/sci/ - Science & Math

>>8615838
Gödel
name one (1) 20th century mathematician that he didn't BTFO

Can someone explain the fuss over set theory and logic to a math noob? As far as I understand it this is what happened

>Geometry was the foundation since Euclid because it has irrational numbers that can be expressed while arthimetic can't do this with just integers.
>fast forward to 19th century
>non euclidean geometry is discovered
>geometry can't be the foundation
>problems start to show up with calculus/analysis?
>Cantor invites set theory
>no one likes it
>Frege starts to use logic to fix maths
>people are catching on to set theory
>russel starts working
>discovers russels paradox
>naive set theory can't work
>people try to find axiomatic set theories using logic
>Cantor tells mathematicians to get their shit together
>around this time Russel and Whitehead publish princpia mathematica
>few decades later Godel btfos it and all other logic foundations.
>people now just accept math is always incomplete

>>8515525
"No."
t. pic related

So many greats not mentioned. Sure, 5 is a little too few to make a good list, but come on, no Euclid yet?

My list (leaving out obvious ones and instead listing greats I personally like):
Cantor
Hilbert
Gödel
Turing
Nash

every great theory has always been anticipated by other people

Newton's achievement in Universal Gravitation was remarkable, but it was anticipated by many of his contemporaries

Einstein's General Relativity another genius accomplishment but again it was anticipated by his contemporaries as well

Godel's Incompleteness Theorems seem like they literally came out of no where, you had Hilbert building his project, and then Godel comes and everyone's like "What the fuck is this.....this is genius"

so is the Incompletenss theorems the one groundbreaking idea that was not anticipated by anyone else besides Godel

https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

on another note, I have personal reservations, that, human consciousness, or even any living consciousness for that matter has it's roots deeper than simple, electical pulses and the "physical" universe, not to jumping to the spiritual explanation, lets skip that for something tangible, even the electron, we know little about it, and most people know less than the previously implied "we". it can reach well into the spectrum of spiritualism I suppose, concepts of the self outside the self, etc. but that's another topic.

"can we make a robot into a hum"
no. no. no. n-NO. why?
maybe this generation is spoiled with technology, especially the kids who didn't grow up with pogs or ham radios. your super sexy robot is essentially bonzi buddy. If-Thans, even if you scripted a new language, it is a physical extension of the coders and engineers.

AI could only ever mimic being human, even if in some subjective sense it could emulate human emotions, even though it doesn't have the evolutionary, biological, cellular, neuro-structural to form them, notwithstanding education.

words don't do it justice because psychoanalyzing AI that doesn't exist, well it's absurd.

point is, lesson learned from that film ex machina is, don't be the tool's tool, you tool. and don't delude yourself that it isn't the case when it is.

What's Gödel's incompleteness theorem? And what importance does it have?

this crazy asshat

Why do you guys hold pure maths in such a high regard when this guy basically fucked you in the ass?

Was mathematics created or discovered?

>>7740281
good choice anon

heres mine

>>7699061
Formal systems in general are memes

>>7691166
You can't, no one can. We cannot make a complete list of axioms from which all mathematical truths can be drawn.

We can't write down the fundamental rules of math, we just know that it works and intuitively believe it to be true.

>>7684626
Prove math/logic are real using only math/logic.

Pro tip: you can't

Is set theory just a meme?

Set theory trys to describe the foundations of math but pic related proved we'll never create a formal system that can explain all of math (the system will always be incomplete or inconsistent).

Why are we still trying to explain everything with formal systems after incompleteness? We just don't know what else to do?

>>7357739
>Applied logic thread? Applied Logic Thread

doesn't sound like logic to me faggot.

Daily reminder that the Incompleteness Theorem is flawed, people accepted it without questioning or understanding. Daily reminder Gauss was the last pure mathematician. There has been a decline in the average cognition that ruined mathematics and now we are experiencing the lack of physicists aswell. Think about it, this is the most polymath friendly age yet the best /sci/ posters are average specialists with mental problems. This way history will have to be often hidden and even corrupted in order to prove that we are the smartest generation, I think this must have happened to a small degree and I fear what will happen. I hope for genetic engineering and A.I., and even a one world government soon.

So if you recall, godel proved a system cannot prove itself, yet physicist pursue this anyway.

What if consciousness is another system to provide completeness?

>logician
>eventually becomes paranoid that someone is going to poison his food
>only trusts his wife to cook his food
>wife is hospitalized
>starves to death

Wouldn't the LOGICAL thing to do be to cook his own meals at that point?

Seems like he was pretty shit at logic.