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  • - What am I ever gonna need this?

  • I'm looking at your screenshot,

  • and I think the answer is never,

  • you are never gonna need this.

  • I'm professor Moon Duchin, mathematician.

  • Today, I'm here to answer any and all math questions

  • on Twitter.

  • This is "Math Support".

  • [upbeat music]

  • At RecordsFrisson 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-Khwarizmi, 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 gonna 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 fuck 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 jesspeacock says, "How can math be misused or abused?"

  • 'Cause 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.

  • In 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 gonna 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.

  • And I think that's an example of math being used

  • to kind of move the needle in a direction

  • that's pretty good.

  • At ChrisExpTheNews.

  • 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 labcoats

  • 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,

  • 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 a little known, is how collaborative it is.

  • Typical math papers have multiple authors

  • and we're just working together all the time.

  • It's kinda fun to look back at the paper correspondence

  • of mathematicians from a hundred years ago

  • who are actually putting all this 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 dYLANjOHNkEMP 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

  • and 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 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 3+2i.

  • So i is now the building block

  • that can and 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 ltclavinny says,

  • "#MovieErrorsThatBugMe The 7th equation down,

  • on the 3rd 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.

  • There's a movie about John Nash

  • who is actually famous for a bunch of things in math world.

  • One of them is 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 is doing is

  • earlier very important work of his,

  • this is like Nash embedding theorems, I think.

  • So this is like fancy geometry.

  • You can't tell 'cause it looks like

  • a bunch of sums and squiggles.

  • You're missing the part of the board that defines the terms.

  • [chuckles]

  • So do I agree with J.K. Vinny

  • that stuff is missing from the bottom row?

  • I don't think that I do, sorry Vinny.

  • [chuckles]

  • At ADHSJagCklub 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 wanna describe about rounds 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 4 and you subtracted 4/3,

  • and then you added back 4/5,

  • and then you subtracted 4/7, 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 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.

  • At cuzurtheonly1,

  • "Bro, why did math people have to invent infinity?"

  • 'Cause it is so convenient.

  • It completes us.

  • Could we do math without infinity?

  • The fact that the numbers go on forever, 1, 2, 3, 4...

  • 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 kinda need that.

  • But we maybe didn't have to create like 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 TheFillWelix, "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 surfaces.

  • It looks like this.

  • This is called Minsky's product regions theorem.

  • So this is the, 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's like a double inner tube.

  • It's sort of like two hollow donuts

  • kind of surgered 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...

  • 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 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 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 x R.

  • Put these all together

  • and you get a three dimensional geometry.