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 number e 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 ex 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 in movies is a really
great sport so what's going on here is i
see a bunch of sums
i see some partial derivatives this
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 um 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 the 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 two 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 pinched 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's 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 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 going to need this
that is like
the
thing that math people do like 6 divided
by 2 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 and
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 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 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 a 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 combined to make
a line were actually controversial and
took hundreds and hundreds of years to
kind of work out to people 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