What are some profound scientific or mathematical truths
>>16454603Literally how do you even understand its implications without having a PhD in maths?
>>16454476What does this even mean? Be honest you just put a bunch of big words together to make you sound smart.
>>16454730The Grothendieck–Riemann–Roch (GRR) theorem has profound implications in several areas of mathematics, particularly algebraic geometry, topology, and complex analysis. Here are some of the key implications:Bridge Between Geometry and Algebraic Topology: The GRR theorem connects algebraic and topological invariants of coherent sheaves on complex manifolds, enabling complex analytic and algebraic information (like sheaf cohomology) to be translated into topological data (like Chern classes and characteristic classes). This creates a pathway between algebraic geometry and topological K-theory, broadening the scope for deeper insights in both areas.Foundation for Index Theory: The GRR theorem serves as a conceptual foundation for the Atiyah-Singer Index Theorem, which calculates the index of elliptic operators on compact manifolds. By relating the Euler characteristic (a topological invariant) of sheaves with integrals of Chern classes, GRR provides tools to handle complex calculations in index theory and differential geometry.Tool for Computing Intersection Numbers: GRR allows for the computation of intersection numbers and dimensions in a more straightforward manner through the use of Chern classes and K-theory. This has practical applications in enumerative geometry, where the aim is often to count the number of solutions to geometric problems.Unified Framework for Riemann–Roch Type Theorems: The classical Riemann–Roch theorem is a specific case of the broader GRR framework. By generalizing Riemann–Roch to higher-dimensional varieties and more general morphisms, it gives a unified theory for computing Euler characteristics across different contexts, from curves to complex varieties.These implications make the GRR theorem a central result in modern geometry and have led to significant advances in the study of moduli spaces, mirror symmetry, and string theory, where connections between geometry, physics, and topology are explored.
a+b=b+a
>>16455164Fuck this ChatGPT output
You may have heard of the study published in PNAS in 2020 concluding that Black newborns have higher survival rates when Black doctors attend to them. https://www.pnas.org/doi/pdf/10.1073/pnas.1913405117It got a huge amount of coverage in the popular press. It was even cited by Supreme Court Justice Ketanji Brown Jackson in her dissent last year on the court’s ruling against racial preferences in college admissions. The newborn research, Brown Jackson claimed, shows the benefits of diversity. “It saves lives,” she wrote. The same journal just published a reanalysis of the data. https://www.pnas.org/doi/10.1073/pnas.2409264121It turns out that the effect disappears once you take into account that Black doctors are less likely to see the higher-risk population of newborns that have low birth weight. It’s like what someone once said about Ginger Rogers and Fred Astaire: They’re both going through all the same moves, but Ginger Rogers is doing them backward and in high heels. A published finding that clashes with the political prejudices of reviewers and editors is a Ginger Rogers Finding. It had to be twice as good. Full details and more examples:https://smallpotatoes.paulbloom.net/p/progressives-should-worry-more-about
>>16452584this post feels a bit more monumentous compared to most of the other shit posted here, I hope it doesn't get buried>>16452846>a sitting US Supreme Court justice writes her opinions based on blatantly false informationthis is actually huge
>>16452584>lithera word almost no one has heard or used once in their lives
>>16452584that lame feminist mischaracterization could only come from someone who never watched any of their movies or knows the first thing about dancing. if you've seen any of the famous fred and ginger routines then you know that fred was doing all the heavy lifting between the duo all the big moves and he was moving backwards as often as she was and usually moving his feet twice as fast too. anyone who knows anything about dancing knows that dancing lead is always twice as difficult as following, thats why men lead and women follow
So are these media and courts and whatever be held liable for spreading fake news?
>>16454511Bezos seems like he is getting ready to hold his employees at least somewhat accountable. He is probably getting tired of them losing $100 million a year of his money.
>you don't exist for billions of years>you are born and then experience a maximum of 100 years of existence before you fade back into non-existence for an infinite amount of time What was the point of being born?
idk
>>16448212https://www.sciencedaily.com/releases/2014/01/140116085105.htm
>>16454288thislibtards gonna hate
>>16448484>The self contained system itself is the you.But the entire universe is one large, self-contained system, in constant connection and exchange within itself
>>16448212Everything is just a dream. I believe that there are infinite number of universes which have their own time passage and laws of physics. We are experiencing some of them trough dreams. Including this one universe. In every dream we have different ammount of power to change things around us. We just appear somewhere and live the experience. There are people who lived whole other lifes in their dream and when they woke up they fall into depression because they lost their loved ones in that dream.
Weinstein sister, have we been too cocky? Our response?
gib qrd
>>16455048professor dave is the bootlickiest midwit redditor on youtube. he gets derangement syndrome about literally anyone who questions an establishment soience narrative about anything
>>16455112Anyone who uses words like "establishment soience" is a totally braindead retard.
>>16455048i heckin love deboonking
>>16455048Why does he pretend to be a professor? Is it merely to get stolen valor points with libshits?
i'm serious
Just curious as to what does the anonymous think of this article.
>>16454649I think it's cool, interesting and funny.
>>16454655thx
>>16454641>>Recently, for example, I’ve been looking into the causes of pain vocalizations—why we say “ow” or “ouch” when we’re hurt. It’s actually quite fascinating: our responses are automatic, and yet they vary across cultures. You might say “ay” in Spanish, but “jao” in Croatian or “aya” in Korean, because there is a level of societal variance to it. All these sounds share some kind of /a/ or /o/ vowel, but we end up getting so used to our culture-specific versions that our brains encode them as part of our instinctive reactions to things.I say a variety of those, like "aah" "ou" "ay" or a muzzled "mmmmmmmhh" , and I suspect the majority of people do too. Never heard anyone simply say "ouch" every time because of their nationality lmao
>>16455131"GODZILLA JONES" ~driver's ed instructor
a circle represents infinity, the spiritmatter is tangible, a squareif the amount of sides of a polygon goes to infinity, then the interior angle goes to 179.999...° = 180° , making it a flat line, or a circle.matter into spirit, spirit into matter
>>16454806Are you using Physical reality as a base-system, or an arbitrary numeration for ease of universal application (even when it no long has significant relevence)?
>>16454807Cult of Fag.We HEAR you, sir
>>16454808>HEARBut do you SEE?
>>16454811This is correlated to "Standard Units of Measure" and where they come from. Where foot, mile, meter, etc, are derived. √153 equalling the number of moons in a year. Time, calendars, units...numeration.Lunar and solar calendars being a major change in hueman perceptions of SpaceTime.
>>16454779>The square root of Phi (1.6180339887…) = 1.2720196495…>4 divided by 1.2720196495… = 3.14460551103…that's coolwhen you take the side length of the base of the great pyramid and divide it by its height you get440 / 280 = 1,571428571428 or ~ Pi / 2if you take the area of the 4 triangles and divide it by the area of the base you get313359,09 / 193600 = 1,61859034 ~ Phi
What are some top tier undergraduate/graduate level math books that have been released recently (last 2-3 years)?
>>16448088you might like this:https://archive.org/details/mir-titles
>>16453396Those are all old, the OP is looking for recent books "(last 2-3 years)".
Why did this thread attract so many schizos and yet only one serious answer so far?
>>16453549oops, sorry OP. i read 'Moscow' and i immediately thought of MIR books.
>>16448223LMAO, literally rent free
>one of the greatest mathematicians of the 20th century>by all accounts lacked completely in femininity and was essentially a man in a skirtmathsisters.....
>>16453383>17Yes? So you are wrong
>>16454749I'm sorry, but are you functionally retarded?
>>16452261If you're trying to say that tomboys are gay you need to leave right fucking now.
>>16453383>judging quantity instead of qualityWhew lad. If you wanna go math mode define a space and its measure first. Just using positive integers isn't cutting it.
>>16452261My mom had shoulder pads too, glad that is out of fashion
I can't believe we'll see a man land on the moon within 2 months. How will NASA do it?
>>16454714We've never had operational cameras on the night side. Apollo missions landed in daylight and left before night fell. Soviet and Chinese have landed rovers, but they are solar powered and go into hibernation when night falls.No one has really put any effort to night photography on the moon because the stars would essentially identical as they do from Earth or Earth orbit. There's no scientific value.There are some photos of the stars from Apollo 15 when they were orbiting over the night side of the moon, but the main purpose was just to test the cameras in low-light conditions.
>>16455006of course he is, they all do the exact same thing - post little tiny clips to avoid having to see anything that doesn't fit into their silly 'its all fake' worldview. you can watch people floating around in the ISS for hours at a stretch but no, with the space-is-fake-and-gay faggots its always 20 seconds at a time. lol. cowards.
>>16455006>>16455039More logical fallacies.I didn't claim the ISS didn't exist or that you can't be in low earth orbit with basically zero gravity.This is /sci/. So emotionally invested they don't ever address what you say.
>>16455047the fallacy is that you're posting something and just claiming it's fake without the slightest bit of evidence. You're stating an opinion based on nothing and acting surprised when nobody takes your claim seriously.
>>16454788>Do you believe they climbed Everest?If they have 16000 super HD photos, hours and hours of 16mm video footage of the whole thing, had people tracking them all the way there and back, had all the equipment to do it and brought back 800lbs of rock samples, yeah, i think i would.
Why do indians in the USA have an iq of 112 but indians in india have an iq of 80?
>>16454872It was found in a study that jeets of different castes living in the same village had genetic distance higher Europeans living in different countries.
>>16452427Except if you are at the top in one country there is no guarantee you will also be at the top in another one - thus the people who emigrate are never the best or the highest class. Also if you emigrate then there is no guarantee your spot back home won't be filled by somebody else. It would be quite stupid to leave India if you are part of the upper class there.
>>16452382They are a very tiny minority though.
>>16453716That's not how regression to the mean actually works though. The regression happens when outliers in a population mate back within the general population. Hence it regresses back because the source genome is being redrawn from again and again.The situation with immigration is different because you are taking outliers, isolating them into a new environment, to which they aren't drawing from the original source as much anymore. So if any "regression" does happen it will generally be to a higher IQ average (since that's among the traits being selected for in this situation) because the genome has been severely restricted (specifically the """randomness""" of the genome). In part due to no longer having broad access to the source population (which itself is more "random" in nature).
>>16452382Fantastic. That means we must have all indians come to the US. Just imagine all the problems we could solve!
im stuck in a limbo where i know all the standard math taught in an engineering degree but i dont really feel like i know it well enough since i never cared much about it and just passed exams, but now i do care.it's very similar to the tutorial hell for programming: books/videos/lectures are either too slow or too fast with no in between.there's ton of resources for math out there but i don't have the time and ability to filter them and not waste my time.i'm asking to the people that were in a situation similar to mine, what did you do?>pic relatedonly skimmed through chapters and it seems very very good. not sure if i will use it.
>>16452456Have you tried the Princeton Companion to Applied Mathematics? If you need exercises you can try the Body and Soul project and Project Eulerhttps://www.bodysoulmath.org/https://projecteuler.net/
>>16454595That body and soul link looks great, thanks for sharing it
>>16454595really great books that you recommended. i already downloaded all three volumes of Applied Mathematics: Body and Soul. The princeton one looks really good too.thank you, if you have more stuff please share it!
>>16455061Reading is for nerds. I recommend no book, but going out there and observing the world, coming to conclusions
>>16455066let me how that worked out for you.
Why is it that whenever someone bring up colors in scientific discussions, there will be someone who mention this color every single time?
>it's just white without greenyellow is white without bluecyan is white without redmagenta is nothing special in that regard
>>16436128>MUHHHHHHHgenta
>>16436128lol
>>16450669that was literally what I was talking aboutcolor is brains interpretation of signals sent by the retinayou could see color with zero waves entering your eyes, just stimulate optical nerve accordingly if you modified someones retina so that red receptors got triggered by shorter blue wavelenght then he would see all blues as redand all color perception is by definition 100% subjective
Magneta is a colourful shade.
>woops.. muh braineeee
How come when I binge eat red meat or drink a fuckton of wine and then passout I get more vivid and normal dreams that I am more likely to remember than otherwise? Is there a biochemical reason for this?
>>16454790What a cute little critter. I want one.
>>16454790Could be cholinergic transmission enhanced by foodAnd glutamate rebound from alcohol consumption I used to dream very lucidly while withdrawaling from alcohol. Ever told an entity in your dream they’ll perish upon your awakening? That sort of shit
>>16454790New and exciting experiences are what create dreams. For a healthier experience, try stepping out of your comfort zone, trying new things, and having a busy day more often.
>>16450296>be obsessed with categorizing your sexuality/gender>develop instinctual category theory because sex is one of the main motivators of the human species. As below, so above.
>>16453360How about intuitionistic category theory, because it's real in their minds?
Pretty strange that a category theorist can make the exact same breakthrough almost a year after its already been made without ever showing any work in that specific area or even any knowledge of that perticular field. Pretty strange to be honest.
>>16450296Liking category theory and troonism are both strong predictors of severe autism.
>>16450296If they understand what a category is they will be able to manipulate the category they were born in.
