Oxford Mathematics Student Tier Ranks Math Theorems (very unhinged, very mindful, very demure) 🤠

there I say it's like the you know the Avengers of theorems maybe and whenever I used to apply it it felt like creativity was not in the room with us anymore I do think it's a tiny bit overrated like did any of you actually use it in a match problem ever like did you actually use it in real life at any point all right Mets fans and fellow geks have you ever wondered which theems deserve the crown and which ones should just stay in the back seat well maybe not because because this is indeed extremely unnecessary but that's why I'm here with you today to provide your daily dose of pretty cringy Med pons and to bring you offense when I will be roasting your favorite theorem of course playfully and let's not forget about putting my Oxford meth degree to good [Music] use okay so today we will be ranking some of the most famous Mets FS based on their utility their Elegance and of course how much they make the average student suffer in an average math class okay so let's see the tiers so we have from the very top which is the very best to the lowest proof positive which is for those theum that are absolutely Essentials they game changers or the most elegant then right below we've got solid foundations which is for those serums that are still pretty crucial but not as iconic as the top tier ones then we have the pretty neat tier which is quite self-explanatory it's for those theems that are interesting they're still useful but they're not quite top League then we've got our Workhorse wonders which are for ones that are functional and reliable but not really mindblowing then you know a little met punon here and there doesn't hurt anyone so as the name suggests serums that are less exciting or only relevant in Niche scenarios and at the very bottom we've got forgotten theorems the ones that are very rarely used or just plain obscure and we'll see which ones fall in each of these the so starting off really really strong with Oilers identity um come on this isn't just a theorem it's a mathematical Masterpiece for real it I Pi + 1 equal 0 ties together five of the most important numbers in the whole of Mets really and it's just one elegant equation there I say it's like the you know the Avengers of theorems maybe all of the big ones all of the big names United for a single cause it gives the same Vibes doesn't it if I'm going even further if this theorem were a piece of art you know it'd be the Mona Lisa and just like her smile it's beautifully enigmatic isn't it so yeah it gets a prove positive for me without any further Ado so okay another classic we've got the quadratic formula ax² + BX + C = 0 has d trusty formula to fall back on you know it's not glamorous but I do remember watching my teacher do the proof in class when I was like 12 years old and at the time I thought that it was pure genius I'm sorry I did not know any B so what can I say yeah it's reliable always gets the job done really you know it's like that one friend who always has a solution even if it's not the most creative one but it can always come up with something I feel like this is how I would describe it quadratic formula so yeah it's pretty mid but pretty neat yeah we'll leave it in pretty neat I think okay we have the central Lim etherum this is the unsung hero of statistic isn't it it tells us that under certain conditions the average of a large number of random variables will be normally distributed in other words it's the reason we can pretty much always use bell curves to predict everything from test scores to stock prices it's not very flashy and it's just an approxim imation after the r but it is very reliable and makes you see the whole picture really quite instantly so yeah I think solid foundations will be reasonable for it to be honest all right the binomial theorem I'm not going to lie I am not the biggest fan of it I know it's very important but still yeah so the binomial theorem gives us the power to expand binomials race to any power saving us from theoretically pretty tedious multiplication ation I remember I Was preparing for Olympiad right and I was desperately in need of a tool to do this kind of thing and I was very disappointed that the binomial theorem was it so it makes your life a tiny bit easier but it's not really saying much like it doesn't give a lot of love you know what I mean I think it's like elevator music or like background music you know it's not like it's not mind-blowing so yeah kind of meh kind of Mech K's integral formula now this is actually a pretty nice one it's pretty Niche but in complex analysis this formula is like magic trust me and it gives you the value of a function within a contour if you know its value around the Contour so it's not Everyday Math but in its domain it's very powerful and elegant so yeah pretty neat pretty neat I would say Okay lal's row quite a big fan of this quite a big fan to be honest it feels like the loophole in calculus you know basically lets us solve in determinate forms like 0 over Z Infinity over infinity it's not the fanciest theorem out there I will give you that and I remember when I first learned calculus I was feeling very rebellious in a way and I just applied it without even checking if we had an indeterminate form which is not ideal it is very practical though if you know when to use it and it's like finding an alternate route you know when the main road is blocked so yeah like it's like a warhorse wander I think that's pretty reasonable for it yeah we have the we weak and strong law of large numbers the laws of large numbers are all about how the average of random uh variables converges to the expected value as the sample size increases as it goes to Infinity it's pretty intuitive and for sure it's very very important in probability but they both tend to be overshadowed by their let's say flashes relatives such as the central Li theorem for example and I remember being very very upset when I um expected the proof of the strong law to be as nice and easy as the proof for the week one and then having to deal instead with backwards marting yels which is not really the nicest memory I have so yeah yeah forgotten theorems it gets overshadowed quite a bit all right we've got the Chinese remainder theorem yeah so that's quite the Staple in number Theory I suppose it helps us solve systems of simultaneous congruences it's pretty decent pretty clever it's got some nice applications in CS as well so in computer science but it's not necessarily A Crowd pleaser it's a bit tedious as I've said and whenever I used to apply it it felt like creativity was not in the room with us anymore so yeah yeah just let's just give it a me I suppose okay we've got basy serum now now this is actually a good one so this Ser bring together the power of probability into the realm of decision making it's very much used in practice it's very useful in everyday situations and it's like everyone understands what it says really so it's basically by updating probabilities based on new evidence is a theorem that lets us refine our initial predictions and just make smarter choices overall so it's basically the theorem that says hey let's think about it logically so yeah it it does deserve a proof positive in my opinion I I feel it's fair all right green theorem this is applied Ms at IS F Min I would say it makes our life easier by turning complex line integrals into double integrals so it gives us a very neat trick I would say and it's a staple in fields such as fluid mechanics or electromagnetism I guess we shall put it in pretty neat yeah that's pretty reasonable after all it's got the older sibling which is Stokes right here which I think deserves a higher the solid foundation simply because it generalizes both greens and Gussy theorems and actually many more it turns a surface integral into a line integral and also vice versa so it's definitely indispensable for both physicists and uh Engineers it does provide a bit of a headache from time to time when you have to deal it especially for the average student but you know you can't argue with you can't argue with the facts solid foundations ah Oilers line I absolutely love geometry I'm not going to lie I will try not to be biased whenever geometry trick appears but I cannot make any promises here so like come on Oiler line must be like the cool kid of geometry is the straight line that goes through some of the most important points in a triangle like the Cent the orto senta the circum stenter and also the center of the npoint circle which is really really cool it's geometrically elegant it's very satisfying and yeah I don't care I don't care if I'm biased it's Pro positive for me all right fubini's theorem it is all about efficiency yeah I would say it's all about efficiency it lets us swap the order of integration in double integrals it's a Workhorse for anyone dealing with multivariable Calculus especially it makes integration a little bit less of a pain than it normally is but you cannot lie to me and say that you have not been guilty of swapping the order regardless without even checking if a applies so yeah it's quite me quite me to be honest caner diagonal argument I cannot really say much about this it just feels like the ultimate mind blown moment in Seth the as a whole I think so by showing that the real numbers are uncomfortable it just opens the door to very bizarre and beautiful worlds of infinity so yeah it's pretty neat pretty neat that's all I can say really we have the Holy Grail of met in front of us ladies and gentlemen this is like the mystery novel of number Theory isn't it nobody solved it but everyone has your opinion but I do put my money on James May are solving it so yeah mark my words I I do think that James May would actually sove it so proving or disproving it could actually redefine the field it would be the ultimate what if I would put it in proof positive simply because it would make so many things true it would unveil so many Mysteries but come on it's not really a theorem cuz it's not proven it doesn't have a proof so I cannot really put it in any of the theor it would just not be fair for the other ones that actually have a proof so I would put it in forgotten theorems just because it hasn't been proved yet and then in a a few years if it's eventually sold we will open up this discussion again all right we have the law of total probability this theum is just about making sure that you account for all possibilities when you calculate probabilities in general so is the leave no stone unturned I would say approach so a word of probability it's very Central in Theory it often is taken for granted in practice but it's it's pretty solid yeah it's a Workhorse W it's a Workhorse W simply because it's very intuitive okay we have the ivt yeah the intermediate value theorem that's the it's a very reassuring theorem it just says that if a nice function is simply moving from one point to the other it would cross every single point in between it's very reliable right like it just says oh don't worry about it we'll get there eventually which I think is quite neat yeah pretty neat nothing else really we have the MV now I guess we can do all of the analysis one in one go I guess so if the ivt was we'll get there eventually the mvt is I Told You So I think it's quite reasonable so it proves that somewhere between two points there is a tangent line uh parallel to the second line passing between the two points it's all about making averages behave and while it's pretty neat it's not exactly lighting up the room by itself it is though used a lot in very foundational proofs in optimization which is essential for ML these days so I think that just moves it up to pretty neat the chain rule the chain rule is that one calculus trick that allows you to differentiate any composite function so it's always handy when things get very tricky it's very satisfying to apply you know the differentiation wor cooking the chamber would be your trusty kitchen knife maybe so it's essential it's quite indispensible yeah solid foundations G in completeness theorem we're getting a bit philosophical guys um yeah so this theorem basically shook the foundations of mathematics by proving that there are some truths in math that cannot be proven simply it's very deep very philosophical as I've said it's like dropping a plot twist at the end of a movie that and just leaving you completely questioning your entire existence so yeah it's quite mind-blowing stuff um but who am I to put it anywhere else but impr proove positive okay okay Pythagoras that's the OG that introduced so many of us to the world of geometry maybe even the world of maths in general a s + B2 = c^2 it's just the formula we all either fell in love with or were tormented by when we first learned matths in school I do think it's a tiny bit overrated like don't judge me it's not even that useful when you get deep enough into math and it's not even that satisfying so we just say work course W I feel it's it's pretty reasonable okay the semicircle law now that's some very particular stuff that we have here the semicircle law deals with distributions of igon values of random matrices and it is very Niche even for M enthusiasts it's that kind of theorem that you appreciate when you are very deep into the subjects but it's not making any headlines either I would say that the whole idea of universality in enville statistics is pretty neat but it's not like it's going to change the world at least anytime soon but who knows maybe in the future like don't code me on that I I'm definitely not an expert but yeah for now it just get we will leave it in Mech and then we yeah yeah all right we've got the residue theorem now in complex analysis this theorem helps you evaluate complex integrals by relating them to the sum of residues of the given functions of the integrant it makes me think of a secret shortcut in a video game you know the kind of thing that not everyone knows about but those that do can just Speed Run for the whole game for the whole tough problem that you have at hand I say it's pretty neat but it will get lowered to Workhorse Wanda simply because calculating the residue of a function will give you a headache 100% like it's not neat it's very tedious so yeah we have the law of cosiness that's like Pythagoras over the but wiser cousin cuz it can be applied in any triangle it just steps in whenever you're dealing with triangles that aren't that tidy that aren't that neat it's not as universally loved it's not that useful in everyday life but I would say it's pretty neat like I solved some problems with it that were quite satisfying so yeah pretty neat then we've got the low of signs which is again it's great for any triangle very satisfying when you realize that oh this is the tool that I need to use for this problem it simply relates the Angles and the sides you know triangle in a very very simple ratio it's very subtile even if it's not it doesn't get as much attention as Pythagoras but I still think it's pretty neat yeah all right forma's little theorem there a sibling living in the shadow of the very famous older brother you know what I mean yeah you do I'm sure you do so while it's very useful in number Theory it's very useful too especially in cryptography I think it liks the wow factor that FMA last theorem has for example it's pretty me if you ask me just because it only deals with primes as well like it doesn't break any records you know we've got the fundamental theorem of calculus now can say right off the bed this should just go into solid foundations really like if you think about it where would we be without the fundamental theorem of calculus like just let it sink for a bit is the backbone of calculus when you think about it it just Bridges the gap between differentiation and integration and without this calculus would just be like a sandwich without the bread you know it be quite messy not quite as satisfying it doesn't get top tier though simply because it feels a bit too intuitive and you might be just tempted to assume it to take it for granted Without Really checking so yeah solid foundations nonetheless the spectral theorem now in the world of linear algebra this is pretty much a hero gives us the ion values ion vectors of normal matrices foundational Shore but it's not everyone's cup of tea it's more like the steady reliable background character in a movie but it doesn't really come nearly close to the main character so yeah a wareh horse wonder I think is quite suitable for it ooh we've got the angle bis sector theorem now this is very solid in triangle geometry it's one of my favorites actually it relates the ratios of the size of a triangle to the segments created by the angled B bis sector yeah it gets the job done not much fun fair about it it's pretty neat I would maybe put it higher but I know I'm biased in that one so pretty neat okay we have talis's theorem now for real this is one of the oldest results in the H of geometry it states that any angle inscribed in a semicircle is a right angle it's pretty classic pretty essential gets overshadowed by flasher theorems in modern times as expected but also fun fact in Romania we call something else talisis theorem so I'm not really show what that's all about and you can do with that information whatever you want but yeah pretty meh overall I guess okay we have L's theorem the one in group Theory so this theor stating that the order of a subgroup divides the order of the group is essential in abute algebra you'll need to deal with it if you study any introductory course in group Theory essentially very fundamental doesn't often get the same attention as other theorems it is very useful though if you work in the area and I would say I did use it quite a bit so Workhorse Wonder suits it I think all right fma's Last Theorem is the Last Theorem in this tier list as well so we're just sneaking this one in at the end aren't we yeah so for centuries you know the story this theorem has taunted mathematicians with its apparent Simplicity but resistance to proof Andrew WS was the one that finally cracked in 1994 proving that you know x to the n + y to the N equal Z to the N for n greater than who does not have any integer Solutions which is mindblowing in itself so simple it's like the M dick of math you know it's elusive but also satisfying to be finally pinned down I would say do I really believe that FMA had that marvelous proof that he just could not fit in the margins of his notebook not really that that just doesn't sound plausible at all especially with the tools that he had available at the time and thinking about how long while his proof wasn't F they literally use so Advanced mats but it's not like we'll ever know that for sure so yeah one can speculate what can I say it's nice looking it's very interesting how something that looks so innocent can just have such a complex proof but did you actually did any of you actually use it in a match problem ever like did you actually use it in real life at any point honestly it is pretty mad for that reason like let's be honest but we do need to give it points for its very unexpected nature when you do think about it in any PSE 2 case has infinitely many solution it gives you that it gives you those very nice Pythagorean numbers and then when you bump it just one step higher you don't get any solutions they just deserve some extra points by itself even if we don't consider the proof so yeah solid foundations despite despite my rent we give it the solid foundations all right and there we have it guys this is our final thealist of very famous meth theorems do you agree do you disagree let me know down in the comments below and also let me know if I missed any of the very important theorems what else would you include in the top tier in the very bottom tier I do think it looks pretty neat let me know what you think of course this was all just for fun and remember that every single theorem has its own place in the tapestry of mathematics so there are no hard feelings at all even if I put your favorite theorem in the bottom tier please don't take any offense I do personally believe that every theorem has its own Beauty in it and it can be applied in very very satisfying situations despite what I've said about them just now so yeah if you enjoy this video please make sure to give it a thumbs up subscribe to my channel if you want to see more funny or more serious Med content and also University content follow me on Instagram for more content if you feel like it I definitely am a lot more active on there and don't forget to hit the Bell to get any notifications whenever I post to be the first one that actually watches my videos and yeah thank you so so much for watching and I do hope that I will see you in the next one I'm sick A Day Dreaming I just want the feeling of you in my bed you in my bed I'm down at this waste time right below your waistline W you B my head