/sci/ - Science & Math

>>9409102
I think a lot will go to analysis of PDE, numerical methods, probability theory, optimization. And rightfully so.

>>9409105
wouldn't many of those only make us slightly better at what we can already do rather than yielding a big breakthrough or insight that lets us do something completely different?

>>9409117
pretty much yea,
but applications generally have a higher return on investment.

>>9409320
money is afterall the biggest motivator for anything a country does, but i think its reasonable to infer that (OP) is talking about game changing shit. id say focus on solving millenium problems

>>9411229
>>9409320
yeah I meant more like what kind of mathematics could help us get "scifi"-like technology.

things that can really improve our ability to manipulate the world to our benefit the way calculus and differential equations greatly improved our engineering and ability to describe electricity and magnetism, or like how group theory ended up so useful in describing quantum physics.

Do you think number theory or algebraic geometry is going to 'strike gold' in this way?
What is the most sensible way to reason or estimate about what field is going to have more useful future findings?

>>9409102
>Which frontiers of mathematics would probably be the most useful for us to make progress in in order to improve our science and technology?
I really like this question, so I'll lurk for it.

>>9409102
You seem to forget that mathematics are themselves 'science'. Many results without a 'direct' application are still fundamental in order to prove other mathematical results that eventually find a 'concrete' application. The actual question would be what in mathematics is utterly useless, and you would hardly find an answer.

>for example, say the government wanted to try and streamline and optimise mathematics research so that more research were being done into the areas that would probably be most useful for science and technology, which areas of mathematics would be given more funding?

Your idea of progress seems naive and silly. It's not like milking a cow.

>>9409102
I have said this before and I will say it again. Number Theory. Whoever created this universe clearly did not want us to learn about number theory. Just look at how there is a strong form of Godel's incompleteness theorems JUST for number theory. Clearly, someone didn't want us to find the secrets behind numbers.

So I say fuck them. Prove the Riemann Hypothesis. I bet if we get to that point whoever is out there will have to come to us.

>>9411500
Mathematics are not themselves 'science'

>>9411500
>You seem to forget that mathematics are themselves 'science'.
No, mathematicians do not use the scientific method.

>>9411558
funny memes ain't no argument

>>9411559
Then all those results deduced from empirical evidence through mathematical reasoning are not science, because they're not themselves empirical.

>>9411500
I bet anon is from an east Asian village.

>>9409102
I'd actually say topology, it is currently having massive success being applied to physics, chemistry, biology, computer science, and 'big data '/data analysis (broadly speaking, this is a big one). PDE and functional analysis have sort already found their homes, while topology is finally being applied to all these fields.

>>9409102
The most obvious answer is: fund the fields that have been useful in the past (PDE, linear algebra, differential geometry...).

The problem is that a field may unexpectedly become relevant. This dumb strategy is the reason for why math as a whole is totally neglected in the funding realm. If mathematicians were rewarded according to the value of their work they would easily be making six figures.

>>9411617
Nice contribution there! You might as well have said that you farted.

>>9409102
Way to many white people in math. Need to decolonize that shit.

>>9411420
The GAGA principle can be used to make really good lasagna. Like, scifi-tier good.

>>9409102
a spiral is how I visualize perfectoids. who is this guy?

>>9411584
Hard science doesnt deal in mathematical reasoning to substantiate their theories, it is strictly results oriented.

>>9412912
...
...
How exactly do you tell the results?

We have this new jet and it delivers more power.

How much more?

A lot more.

Yay.How efficient is it?

Well, the previous has less power, but uses lots of fuel. This one has more power, but uses lots of fuel.

Yay! So can it break through the fishbowl?

No, it is less power than break fish bowl.

Boo!

>>9412912
t. idiot
"The scientific method" is obviously not what you think it is. Where deductions can be made with certainty, it's allowed. If you have an empirical observation that there are 40 geese flying overhead today and there were 20 yesterday, you are allowed to deduce that there are twice as many today.
I suggest you plebs read this for starters.
https://maartens.home.xs4all.nl/philosophy/Dictionary/R/Reasoning%20Newtons%20Rules%20of.htm

>>9412980

Wrong, we science don't math.

I saw all gooses yesterday, and I could not see all today. Twice is number, gooses not number. There are more gooses not more number. Get out of class more geek.

>>9412986
You need to stop posting.

>>9412703
Creator of horror mangas. He's a god.

>>9412703
>>9412988
Psychologic horror*
Search for it, it's cool as fuck.

Machine learning

>>9412991

>>9412956
>>9412980
I was couching my point in the theorist vs experimentalist. I should have expanded though as it is not particularly clear. To use your example, I create an ingenious mathematical model for geese observation which correctly predicts geese obs for a lengthy period of time. It is then then discovered, repeatably, that there are situations where it is incorrect. My theory is then thrown out despite its perfect mathematical logic because it simply doesnt reconcile with results, regardless of the logical consistency of the results.

>>9411765
I just farted

>>9413356
Perfect Autist bait

>>9413364
Nice. What did it smell like?

>>9413676
ass

>>9411420
Still optimization and statistical learning type research. That gets us better AI which will in turn invent ftl technology after it's done murdering us.

>>9412980
>"The scientific method"
No such thing.

>>9414335

>>9411420
Chaos theory I guess. Being able to get accurate weather forcasts would be cool.`