#millennium problem

[anremithrl]

Why undoing things is hard:

I am inherently, a very lazy person. And I cannot stand being bored. This has, of course, resulted in me being really into coding and automation.

And when I begin my journey as a mathematician, thirteen-year-old me was really sure I'd figure out how to write just the right algorithm that would automatically solve all math problems. But this is actually really hard.

Now, naively, it's really easy. You just write a code that takes the axioms of a system, your premises, and then just tries to apply every single possible rule to generate more statements until it either proves or disproves what you want.

But two problems arise: halting problem, and the fact that it takes a really, really, long time to get anything done.

Maybe you can mitigate the halting problem somehow or something, you could additionally try adding proving the statement is unprovable as a stopping condition, but maybe it is unprovable that it's unprovable, or maybe it's unprovable that it's ... I'll stop.

But that doesn't much matter if it's going to take a twenty years to prove a single statement. At that point, you might as well prove it yourself.

Let's say we have a proof checker, it starts with a proof and then tells you that it is valid. If we run this algorithm backwards, then... shouldn't we get a valid proof?

This, quite obviously, doesn't work. Or at least, doesn't work easily. (The fact that it doesn't work is tied with P vs NP) It's less obvious when you're trying to do this without realising you're trying to do this. But for some reason it took me a while to realise why that wasn't 'easier'.

The reason it doesn't work finally clicked with a Rubik's cube. If I run an algorithm like CFOP on a cube to solve it, then I can run CFOP backwards to get the original position, starting from a solved cube? Nope. Mathematically, the best I can do is reduce it to 1/12th of the states, leaving some 43 quintillion (43,252,003,274,489,856,000) possible starting points which all end up in the same ending point. Running an algorithm backward isn't just some trivial thing. It's a whole millennium problem, you get a million dollars if you figure all of this out, since running verification backwards is what all of P vs NP is.

At some point after that, I learned there's a whole field of math devoted to this.

And today, I watched a YouTube video about someone trying to run Conway's Game of Life backwards. It's not easy to find even one possible backwards step. And I remembered this.

So, to everyone here, I suggest learning about SAT solvers! They're cool! That's a whole branch of math devoted to doing this.

[queenlua]

okay let's make tibarn/naesala happen

let's enumerate every possible way to make them work. for funsies. because i am normal and have normal 3am hobbies:

option 1: reyson and leanne both die tragically somehow; tibarn and naesala have weird sex about it

pros: ngl this is my Default Option for like 80% of my ships for a reason. it's just fundamentally neat when ppl are sad about their dead former lover and think about them constantly even whilst they are flinging themselves into the arms of a new one. if you can get TWO people doing that simultaneously? with each other?? hell yes

cons: honestly...,,, both of these boys seem enormously terrible at providing anything remotely resembling comfort. like, i feel like they try to have weird angsting-over-reyson-and-leanne sex, but then they just have normal-ish, boring, wham-bam-thank-you-m'am, vaguely-unsatisfying sex, so then you're not even getting Demented Catharsis out of it, and then WHAT IS THE POINT. like have you ever known a dude who takes up jogging to try and get over his ex? and then he quits after a couple weeks when he remembers Wait Cardio Is Boring As Fuck? it's like that. i think they try it for a bit and it's blah and all purely physical and then they're done. i'm just not quite seeing it here!

option 2: naesala's the weird skrunky sometimes-third-wheel sometimes-third-partner to reyson/tibarn

pros: i think this meshes best with all their personalities as presented in canon. tibarn & reyson keep letting naesala off easy because, y'know, he's more useful to keep around and guilt-trippable, but also because he's pretty fun to drag into bed sometimes, right

cons: this is avoiding the tricky bit, right? i specifically said naesala/tibarn because i want to figure out how to emulsify these oil-n-water bitches together. if you let reyson be the glue between them, you're taking the easymode way out!

option 3: do you think love can bloom even on a battlefield

(aka, naesala and tibarn both murder the hell out of some senator who dicked both of them over, and they look into each other's eyes and realize that despite all their differences they do both find Murderous Justice very hot, deep down. and maybe also each other? like it's hot that this guy also Gets It right)

pros: ok, come to think of it, you could make this one really funny. like, suppose Reyson's been kidnapped or something, right, and Tibarn's like I Will Do Anything (Even Ally With Naesala) To Get Him Back

and so Tibarn fights Through Hell And High Water to rescue his twinky boyfriend

and they SUCCEED, and Reyson's super-unconscious but safe, and in that moment he looks into Naesala's eyes and... they get supremely frisky, and it feels incredible and right in the moment but boy that's gonna be awkward the second Reyson actually wakes up lmao

cons: dissolves the second reyson wakes up, alas. like the Weirdness hangs around after, that's still fun, but.

option 4: naesala has a little bit too much fun being the powerful one for a change

i'm pretty sure naesala would Literally Die rather than ask tibarn for help, ever. but tibarn? tibarn might in fact get desperate enough to call on naesala for help. you could probably spin some toxic yaoi out from there, right. tibarn very much trying to hold onto a sense of self and telling himself he's just doing this for instrumental reasons, but also having his sense of self lowkey fucked up by having to play second fiddle to naesala. naesala very much enjoying stringing this guy along. that kind of deal

pros: wasn't thorki big for a while or something. i feel like we get thorki vibes out of this. can i steal some MCU ppl away to spur on a Second Great Awakening Of Tellius...

cons: this would require me to have a good Theory Of Mind for Tibarn in particular, which i do not, alas!

anyway god i should get some sleep. further options welcome

[cpericardium]

People love inventing extremely difficult problems in the field of mathematics. They always do this. Make up problems and then go "ah man this one is too hard… I'll put a bounty on it"

[bookishbrigitta]

Shoutout to my apartment building's maintenance man who showed up like an hour after I called on the Friday before Christmas to remove a rat-sized ball of hair from my shower drain all while assuring me it was "normal."

Merry Christmas, bro. You're a real one.

[ranidspace]

The Millennium Prize Problems are a set of 7 mathematical problems that each have a one million dollar prize if you are the first to find a correct solution of the problem. (simplified, very bad) Explanations for all of them in the bottom, but feel free to reblog as to why your favourite is the best

The Riemann Hypothesis: For the following equation,

The Hypothesis states that all non-trivial zeroes lie on the n=1/2+ti line, where t is a real number, and i is the imaginary unit

Yang-Mills Theory and the Mass Gap Hypothesis: The Yang-Mills Theory explains the "Standard Model". Which is the behaviour and interactions between elementary particles, such as quarks, gluons, and leptons. It however does not explain the interactions in the nucleus. To prove it you must prove that the Yang-Mills theory holds true for any "compound simple gauge group", and the mass of all particles predicted by it must be greater than 0(mass gap)

The P vs. NP Problem: In computer programming, P problems are anything can be solved by a turing machine(computer) in a "polynomial"(ie: ax^2+bx+c) amount of computation time (considered to be easily solvable, though not all P problems have a known solution etc etc). NP problems are problems, that while not solvable in a polynomial amount of time, a solution is able to be verified in a polynomial amount of time. The definitions of these are a bit fuzzy, and P vs NP asks if there's a fundamental difference between the two at all.

Navier–Stokes equations: These equations predict the movement of viscous newtonian fluids (almost all fluids you can think of that dont have debate over "is it a solid or a liquid" so not like, jello, jam, ketchup, shaving cream whatever). This asks if for any fluid in three dimensions, a "smooth"(differentiable at all points) solution to the equations can always be found

The Poincaré conjecture: In topology, the conjecture states that for any finite 3d topological space, where every loop in the space can be tightened to a point, it's necessarily topologically identical to a 4 dimensional sphere (A normal sphere is a 3d sphere, however it's a 2 dimensional topological space, as loops can only be placed on the "flat" surface, see photo below)

The Birch and Swinnerton-Dyer conjecture: Elliptic curves(see photo below) are defined by y^2=x^3+ax+b. Some of them have an infinite amount of rational solutions, and some only have a finite amount, and this conjecture states that there is an associated function, that when it equals 0, there's infinite rational solutions, and when it is not 0, it's finite.

The Hodge Conjecture: "The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations." (im gonna be honest i have no idea, i lifted this definition straight from the clay mathematics institute)

The pointcaré conjecture has actually been solved, it's the only one on the list that has, but dont let that influence your decision

[thegreatyin]

y'know in hindsight i think michael might be the only ""villain oc"" i have that's not like. actively pathetic in some capacity

[joellesolo]

Ugghh.

My dash is doing the thing where it's only showing me posts from over five days ago (with the exception of one, JUST ONE, post from four hours ago which I'm quite glad I saw, so I could offer support to a friend) but it's just so freaking frustrating! Because who knows if you'll see this? Who knows WHEN you'll see this?!

Anyway. A tumblr friend from NJ sent me really cool Star Wars stuff ten years ago (if you were around then I posted it) and she JUST FUCKING DID IT AGAIN 😭 I'm literally on the verge of tears. I had the worst fucking weekend, and the worst fucking day today, and just... oh my god. I didn't even know it on its way, and there's a fucking MILLENNIUM FALCON THAT FUCKING OPENS and it has LANDO AND NIEN AND A MYNOCK?! and I was googling the micro machine set to see if I could figure out where this weird windowshield thing went and saw that the original set came with Han and Leia (and others) and a sensor dish and was like... oh my god! What if, when she sent me the stuff ten years ago, it's in that box?!

So I went digging through that box (which, here it is, some of it!) and HOLY FUCKING SHIT, Han and Leia AND THE FUCKING SENSOR DISH ARE IN IT 😂😭😂😭😂 and this just made my day, my week, my MONTH, and wowza, I don't have words!!

So even though she's no longer on tumblr anymore, I'm just so fucking grateful to mosymoseys, for expanding my Star Wars collection, I will definitely be taking pictures later when I can (and I have to now figure out my shelf situation because, I don't know where I'm going to put all this amazing stuff but I'm going to fucking MAKE THE ROOM FOR IT 😍).

[sereendys]

im gonna rant about this but prince endymion in almost every silmil fanfics has the characteristics of fred (velma) like writers need to make him a misogynistic sexist douchebag and always make him either cheat on serenity or make him demande like WHAT THE FUCK IS WRONG WITH YOU?? and hes always like “women are the most vile creatures on the planet!” then proceeds to force himself on serenity treating her like an object. crystal/manga endymion would never do that, he isnt a bitchface

[mr-aftons-rotting-pussy]

i wish there was a way to turn it off fast style w/o like full on restarting it. that would fix all my problems

[rindomness]

rereading a bunch of the stuff i wrote about azar and asha for ask games in the past and having the slow realization that oh. oh no azar is a lot like glenn

[tyrannuspitch]

i get why ppl (myself included) like to use old norse as a substitute for asgardian, and as obviously a storytelling device that's absolutely fine, but given the way mcu history seems to have gone, i think it's actually much more likely that asgardians speak their own entirely unrelated language, but they think modern humans all speak old norse. and given the kinds of days loki and thor were having on earth 2011-2013, they might have taken a very long time to notice that that wasn't true. so when avengers tower¹ is hit with some allspeak-deactivating plot device i feel like it's less that they start speaking norse straight away and more that loki is like "[𝔰𝔠𝔬𝔣𝔣𝔰 𝔦𝔫 𝔞𝔰𝔤𝔞𝔯𝔡𝔦𝔞𝔫] the supervillain of the week thinks one mediocre spell is enough to outmanoeuvre me? i have known The Midgardian Tongue my entire life. ᚼᛁᚢᚱᛁᚦ, ᚢᛋᚾᛁᛅᛚᛅ ᚼᛁᚱᛏᚱᛁᚴᛁ, ᚠᚢᛚᚴᛁᚦ ᛘᛚᚴ!"

¹where loki just is for some reason. u know how it is

[decepti-geek]

i ADORE that the message in one of the 90s S3 episodes is 'if a boy picks on you, it means he likes you - and if you do not care for his attention, you can use this fact to your own tactical advantage against him.'

[mangled-by-disuse]

I do feel I should clarify that Piers Gaviston was not in the 1660s (he was WAY earlier, in the late 13th and early 14th century) and that those tags were a result of my brain careening off at 4am from not being able to remember the name of the wool monopolist who outsourced the British wool trade to Holland in the 1630s and tanked the already fading textile economy in the name of efficiency

and then thinking "haha man just like Elon Musk" and then going "NO ACTUALLY YOU KNOW WHO WAS JUST LIKE ELON MUSK"

anyway this is a pre-emptive Historian Self-Defence in case anyone thinks I'm 400 years out on my Piers Gaviston lore bc looking at these tags in daylight that's how they read

I don’t know how to explain this well…but I’m 30 years old and I feel like I’ve had to ‘sacrifice’ my entire adult life to unprecedented times, the pandemic and daily anxiety over hateful politicians and whatever rights they want to take away on any given day and I’m just so fucking tired

[whosmaggy]

the guy on tiktok pretending to have solved the riemann hypothesis is either the funniest person alive or going thru a manic episode. either way, ive seen so many more math related videos on my fyp recently (many of them are people making jokes about solving millenium problems). and because i assume everyone comsumes the same content as me, i assume more people will become interested in math. hate the idea of someone going thru something and then having that documented and clowned on. love the idea of someone trolling and subsequently causing people to have a new found interest in math!

anyways, yesterday i solved the collatz conjecture! it is true that every number converges! the proof came (;)) to me in a wet dream that i cannot document so you will just have to believe me.

[reasonsforhope]

"The first modern attempt at transferring a uterus from one human to another occurred at the turn of the millennium. But surgeons had to remove the organ, which had become necrotic, 99 days later. The first successful transplant was performed in 2011 — but even then, the recipient wasn’t immediately able to get pregnant and deliver a baby. It took three more years for the first person in the world with a transplanted uterus to give birth. 

More than 70 such babies have been born globally in the decade since. “It’s a complete new world,” said Giuliano Testa, chief of abdominal transplant at Baylor University Medical Center.

Almost a third of those babies — 22 and counting — have been born in Dallas at Baylor. On Thursday, Testa and his team published a major cohort study in JAMA analyzing the results from the program’s first 20 patients. All women were of reproductive age and had no uterus (most having been born without one), but had at least one functioning ovary. Most of the uteri came from living donors, but two came from deceased donors.

Fourteen women had successful transplants, all of whom were able to have at least one baby.  

“That success rate is extraordinary, and I want that to get out there,” said Liza Johannesson, the medical director of uterus transplants at Baylor, who works with Testa and co-authored the study. “We want this to be an option for all women out there that need it.”

Six patients had transplant failures, all within two weeks of the procedure. Part of the problem may have been a learning curve: The study initially included only 10 patients, and five of the six with failed transplants were in that first group. These were “technical” failures, Testa said, involving aspects of the surgery such as how surgeons connected the organ’s blood vessels, what material was used for sutures, and selecting a uterus that would work well in a transplant. 

The team saw only one transplant fail in the second group of 10 people, the researchers said. All 20 transplants took place between September 2016 and August 2019.

Only one other cohort study has previously been published on uterus transplants, in 2022. A Swedish team, which included Johannesson before she moved to Baylor, performed seven successful transplants out of nine attempts. Six women, including the first transplant recipient to ever deliver a baby back in 2014, gave birth.

“It’s hard to extract data from that, because they were the first ones that did it,” Johannesson said. “This is the first time we can actually see the safety and efficacy of this procedure properly.”

So far, the signs are good: High success rates for transplants and live births, safe and healthy children so far, and early signs that immunosuppressants — typically given to transplant recipients so their bodies don’t reject the new organ — may not cause long-term harm, the researchers said. (The uterine transplants are removed after recipients no longer need them to deliver children.) And the Baylor team has figured out how to identify the right uterus for transfer: It should be from a donor who has had a baby before, is premenopausal, and, of course, who matches the blood type of the recipient, Testa said...

“They’ve really embraced the idea of practicing improvement as you go along, to understand how to make this safer or more effective. And that’s reflected in the results,” said Jessica Walter, an assistant professor of reproductive endocrinology and infertility at Northwestern University Feinberg School of Medicine, who co-authored an editorial on the research in JAMA...

Walter was a skeptic herself when she first learned about uterine transplants. The procedure seemed invasive and complicated. But she did her fellowship training at Penn Medicine, home to one of just four programs in the U.S. doing uterine transplants. 

“The firsts — the first time the patient received a transplant, the first time she got her period after the transplant, the positive pregnancy test,” Walter said. “Immersing myself in the science, the patients, the practitioners, and researchers — it really changed my opinion that this is science, and this is an innovation like anything else.” ...

Many transgender women are hopeful that uterine transplants might someday be available for them, but it’s likely a far-off possibility. Scientists need to rewind and do animal studies on how a uterus might fare in a different “hormonal milieu” before doing any clinical trials of the procedure with trans people, Wagner said.

Among cisgender women, more long-term research is still needed on the donors, recipients, and the children they have, experts said.

“We want other centers to start up,” Johannesson said. “Our main goal is to publish all of our data, as much as we can.”"

-via Stat, August 16, 2024