News for hackers. Stuff that matters.

A comment on How has mathematics gotten so abstract?. Parent comment

Re:How has mathematics gotten so abstract? by nitwit005 on Tuesday September 30, 2025 @03:03PM (#45429724)
A proof is just an argument that something is true. Ideally, you've made an extremely strong argument, but it's still a human making a claim something is true. Plenty of published proofs have been shown to be false.

Math is scientific in the sense that you've proposed a hypothesis, and others can test it.

[ Parent | on HN ]
Re:How has mathematics gotten so abstract? by goatlover on Tuesday September 30, 2025 @03:58PM (#45430481)
Difference is mathematical arguments can be shown to be provably true when exhaustively checked (which is straight forward with simpler proofs). Something you don't get with the empirical sciences.

Also the empirical part means natural phenomena needs to be involved. Math can be purely abstract.

[ Parent | on HN ]
Re:How has mathematics gotten so abstract? by nitwit005 on Tuesday September 30, 2025 @04:36PM (#45430904)
You're making a strong argument if you believe you checked every possibility, but it's still just an argument.

If you want to escape human fallibility, I'm afraid you're going to need divine intervention. Works checked as carefully as possible still seem to frequently feature corrections.

[ Parent | on HN ]
Re:How has mathematics gotten so abstract? by griffzhowl on Tuesday September 30, 2025 @09:04PM (#45433191)
The difference is that in mathematics you only have to check the argument. In the empirical sciences you have to both check the argument and also test the conclusion against observations
[ Parent | on HN ]
Re:How has mathematics gotten so abstract? by Jensson on Wednesday October 01, 2025 @03:10AM (#45435150)
> In the empirical sciences you have to both check the argument and also test the conclusion against observations

That isn't true, you just test new axioms but most stuff we do in empirical sciences don't require new axioms.

The only difference between material sciences and math is that in math you don't test axioms while in empirical sciences you do.

[ Parent | on HN ]
Re:How has mathematics gotten so abstract? by griffzhowl on Wednesday October 01, 2025 @10:41AM (#45438283)
Empirical science uses both deductive logic to make predictions, and observations to check those predictions. I'm not saying that's all it involves. Not sure which part of that you disagree with

And a lot of what goes on in foundations of mathematics could be described as "testing the axioms", i.e. identifying which theorems require which axioms, what are the consequences of removing, adding, or modifying axioms, etc.

[ Parent | on HN ]