How has mathematics gotten so abstract? • Hacker News Board

Re: How has mathematics gotten so abstract?

#21

Post by pdpi » Tue, Sep 30, 2025, 1:39 PM UTC

Tazerenix wrote: post #13

>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition . Arnol'd argued vehemently and much more convincingly for the viewpoint that all mathematics is (and must be) linked to the natural sciences. >On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs…

> Pure mathematics is regarded as an abstract science, which it is by definition.

I'd argue that, by definition, mathemtatics is not, and cannot be, a science. Mathematics deals with provable truths, science cannot prove truth and must deal falsifiability instead.

Re: How has mathematics gotten so abstract?

#22

Post by grues-dinner » Tue, Sep 30, 2025, 1:39 PM UTC

thadt wrote: post #2

This reminds of of that one time when I was on a date with a girl from the history department who somehow bemusedly sat through my entire mini-lecture on comparing infinite sets. Twenty years and three kids later, she'll still occasionally look me straight in the eye and declare "my infinity is bigger than your infinity."

Fittingly this is roughly the same vintage as your relationship then: https://youtu.be/BipvGD-LCjU

Re: How has mathematics gotten so abstract?

#23

Post by ndriscoll » Tue, Sep 30, 2025, 1:40 PM UTC

Tazerenix wrote: post #13

>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition . Arnol'd argued vehemently and much more convincingly for the viewpoint that all mathematics is (and must be) linked to the natural sciences. >On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs…

Not only is intuition important (or the entire point; anyone with some basic training or even a computer can follow rules to do formal symbol manipulation. It's the intuition for what symbol manipulation to do when that's interesting), but it is literally discussed in a helpful, nonjudgmental way on Math Stack Exchange. e.g.

https://math.stackexchange.com/questions/31859/what-concept-...

Other great sources for quick intuition checks are Wikipedia and now LLMs, but mainly through putting in the work to discover the nuances that exist or learning related topics to develop that wider context for yourself.

Re: How has mathematics gotten so abstract?

#24

Post by rob74 » Tue, Sep 30, 2025, 1:41 PM UTC

How has mathematics gotten so abstract? My understanding was that mathematics was abstract from the very beginning. Sure, you can say that two cows plus two more cows makes four cows, but that already is an abstraction - someone who has no knowledge of math might object that one cow is rarely exactly the same as another cow, so just assigning the value "1" to any cow you see is an oversimplification. Of course, simple examples such as this can be translated into intuitive concepts more easily, but they are still abstract.

Re: How has mathematics gotten so abstract?

#25

Post by jjgreen » Tue, Sep 30, 2025, 1:47 PM UTC

The number 1 is what a cow, a fox, a stone ... have in common, oneness. Mathematics is abstraction, written down.

Re: How has mathematics gotten so abstract?

#26

Post by tiahura » Tue, Sep 30, 2025, 1:49 PM UTC

pdpi wrote: post #21

Tazerenix wrote: post #13

>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition . Arnol'd argued vehemently and much more convincingly for the viewpoint that all mathematics is (and must be) linked to the natural sciences. >On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs…

> Pure mathematics is regarded as an abstract science, which it is by definition. I'd argue that, by definition, mathemtatics is not, and cannot be, a science. Mathematics deals with provable truths, science cannot prove truth and must deal falsifiability instead.

Mathematics is a science of formal systems. Proofs are its experiments, axioms its assumptions. Both math and science test consistency—one internally, the other against nature. Different methods, same spirit of systematic inquiry.

Re: How has mathematics gotten so abstract?

#27

Post by DonHopkins » Tue, Sep 30, 2025, 1:49 PM UTC

MontyCarloHall wrote: post #19

muragekibicho wrote: post #4

Earlier quoted context omitted.

[flagged]

Get this incel trolling out of here. No, all that would happen if your date weren’t interested in math/whatever you’re into is a polite message “I had a great time but I don’t think we have much in common” and leave it at that.

His oddly specific fear of being "plastered on a bunch of facebook new-york-dating-experience groups" sounds like women have had to warn each other about him before, and it probably wasn't about his interest in math, but something much worse.

Re: How has mathematics gotten so abstract?

#28

Post by intrasight » Tue, Sep 30, 2025, 1:50 PM UTC

There was a time, not that long ago in human history, that zero was "so abstract".

Re: How has mathematics gotten so abstract?

#29

Post by myrmidon » Tue, Sep 30, 2025, 1:54 PM UTC

pdpi wrote: post #21

Tazerenix wrote: post #13

>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition . Arnol'd argued vehemently and much more convincingly for the viewpoint that all mathematics is (and must be) linked to the natural sciences. >On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs…

> Pure mathematics is regarded as an abstract science, which it is by definition. I'd argue that, by definition, mathemtatics is not, and cannot be, a science. Mathematics deals with provable truths, science cannot prove truth and must deal falsifiability instead.

You could turn the argument around and say that math must be a science because it builds on falsifiable hypotheses and makes testable predictions.

In the end arguing about whether mathematics is a science or not makes no more sense than bickering about tomates being fruit; can be answered both yes and no using reasonable definitions.

Re: How has mathematics gotten so abstract?

#30

Post by fidotron » Tue, Sep 30, 2025, 1:55 PM UTC

Unlike Zeno's famous example the paradox which does better at explaining the problem is https://en.wikipedia.org/wiki/Coastline_paradox which Mandelbrot seemed particularly keen on.

The tendency towards excessive abstraction is the same as the use of jargon in other fields: it just serves to gatekeep everything. The history of mathematics (and science) is actually full of amateurs, priests and bored aristocrats that happened to help make progress, often in their spare time.