who's your favorite mathematician I
always find favorite questions kind of
silly but I will tell you about two
different mathematicians that have been
on my mind lately so a month or two ago
I watched this documentary about Claude
Shannon called the bit player and then
that prompted me to read a little bit
more about Shannon in books like the
idea Factory or James clicks the
information and this guy was super
interesting I almost think of him as
kind of a mixture between Donald Knuth
and Adam Savage so on the one hand you
know he's the father of information
theory he wrote this absolutely seminal
super important paper about transmitting
information and storing it and encoding
it and things like that it really gave
birth to the information age and a lot
of the foundations for computer science
to give you some indication of just how
important this work was there's this one
science fiction novel where all of the
years instead of being measured BC and
AD with respect to the birth of Christ
everything is before Shannon or after
Shannon it's viewed where the foundation
of information theory is so pivotal in
any kind of civilization
that it's worth setting your entire
timeline around that point so that's
Janet super influential on that one hand
on the other hand he was incredibly
playful and very willing to kind of pour
his life into totally useless toys so he
spent a lot of time building different
kinds of unicycles he built this flaming
trumpet for his son he you know built
this automatic juggling machine this
mechanical calculator that would do
computations in Roman numerals just
wholly completely useless things done
for the purpose of play and nothing else
what I think you have to wonder is if
this playfulness is wholly
incidental and unrelated to the
important work that he did or if there's
something that's necessary about it
right if it's required that the kind of
personality who's coming up with
something totally new like original
enough that it is a foundational moment
for a new kind of science almost has to
be the kind of personality that's also
willing to make gizmos and toys for his
own pleasure that other people look at
and see is useless if somewhat fun
another mathematician I've been thinking
about for
elated reasons is Edward Lorenz who is
maybe not the father of chaos theory but
certainly one of the fathers and he
wasn't even a mathematician actually he
was a meteorologist but really he was a
mathematician to his core but wearing
the external veneer of a meteorologist
and he's maybe most famous for this
system of equations it's just three
variables three unknowns
it's one of the earliest examples of
something called a strange attractor but
it came about when he was studying
weather patterns right and weather is
famously hard to understand you know at
the extreme there's a huge number of
unknown variables if you go all the way
to one extreme you could say that every
atom in the atmosphere has six degrees
of freedom so you could have this truly
ungodly monstrous system of equations
that no one could ever hope to analyze
so inevitably you have to do something
to simplify things down for pragmatism
sake and a lot of people I think thought
that the reason weather is hard to
predict is simply because of the number
of variables at play and one of the
important contributions from Lorentz was
to be able to simplify down the
unpredictability of it into a
surprisingly simple set of equations to
say hey some of the facts here that are
hard to predict when you make a you know
when you make some kind of measurement
with a little bit of error around it and
that error kind of propagates that's not
just because of the number of variables
at play you can have that kind of chaos
arising from surprisingly simple
circumstances so in order to do this
right you have to have the strange
mixture again of a kind of pragmatism
with a kind of more pure mathematician
instinct and I wonder if this is ever
something that a pure mathematician
could have done if he wasn't grounded in
a problem like weather where he was
doing all of these computational models
and really just in the weeds of you know
convection or whatever else it might be
so in the same way that Shannon kind of
represents this contrast between
playfulness and pragmatism and my mind
Lorenz sort of represents this contrast
between like applied science and then
pure math and just as Shannon is the
father of information theory it doesn't
seem like a coincidence that we find in
the father of another very instrumental
science to our modern age chaos theory
this sort of middle ground between those
now obviously there's a lot of selection
bias at play here right like most people
define themselves somewhere between peer
and applied are somewhere between
pragmatic and playful don't give rise to
completely new fields of study but I do
have to wonder if the novelty required
to father a new field necessitates
breaking the norm and not falling into
one clear-cut path some of you might be
wondering if every question in this Q&A
will have me pontificating for many
minutes but I do have a broader point
here which is that I think a number of
people watching this channel especially
those on the younger end are clearly
into pure math right they're curious
about it I wouldn't be surprised if a
lot of them are contemplating becoming
mathematicians and for that set of
people I kind of want to put out the
question of where do you think there's
more value do you think it's if all of
these people with this inclination
towards pure math go into that field and
that's where they get to collaborate
with a lot of folks who are like-minded
who think like them they resonate on the
same wavelength maybe they amplify each
other's strengths or is there more value
if each one of them kind of gets
dispersed into some completely different
field and each one is not so much a
mathematician as a mathematician plus X
right they're mathematician plus a
builder plus a meteorologist plus
whatever have you and they take those
instincts of playfulness towards puzzles
or desire to abstract the simplest form
of a specific kind of hardness and
basically bring that mathematician
instinct to something totally different
right which of those worlds has more
value
a teenage kid walks up to you and says
they hate math what do you tell or show
them
I get the impression that the spirit of
this question is for me to answer with
some piece of math that's so enticing
that even the most ardent of math haters
would have to bring about some kind of
affection for the subject but the thing
is if someone comes to you and they
admit that they don't like math or that
they hate math I don't think you should
show them a piece of math even if you do
want to convert them it's a little bit
like if let's say you really love coffee
right and someone comes to you and they
say I just hate coffee but you like it a
lot and you're kind of this snob and you
really want to turn them on to it the
way to do it is not to try to find the
world's best cup of coffee and then give
it to them there's no matter what it's
going to taste like dirt they don't like
it they're not addicted to it at this
point instead if you want to turn
someone on to it we have a couple
options one of them can be to first read
necessity and then from there maybe get
an addiction so let's say it's a student
and they need to stay up all night to
finish some kind of paper and you know
so they progressing we'll have to take
some caffeine and after that a kind of
culinary Stockholm Syndrome kicks in and
through the addiction they come to kind
of like the substance that's not the
greatest but that's a way to do it the
analog with the world of math might be
hmm
trying to find something where math is
the drug necessary for someone to
accomplish what they want to you know
maybe they're really into video games so
they want to make their own video game
and often in writing the software for
that you have to use geometry
trigonometry maybe if it's a calculus it
kind of depends on the game that you're
building
so you breed the necessity but in either
case I think the key is to just try to
build up familiarity just be exposed to
math in a lot of different contexts and
importantly for it to not ever be
traumatic when that happens I think the
reason a lot of people say that they
hate math it says their only exposure to
it is tightly linked with a sense of
failure right it's a hard subject but
importantly it's a very cumulative
subject so if you miss one little part
it looks like you're failing in all of
the later parts even if you would have
been really good at those other parts
without that missing link so instead if
the math comes about in a less
judgmental context something where
there's no grading you know maybe it's
just playing with puzzles with friends
or it's writing that bit of software for
the video game or whatever it is where
you're gaining exposure without that
trauma
I think after enough time you're just
gonna like the subject because I think
if we're all really honest with
ourselves and we look back on why we
like the things that we like it's often
because someone in our life liked it the
time we were spending with them brought
us to spending time with that thing and
then it just stuck with us what advice
would you give to a math enthusiast
suffering from anxiety disorder clinical
depression and ADHD I'm not entirely
sure how the word math enthusiast and
the question changes the answer but I
will say that for anything
health-related and this goes double for
mental health definitely seek
professional help earlier than you think
you need to so don't be shy about
finding a therapist or asking your
doctor about these kinds of things one
thing I will say as a professional
youtuber I do think it's probably
healthy for people to spend less time on
the Internet you know I always get this
uneasy feeling if I hear about someone
binge watching all of my videos or
something like that because on the one
hand I often do measure success in terms
of how much time people are watching the
videos it's some indication of how much
it's reaching the world how deeply
people want to engage with it and all of
that but on the other hand if I think of
someone kind of staying up all night to
watch YouTube or even just sitting in
their house all day to watch YouTube no
matter what that video is no matter how
enlightening or how educational it seems
to be that's got to be bad for you and
unhealthy in comparison to occasionally
you know going outside or spending time
with real people in the world or if you
want to engage with math doing it in a
more physical social kind of way he's
Ben Ben and blue still a thing ah yes
the podcast with the Ben's no I don't
think it'll continue I don't think
that's a bad thing I think we had some
really good conversations about
education in there I'm not sure how much
we necessarily had to say and I don't
think all projects should live forever I
think there's something kind of nice
about doing something a little different
a little experimental and then being
willing to just walk away from it if it
seems better to spend time on say
animated math videos or whatever else
your main occupation might be favorite
podcasts
all right so there's three different
podcasts where I get actively excited if
I see something new in the feed and it's
unfortunate because each one doesn't
upload super regularly first one is the
anthropocene reviewed by John Green so
as many of you probably know John Green
is an excellent writer the podcast
itself he kind of reviews everyday
things or aspects of human existence
that range from deeply philosophical
ones to very mundane like the Taco Bell
breakfast menus it's maybe 70% personal
memoir and you get this view into his
own very thoughtful but also very
twisted and tortured mind so highly
recommended the second which i think is
super popular so certainly don't need me
saying this is hardcore history by Dan
Carlin he often likes to go deep into
the human experience of certain wars are
certain very violent times in human
history that shaped the direction of
things and he does a good job just
giving a super abundant amount of
context maybe way too much context which
is why these podcasts sometimes last as
long as six hours and will be many many
part series but sometimes you like that
in a podcast and then maybe for most
that I like a lot and this will just
come as no surprise is the numberphile
podcast I am slightly biased because I
was on it but I actually think I'm the
least interesting guest they're super
interesting to hear from different
mathematicians what their story is how
they relate to the subject what
motivates them and of course Brady Haran
is a phenomenal interviewer so it's just
perfect for anyone who's into math even
in the slightest of ways if you had both
the responsibility and opportunity to
best introduce the world of mathematics
to curious and intelligent Minds before
they are shaped by the antiquated
disempowering and demotivational
educational system of today what would
you do asking because I will soon be a
father first of all let's just
acknowledge that it's very weird for me
to be asked a question that has anything
with the flavor of parenting advice
because well look at me like I'm 27 what
the hell do I know
but one interesting place to look here
if we're thinking how do you make a
child entering the world love math or
things related to math is Richard
Feynman's dad
evidently hyneman's dad was incredibly
interested in making him into like a
physicist or an engineer or something
like that and even when young Richard
was just a newborn baby he would paint
these interesting patterns they were
meant to instill young Richards mind
with a sense of mathematical patterns
through the raw exposure and as he grew
up a little bit later he would give
these very deep thoughtful answers to
questions about how the world worked or
why when you like tug at a wagon that
has a ball in it the ball doesn't move
fine one would tell all of these stories
there were some of his favorites to tell
you know if I look back in my own
childhood there's definitely a lot of
influence from a very attentive
thoughtful father in that respect I
think I said this in a previous Q&A but
I'll just say it again here I remember
these games where he would stack these
sugar cubes and interesting geometric
arrangements and I would be asked to
count how many there are and you
couldn't just straight-up count because
it was some of them were hidden in
certain ways right so you are
effectively cubing numbers or something
like that and of course if I got it
right then I would get one of the sugar
cubes as this Pavlovian reward and if
you look at the success of someone like
Fineman when it comes to problem solving
and I definitely don't view myself as
like a great problem solver but I do
love this object I have this like
deep-seated affection for it that
probably is not unassociated to the kind
of games my dad would play with me it's
not so much that I think oh the painting
of those patterns really didn't still
young Richards mind with a sense of math
or that the answers that his father gave
to certain questions were the ones that
made him deep and thoughtful later I
think it's just that when you're a
parent and you're showing a lot of
attention towards something you're
signaling to the kid that that something
is important and it's worth thinking
about so all of the signaling that
probably came from young Richard
Feynman's dad showing this deep
attentiveness to questions about the
physical world about mathematical
patterns probably made it such that
young Richard would spend a lot of his
own time thinking about those things
because they just had a match off of
their parents another thing I might say
is try to draw a distinction between
school math and math right they can just
be very separate things and kind of
separating the brand of those two can't
hurt what's something you think could
have been discovered long before it was
actually discovered
well just last week all of the internet
has been very abuzz about a certain
result that came from these three
physicists studying neutrinos about
eigenvectors and eigenvalues which is a
crazy fundamental thing you kind of
wouldn't imagine that there are any new
things to be discovered about computing
eigenvectors are computing eigenvalues
because it's so was kind of old and it's
very I don't know routine at this point
but they found what they thought was a
result and they sent it to Terry Tao who
actually responded and his initial
thought was this can't be true it would
be in every text book if it was true and
then within two hours I think he found
three independent proofs of the thing
and yeah it's just a different way to
compute eigenvectors that was discovered
in 2019 even though that totally could
have been discovered hundreds of years
ago can we fix math on Wikipedia really
serious here I constantly go there after
your vids for a bit of a deeper dive and
learn nothing more ever compared to
almost any other topic in the natural
sciences or physics where at least I get
an outline of where to go next it's such
a shame so this question kind of reminds
me of that classic trope or you've got a
girl and she's dating a boy and you know
he's kind of a bad boy he does a couple
things that are wrong that adds to his
allure he's kind of sexy in that way but
she's thinking oh I can change him right
he's flawed but I can fix him and
everyone in her life is looking and
saying oh honey like he's not gonna
change people don't change you have to
find someone else in the same way if I
see someone trying to learn math from
Wikipedia and not use it as a reference
it's like it's not gonna change don't
try to change it you've got to find a
different source there's lots of really
great blogs that you can go to or math
exchange and Cora are great in terms of
people trying to explain things in
approachable ways and don't forget about
just good old textbooks in math more so
than a lot of fields I think there's a
strong contrast between what makes good
reference material and what makes good
pedagogical materials and a general rule
of thumb this is not universal but
general rule of thumb things that are
single authored I believe are better
pedagogically and I suspect the reason
for this is that when you want to
explain a topic often the best route to
making it understandable is to start off
by being a
it wrong you explain kind of a
simplified version of something that
isn't entirely accurate but it's easier
to get a foothold end then once you have
that foothold you slowly carve away
what's wrong about it until you end up
at what is entirely accurate but more
complicated but you've taken this path
through in correctness now when you have
multiple authors I think the tendency is
that you sort of wipe away and edit away
the things that are incorrect that's
like the stable equilibrium that you
reach so what you're left with is a
source that's entirely factually correct
but it's harder to get a foothold into
for that reason and Wikipedia just
represents the extreme of this but I
also think you see it if you look at a
textbook that has you know three or four
authors again there are exceptions but I
like that as a rule of thumb
real quick I want to tell you about two
new items that have been added to the
three blue one brown store for any math
enthusiasts the first one in the spirit
of upping the level of formality on
things
is this not Theory themed tie so as you
can see the pattern includes a lot of
different simple mathematical knots so
almost any knot that you are likely to
tie with your tie anyway is going to be
topologically equivalent to one of these
unless you just go totally crazy in
sourcing this we wanted to make sure
that it was you know a legitimately high
quality tie and I'm really happy with
what we found then as a supplement to
the ties I also got these vector field
socks produced and what they represent
is the phase space of a pendulum which
some of you may know is most naturally
represented on a cylinder hence printing
it on a sock so the whole item is just
sort of a subtle nod to that fact I
believe dftba is gonna do some kind of
sale on Black Friday and Cyber Monday so
if you're watching this before then
definitely check it out and with that I
will see you all in the next probably
much more typical video
[Music]
you