The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise By taking away all the non-essential things and leaving only on what you need, it allows you to truly understand the structures that you are studying. Definitely rings true when I work in ML/Haskell-style type systems…

> By taking away all the non-essential things and leaving only on what you need, it allows you to truly understand the structures that you are studying.

This is the essence of type abstraction and parametricity!

Re: Habits of highly mathematical people

#30

Post by cm3 » Sat, Jul 30, 2016, 3:27 PM UTC

sidek wrote: post #21

raldu wrote: post #18

Earlier quoted context omitted.

Nice spot on. The described qualities would also apply to philosophers, logicians, etc. I think a broader term would be, habits of highly "analytical" people.

Philosophers? Using precise definitions? Maybe some philosophers do... But not most.

I took parent's comment to mean it's about philosophers who deal with logic. You may recall that logic as a tool free of opinion originated with Aristotle, and the first thing that comes to my mind in this context is Principia Mathematica.