Mathematician Answers Math Questions From Twitter | Tech Support | WIRED

when am i ever going to need this i'm looking at your screenshot and i think the answer is never you are never going to need this i'm professor moon duchen comma mathematician today i'm here to answer annie and all math questions on twitter this is math support [Music] at records for song says what is an algorithm keep hearing this word hmm the way you spelled algorithm like it has rhythm in it i like it i'm gonna keep it a mathematician what we mean by algorithm is just any clear set of rules a procedure for doing something the word comes from 9th century baghdad where al juarez me his name became algorithm but he also gave us the word that became algebra he was just interested in building up the science of manipulating what we would think of as equations usually when people say algorithm they mean something more computery right so usually when we have a computer program we think of the underlying set of instructions as an algorithm given some inputs it's going to tell you kind of how to make a decision if an algorithm is just like a precise procedure for doing something then an example is a procedure that's so precise that a computer can do it at llamalord1091 asks how the did the mayans develop the concept of zero everybody's got a zero in the sense that everybody's got the concept of nothing the math concept of zero is kind of the idea that nothing is a number the heart of it is how do different cultures incorporate zero as a number i don't know much about the mayan example particularly but you can see different cultures wrestling with is it a number what makes it numbery math is decided kind of collectively is that it is useful to think about it as a number because you can do arithmetic to it so it deserves to be called a number at jess peacock says how can math be misused or abused because the reputation of math is just being like plain right or wrong and also being really hard it gives mathematicians a certain kind of authority and you can definitely see that being abused and this is true more and more now that data science is kind of taking over the world but the flip side of that is that math is being used and used well about five years ago i got obsessed with redistricting and gerrymandering and trying to think about how you could use math models to better and fairer redistricting ancient ancient math was being used if you just close your eyes and do random redistricting you're not going to get something that's very good for minorities and now that's become much clearer because of these mathematical models and when you know that you can fix it but i think that's an example of math being used to kind of move the needle in a direction that's pretty good at crisp x chris x the news that is hard to say analytic valley girl i honestly have no idea what math research looks like and all i'm envisioning is a dude with a mid-atlantic accent narrating over footage of guys in lab quotes looking at shapes and like a number four on a whiteboard there's this fatal error at the center of your account the whiteboard like no mathematicians are fairly united on this point of disdaining whiteboards together so we really like these beautiful things called chalkboards and we especially like this beautiful fetish object japanese chalk and then when you write it's really smooth the things that are fun about this like the colors are really vivid and also it erases well which matters you just feel that much smarter when you're using good chalk one thing i would say about math research that probably is little known is how collaborative it is typical math papers have multiple authors and we're just working together all the time it's kind of fun to look back at the paper correspondence of mathematicians from like 100 years ago who are actually putting all this like cool math into letters and sending them back and forth we've done this really good job of packaging math to teach it and so that it looks like it's all done and clean and neat but math research is like messy and creative and original and new and you're trying to figure out how things work and how to put them together in new ways it looks nothing like the math in school which is sort of a much polished up after the fact finished product version of something that's actually like out there and messy and weird so dylan john kemp says serious question that sounds like it's not a serious question for mathematician scientists and engineers do people use imaginary numbers to build real things yes they do you can't do much without them in particular you equation solving requires these things they got called imaginary at some point because just people didn't know what to do with them there were these concepts that you needed to be able to handle and manipulate but people didn't know whether they count as numbers no pun intended here's the usual number line that you're comfortable with 0 1 2 and so on real numbers over here and then just give me this this number up here and call it i that gives me a building block to get anywhere so now i come out here this will be like three plus two i so i is now the building block that can get me anywhere in space yes every bridge and every spaceship and all the rest like you better hope someone could handle imaginary numbers well at lit clavini says hashtag movie errors that bug me the seventh equation down on the third chalkboard in a beautiful mind was erroneously shown with two extra variables and an incomplete constant boy that requires some zooming i will say though for me and lots of mathematicians watching the math and movies is a really great sport so what's going on here is i see a bunch of sums i see some partial derivatives there's a movie about john nash who is actually famous for a bunch of things in math world one of them is like game theory ideas and economics but i do not think that's what's on the board here if i have to guess i think what he's doing is earlier very important work of his um this is like nash embedding theorems i think so this is like fancy geometry you can't tell because it looks like a bunch of sums and squiggles you're missing the part of the board that defines the terms so um do i agree with jk vinnie that stuff is missing from the bottom row i don't think that i do sorry vinnie at adhs jag club asks question without using numbers and without using a search engine do you know how to explain what pi is in words you sort of need pi or something like it to talk about any measurements of circles everything you want to describe about round things you need pi to make it precise circumference surface area area volume anything that relates length to other measurements on circles needs pi here's a fun one so what if you took four and you subtracted four four-thirds and then you added back four-fifths and then you subtracted four-sevenths and so on so it turns out that if you kept going forever this actually equals pi i don't teach you this in school so this is what's called a power series and it's it's pretty much like all the originators of calculus we're kind of thinking this way about these like infinite sums so that's another way to think about pi if you like are allergic to circles and because you're the only one bro why did math people have to invent infinity because it is so convenient it completes us um could we do math without infinity the fact that the numbers go on forever one two three four dot dot dot it would be pretty hard to do math without the dot dot dots in other words without the idea of things that go on forever we kind of need that but we maybe didn't have to like create a symbol for it and create an arithmetic around it and create like a geometry for it where there's like a point at infinity that was optional but it's pretty at the phil whelix what is the sexiest equation i'm gonna show you an identity or a theorem that i love i just think is really pretty and that i use a lot so this is about surfaces and the geometry of of surfaces it looks like this this is called minsky's product regions theorem so this is a kind of almost equality that we really like in my kind of math the picture that goes along with this theorem looks something like this you have a surface you have some curves this is called a genus 2 surface it it's like a double inner tube it's sort of like two hollow donuts kind of serger together in the middle and so this is telling you what happens when you take some curves like the ones that i've colored here and you squeeze them really thin so it's the thin part for a set of curves and it's telling you that um this looks just like what would happen if you like pinch them all the way off and cut open the surface there you'd get something simpler and a leftover part that is well understood at avsa says what if blockchain is just a plot by math majors to convince governments vc funds and billionaires to give money to low-level math research no and here's how i know we're really bad at telling the world what we're doing and incidentally getting money for it most people could tell you something about new physics ideas new chemistry new biology ideas from say the 20th century and most people probably think there aren't new things in math right there are breakthroughs in math um all the time one of the breakthrough ideas from the 20th century is turns out there aren't three basic three-dimensional geometries there are eight flat like like a piece of paper round like a sphere and then the third one looks like a pringle it's this hyperbolic geometry or like saddle shape another one is actually instead of a single pringle you pass to a stack of pringles so like this so we call this h2 cross r put these all together and you get a three dimensional geometry and then the last three are nil this guy over here saul which is a little bit like nil but it's hard to explain and then the last one which i i kid you not is called sl2r twiddle really that's what it's called finally it was proved to like the community satisfaction what is now called the geometrization theorem the idea of how you can build stuff out of those eight kinds of of worlds it's just one example of the publicity mathematicians are failing to generate did we invent blockchain to like get money for ourselves no we did not at riley alonso is geometric group theory just annabellian topology and then there's this like my absolute favorite part of this is the laughing crying emoji because riley is just like cracking herself up here what riley's i think really saying here has to do with just like how much things commute right so you're used to a b equals b a that's when things commute and then you can sort of do math where that's not true anymore for like you know a b equals b a times a new thing called c that's just not the math you learned in school like what is this new thing and and how do you understand it well it turns out this is the math of this model here this is a model of what's called nil or no potent geometry it's pretty cool as i rotate it you can probably see that there's some complexity here from some angles that looks one way from some angles you see different kinds of structure this is my favorite i love to think about this one a and b are kind of moving horizontally and c is kind of moving up in this model so that really shows you something about what riley's calling geometric group theory you start with just like the group theory of how to multiply things and it builds geometry for you but is it hilarious like no it's sort of stringing a bunch of words together and trying to make meaning out of them and i think that's the joke here and like all jokes when you try to explain it it sounds desperately unfunny at ruth townsend law question for mathematicians why do we solve maths problems in a particular order of operations eg why multiplication first this is like asking in a chess game how come bishops move diagonally it's because over time those rules were developed and they produced a pretty good game i could make up a chess game where the bishops moved differently but then it would be my burden to show that it's a good game we could do arithmetic differently and we do in math all the time we set up other number systems with other arithmetics you just have to show that they have some internal consistency that you can build a good theory around them and maybe that they're useful for modeling things in the world and then you're in business at hey irini how is math supposed to be universal when all our teachers in the same state teach different the thing about math being universal there might be like 10 different ways to do long division and get the answer right we're trying to stabilize math around the world we're trying to take lots of different mathematical practices and turn them into something where we have enough consensus that we can communicate at sham sandwich says music is just math that i'm not quite sure what you mean by that um but there is a lot of math in music if you think about constructing notes that are going to sound good to a mathematician you're just doing rational approximations to logarithms transcendental numbers again like pi numbers that can't be made into exact fractions but can only be approximated in order to decide on the distances between keys on a keyboard in order to make it sound good we're trying to approximate something that is a number that can't be exactly captured with fractions there's a lot to say about um the math that's in music as to the rest of your proposition i will just um trust you on that at tuktaku how does math make sense lots of punctuation um why put a fraction on top of another fraction when am i ever gonna need this that is like the thing that math people do like six divided by two and that's a very basic thing we like to be able to do and so the math people come along and say well what if i put in different kinds of numbers what is six over minus two but that's what mathematicians do we take a system and we just like try to put in other kinds of inputs that it wasn't expecting you teach me how to add and then i come along and i want to add shapes you're like you don't add shapes you add numbers and i'm like but why we're going to do it every time we can't be stopped when am i ever going to need this looking at your screenshot and i think the answer is never you are never going to need this at neil vaughn first a question for mathematicians is 0 an odd or even number even number is any number that can be written as 2 times k where k is a whole number 0 is even if zero is a whole number is zero whole number and you get down a rabbit hole zero is even because it's convenient for some things it is definitely different from the rest of the numbers you're you're not wrong about that at deftsoulal asks who's the greatest mathematician in history does anybody know and if so explain why there are all kinds of incredibly interesting people that are not well enough known so i'm just going to tell you about a few like of my favorites felix halsdorf he's awesome he basically built the math behind fractals and did all kinds of other creative stuff and nobody's ever heard of him outside of math emmy nother you cannot go wrong with emmy nother she's so interesting she's a great mathematician had kind of a cult following her math is great her ideas are deep she like was very powerful builder of abstraction and i think you can't go wrong learning about emmy nother math is full of these really colorful characters having like out of control original great ideas it'd be great if we figured out how to tell their stories a little better at jhatch17 says i have a question for math people if there are an infinite amount of points between any two points but we can still walk from point a to point b do we walk through infinite points to get there how do we get anywhere this is an old and deep question the idea that math is math is math and that it's universal and that it's all the same and then it's all figured out hides a lot of mess and this is a good example the theories that let you do that that let you describe how points combine to make a line were actually controversial and took hundreds and hundreds of years to kind of work out to people's satisfaction the best way to explain how math has built structure to answer this question is calculus it's about the difference between durations and instance it's the difference between lines and points calculus and what comes after it measure theory those are the ways that mathematicians have built to to answer questions like this at alejandra turtle says i have a question for mathematicians why letters in an equation it's kind of hell this is one of those great examples where it didn't have to be this way but like some people made some decisions and they caught on and they traveled around the world and people were like well it'd be kind of nice if we all did it the same way and so letters caught on this is very arbitrary it's just a convention and we kind of all agreed that we'd do it the same way those are all the questions for today so thank you to math twitter and thanks for watching math support

Channel: WIRED

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Keywords: anabelian topology, innovation, math expert, math explained, math questions, math questions from twitter, math tech support, math theories, math wired, mathematician, mathematician moon duchin, mathematics explained, maths, maths questions, moon duchin, ott tech support, pi, pi expalined, pi explained, science & technology, tech support expert, tech support math, wired, wired tech support math

Id: uMMQbcisins

Length: 17min 13sec (1033 seconds)

Published: Thu Feb 17 2022