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Mathematician Answers Math Questions From Twitter | Tech Support | WIRED - YouTube
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when am i ever going to need this i'm
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looking at your screenshot and i think
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the answer is never you are never going
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to need this
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i'm professor moon duchen comma
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mathematician today i'm here to answer
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annie and all math questions on twitter
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this is math support
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[Music]
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at records for song says what is an
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algorithm keep hearing this word hmm the
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way you spelled algorithm like it has
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rhythm in it i like it i'm gonna keep it
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a mathematician what we mean by
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algorithm is just any clear set of rules
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a procedure for doing something the word
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comes from 9th century baghdad where al
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juarez me his name became algorithm but
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he also gave us the word that became
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algebra he was just interested in
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building up the science of manipulating
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what we would think of as equations
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usually when people say algorithm they
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mean something more computery right
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so usually when we have a computer
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program we think of the underlying set
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of instructions as an algorithm given
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some inputs it's going to tell you kind
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of how to make a decision if an
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algorithm is just like a precise
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procedure for doing something then an
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example
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is a procedure that's so precise that a
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computer can do it at llamalord1091
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asks how the did the mayans develop
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the concept of zero everybody's got a
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zero in the sense that everybody's got
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the concept of
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nothing the math concept of zero is kind
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of the idea that nothing is a number the
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heart of it is how do different cultures
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incorporate zero as a number i don't
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know much about the mayan example
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particularly but you can see different
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cultures wrestling with is it a number
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what makes it numbery math is decided
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kind of collectively is that it is
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useful to think about it as a number
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because you can do arithmetic to it so
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it deserves to be called a number at
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jess peacock says how can math be
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misused or abused
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because the reputation of math is just
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being like plain right or wrong and also
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being really hard it gives
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mathematicians a certain kind of
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authority and you can definitely see
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that being abused and this is true more
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and more now that data science is kind
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of taking over the world but the flip
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side of that is that math is being used
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and used well about five years ago i got
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obsessed with redistricting and
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gerrymandering and trying to think about
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how you could use math models to better
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and fairer redistricting ancient ancient
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math was being used if you just close
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your eyes and do random redistricting
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you're not going to get something that's
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very good for minorities and now that's
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become much clearer because of these
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mathematical models and when you know
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that you can fix it but i think that's
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an example of math being used to kind of
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move the needle in a direction that's
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pretty good at crisp x chris x the news
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that is hard to say analytic valley girl
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i honestly have no idea what math
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research looks like and all i'm
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envisioning is a dude with a
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mid-atlantic accent narrating over
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footage of guys in lab quotes looking at
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shapes and like a number four on a
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whiteboard there's this fatal error at
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the center of your account the
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whiteboard like no mathematicians are
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fairly united on this point of
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disdaining whiteboards together so we
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really like these beautiful things
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called chalkboards and we especially
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like this beautiful fetish object
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japanese chalk and then when you write
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it's really smooth
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the things that are fun about this like
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the colors are really vivid and also it
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erases well which matters you just feel
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that much smarter when you're using good
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chalk one thing i would say about math
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research that probably is little known
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is how collaborative it is typical math
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papers have multiple authors and we're
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just working together all the time it's
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kind of fun to look back at the paper
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correspondence of mathematicians from
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like 100 years ago who are actually
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putting all this like cool math into
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letters and sending them back and forth
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we've done this really good job of
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packaging math to teach it and so that
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it looks like it's all done and clean
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and neat but math research is like messy
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and creative and original and new and
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you're trying to figure out how things
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work and how to put them together in new
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ways it looks nothing like the math in
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school which is sort of a much polished
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up after the fact
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finished product version of something
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that's actually like
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out there and messy and weird
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so dylan
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john kemp says serious question that
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sounds like it's not a serious question
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for mathematician scientists and
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engineers do people use imaginary
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numbers to build real things yes they do
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you can't do much without them in
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particular you equation solving requires
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these things they got called imaginary
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at some point because just people didn't
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know what to do with them there were
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these concepts that you needed to be
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able to handle and manipulate but people
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didn't know whether they count as
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numbers no pun intended here's the usual
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number line that you're comfortable with
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0 1 2 and so on real numbers over here
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and then just give me this this number
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up here and call it i
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that gives me a building block to get
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anywhere so now i come out here this
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will be like three plus two i so i is
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now the building block that can get me
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anywhere in space
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yes every bridge and every spaceship and
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all the rest like you better hope
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someone could handle imaginary numbers
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well at
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lit clavini
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says hashtag movie errors that bug me
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the seventh equation down on the third
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chalkboard in a beautiful mind was
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erroneously shown with two extra
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variables and an incomplete constant boy
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that requires some zooming i will say
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though for me and lots of mathematicians
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watching the math and movies is a really
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great sport so what's going on here is i
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see a bunch of sums
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i see some partial derivatives there's a
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movie about john nash who is actually
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famous for a bunch of things in math
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world one of them is like game theory
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ideas and economics but i do not think
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that's what's on the board here if i
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have to guess i think what he's doing is
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earlier very important work of his um
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this is like nash embedding theorems i
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think so this is like fancy geometry you
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can't tell because it looks like a bunch
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of sums and squiggles you're missing the
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part of the board that defines the terms
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so um do i agree with jk vinnie that
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stuff is missing from the bottom row
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i don't think that i do sorry vinnie
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at adhs jag club asks question without
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using numbers and without using a search
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engine do you know how to explain what
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pi is in words you sort of need pi or
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something like it to talk about any
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measurements of circles everything you
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want to describe about round things you
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need pi to make it precise circumference
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surface area area volume
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anything that relates length to other
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measurements on circles needs pi here's
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a fun one so what if you took four
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and you subtracted
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four four-thirds and then you added back
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four-fifths and then you subtracted
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four-sevenths
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and so on so it turns out that if you
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kept going forever this actually equals
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pi i don't teach you this in school so
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this is what's called a power series and
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it's it's pretty much like all the
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originators of calculus we're kind of
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thinking this way about these like
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infinite sums so that's another way to
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think about pi if you like are allergic
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to circles and because you're the only
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one bro
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why did math people have to invent
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infinity because it is so convenient it
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completes us um
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could we do math without infinity the
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fact that the numbers go on forever one
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two three four dot dot dot it would be
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pretty hard to do math without the dot
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dot dots in other words without the idea
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of things that go on forever we kind of
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need that but we maybe didn't have to
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like create a symbol for it and create
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an arithmetic around it and create like
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a geometry for it where there's like a
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point at infinity
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that was optional but it's pretty
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at
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the phil whelix what is the sexiest
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equation i'm gonna show you an
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identity or a theorem that i love i just
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think is really pretty and that i use a
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lot so this is about surfaces and the
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geometry of of surfaces it looks like
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this this is called minsky's product
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regions theorem so this is a kind of
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almost equality that we really like in
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my kind of math
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the picture that goes along with this
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theorem looks something like this
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you have a surface
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you have some
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curves
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this is called a genus 2 surface
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it it's like a double inner tube it's
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sort of like two hollow donuts kind of
[510]
serger together in the middle and so
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this is telling you what happens when
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you take some curves like the ones that
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i've colored here and you squeeze them
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really thin so it's the thin part
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for a set of curves and it's telling you
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that um this looks just like what would
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happen if you like pinch them all the
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way off and cut open the surface there
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you'd get something simpler and a
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leftover part that is well understood at
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avsa says what if blockchain is just a
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plot by math majors to convince
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governments vc funds and billionaires to
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give money to low-level math research no
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and here's how i know we're really bad
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at
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telling the world what we're doing and
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incidentally getting money for it most
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people could tell you something about
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new physics ideas new chemistry new
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biology ideas from say the 20th century
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and most people probably think there
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aren't new things in math right there
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are breakthroughs in math um all the
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time one of the breakthrough ideas from
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the 20th century is turns out there
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aren't three
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basic three-dimensional geometries there
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are eight
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flat like like a piece of paper round
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like a sphere
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and then the third one
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looks like a pringle it's this
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hyperbolic geometry or like saddle shape
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another one is actually instead of a
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single pringle
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you pass to a stack of pringles so like
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this so we call this h2 cross r put
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these all together and you get a three
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dimensional geometry and then the last
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three
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are nil this guy over here saul which is
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a little bit like nil but it's hard to
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explain
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and then the last one which i i kid you
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not is called sl2r twiddle really that's
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what it's called finally it was proved
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to like the community satisfaction what
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is now called the geometrization theorem
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the idea of how you can build stuff out
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of those eight kinds of of worlds it's
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just one example of the publicity
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mathematicians are failing to generate
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did we invent blockchain to like get
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money for ourselves no we did not at
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riley alonso is geometric group theory
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just annabellian topology and then
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there's this like my absolute favorite
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part of this is the laughing crying
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emoji because riley is just like
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cracking herself up here what riley's i
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think really saying here has to do with
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just like how much things commute right
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so you're used to a b equals b a
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that's when things commute and then you
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can sort of do math where that's not
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true anymore for like you know a b
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equals b a times a new thing called c
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that's just not the math you learned in
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school like what is this new thing and
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and how do you understand it well it
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turns out
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this is the math
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of
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this model here
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this is a model of what's called nil or
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no potent geometry it's pretty cool as i
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rotate it you can probably see that
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there's some complexity here from some
[681]
angles that looks one way from some
[683]
angles you see different kinds of
[684]
structure this is my favorite i love to
[686]
think about this one a and b are kind of
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moving horizontally and c is kind of
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moving up in this model so that really
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shows you something about what riley's
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calling geometric group theory you start
[697]
with just like the group theory of how
[699]
to multiply things and it builds
[701]
geometry for you but is it hilarious
[703]
like
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no
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it's sort of stringing a bunch of words
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together and trying to make meaning out
[709]
of them and i think that's the joke here
[711]
and like all jokes when you try to
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explain it it sounds desperately unfunny
[715]
at ruth townsend law question for
[717]
mathematicians why do we solve maths
[719]
problems in a particular order of
[721]
operations eg why multiplication first
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this is like asking in a chess game how
[726]
come bishops move diagonally it's
[728]
because over time those rules were
[730]
developed and they produced a pretty
[731]
good game i could make up a chess game
[733]
where the bishops moved differently but
[736]
then it would be my burden to show that
[737]
it's a good game we could do arithmetic
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differently and we do in math all the
[741]
time we set up other number systems with
[743]
other arithmetics you just have to show
[745]
that they have some internal consistency
[748]
that you can build a good theory around
[750]
them and maybe that they're useful for
[751]
modeling things in the world and then
[753]
you're in business at hey
[756]
irini how is math supposed to be
[758]
universal when all our teachers in the
[759]
same state teach different the thing
[761]
about math being universal there might
[763]
be like 10 different ways to do long
[765]
division and get the answer right we're
[767]
trying to stabilize math around the
[770]
world we're trying to take lots of
[771]
different mathematical practices and
[773]
turn them into something where we have
[775]
enough consensus that we can communicate
[777]
at sham sandwich says music is just math
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that
[782]
i'm not quite sure what you mean by that
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um but there is a lot of math in music
[787]
if you think about constructing notes
[790]
that are going to sound good to a
[792]
mathematician you're just doing rational
[794]
approximations to logarithms
[796]
transcendental numbers again like pi
[798]
numbers that can't be made into exact
[800]
fractions but can only be approximated
[803]
in order to decide on the distances
[805]
between keys on a keyboard in order to
[807]
make it sound good we're trying to
[809]
approximate something that is a number
[811]
that can't be exactly captured with
[813]
fractions there's a lot to say about um
[816]
the math that's in music as to the rest
[818]
of your proposition i will just um trust
[822]
you on that
[823]
at
[824]
tuktaku
[827]
how does math make sense
[829]
lots of punctuation um why put a
[831]
fraction on top of another fraction when
[833]
am i ever gonna need this
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that is like
[836]
the
[837]
thing that math people do like six
[840]
divided by two and that's a very basic
[841]
thing we like to be able to do and so
[843]
the math people come along and say well
[845]
what if i put in different kinds of
[847]
numbers
[848]
what is
[849]
six over minus two but that's what
[851]
mathematicians do we take a system and
[854]
we just like try to put in other kinds
[856]
of inputs that it wasn't expecting you
[858]
teach me how to add and then i come
[860]
along and i want to add shapes you're
[862]
like you don't add shapes you add
[863]
numbers and i'm like but why we're going
[865]
to do it every time we can't be stopped
[867]
when am i ever going to need this
[868]
looking at your screenshot and i think
[870]
the answer is never you are never going
[872]
to need this at neil vaughn first a
[874]
question for mathematicians is 0 an odd
[877]
or even number even number is any number
[879]
that can be written as 2 times k where k
[881]
is a whole number 0 is even if zero is a
[883]
whole number is zero whole number and
[885]
you get down a rabbit hole zero is even
[887]
because it's convenient for some things
[889]
it is definitely different from the rest
[891]
of the numbers you're you're not wrong
[893]
about that at deftsoulal
[896]
asks who's the greatest mathematician in
[898]
history does anybody know and if so
[900]
explain why there are all kinds of
[902]
incredibly interesting people that are
[904]
not well enough known so i'm just going
[906]
to tell you about a few like of my
[908]
favorites felix halsdorf he's awesome he
[912]
basically built the math behind fractals
[915]
and did all kinds of other creative
[917]
stuff and nobody's ever heard of him
[919]
outside of math emmy nother you cannot
[921]
go wrong with emmy nother she's so
[923]
interesting she's a great mathematician
[925]
had kind of a cult following her math is
[928]
great her ideas are deep she like was
[931]
very powerful builder of abstraction and
[933]
i think you can't go wrong learning
[935]
about emmy nother math is full of these
[938]
really colorful characters having like
[940]
out of control original great ideas it'd
[943]
be great if we figured out how to tell
[945]
their stories a little better at
[947]
jhatch17 says i have a question for math
[949]
people
[950]
if there are an infinite amount of
[951]
points between any two points but we can
[953]
still walk from point a to point b
[956]
do we walk through infinite points to
[957]
get there how do we get anywhere this is
[959]
an old and deep question the idea that
[962]
math is math is math and that it's
[963]
universal and that it's all the same and
[965]
then it's all figured out hides a lot of
[966]
mess and this is a good example the
[968]
theories that let you do that that let
[970]
you describe how points combine to make
[972]
a line were actually controversial and
[974]
took hundreds and hundreds of years to
[976]
kind of work out to people's
[977]
satisfaction the best way to explain
[981]
how math has
[982]
built structure to answer this question
[984]
is calculus it's about the difference
[987]
between durations and instance it's the
[989]
difference between lines and points
[991]
calculus and what comes after it measure
[994]
theory those are the ways that
[996]
mathematicians have built to to answer
[997]
questions like this at alejandra turtle
[1001]
says i have a question for
[1002]
mathematicians why letters in an
[1004]
equation it's kind of hell this is one
[1006]
of those great examples where it didn't
[1008]
have to be this way but like some people
[1010]
made some decisions and they caught on
[1012]
and they traveled around the world and
[1014]
people were like well it'd be kind of
[1015]
nice if we all did it the same way and
[1017]
so letters caught on this is very
[1018]
arbitrary it's just a convention and we
[1021]
kind of all agreed that we'd do it the
[1022]
same way those are all the questions for
[1024]
today so thank you to math twitter and
[1027]
thanks for watching math support
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