Who created math problems?

At But Why, we believe that curiosity is key to learning. That's why we bring kids questions to life with experts, fun stories, and fascinating facts in our podcasts and video episodes. But we can't do this without you. Support from people who love the show and believe in what we do helps keep curiosity thriving. Head to butwykids.org slash donate to become a But Why fan club member or make a gift in any amount to support the show. Thanks and stay curious. This is But Why, a podcast for curious kids from Vermont Public. I'm Jane Lindholm. On this show, we take questions from curious kids just like you and we find answers. I had a math teacher for a parent, so for as long as I can remember, math has been a part of my life. My stepdad made me and my brother do math games on long car rides, and he still gives us math riddles whenever we go visit him now, even though we're adults. He wishes us a happy Pi Day every March 14th, and suggested we use the Fibonacci sequence for our essential passcode numbers. Don't know what the Fibonacci sequence is? You will by the end of this episode. Math and numbers are fascinating, but I also know it can sometimes get difficult to wrap your head around big math concepts in school or on long car rides with a math-loving adult. So today we're going to demystify math. You've sent us a lot of mathematical questions, and our guest today loves all of them. Dr. Melania Alvarez is the outreach coordinator for the Department of Mathematics at the University of British Columbia in Canada, and she's the education coordinator for the Pacific Institute for the Mathematical Sciences. So my job is to go all around showing people how wonderful and interesting and exciting mathematics it really is. If you invite me to your school, I go to your school and bring some interesting games and puzzles and things like that to show you how much fun you can have doing mathematics. Can you give me a puzzle? Oh, there are many. But one that I have. So there's a farmer, and he sells chickens. So he goes to the market, and he's going to go to three markets. And so he goes to the first market, and he sells half of his chickens, plus half a chicken. Okay? Okay. So he goes to the second market, and he sells half of his chickens, plus half of a chicken. And then he goes to the third market, and sells half of the chickens that are left, plus half a chicken. And that's it. And then he has zero chickens, right? That's it after that. He sold all of his chickens. He has no chickens left. He sold all of his chickens. So he had no chickens left. So how many chickens did he have when he sold the chickens that were all alive? I don't know. Yeah, I'm trying to think of that. He sold all live chickens. All of his chickens, right? All the chickens were alive. Yes. Half a chicken cannot be alive, right? So how many chickens did he originally have? I see. Okay. I feel like I need to write it down on paper, though. So while I'm working on this, let me ask you some of the questions that kids have sent us about math. Starting with some kids who want to understand who created math. Hi. I'm Sophie and I'm eight years old and live in Ireland in Virginia. Who invented math? My name is Una and I'm six and a half years old and I live in Brooklyn, New York. Who invented math? Math is something that grew through thousands of years. It's like a magical tree that was planted by many, many people, by the Chinese, the Maya, you know. So ancient people needed to count at some point. When populations started to grow and we started to have cities, people needed to count. We needed people to look at how much property they had. There are some cultures where they only have one, two and many. But the more you have, you need to not to count. You need to measure. You need to trade. So we started inventing numbers. Humans started to invent numbers and systems and symbols and rules. But here is the twist. So we started to invent that, but at the same time math is not just invented. It's also discovered. There are also things there that are there and we discover. Like a triangle has three sides. We didn't, you know, invented that, you know, it's that something that is true. So there are things that we created in order to make sense of a lot of things. And with that invention, we also discovered a lot of things. So who invented math? Is we humans started to observe, starting to look for patterns out of need. And we created systems that allowed us to describe what we were seeing. And that's what math is. So Lele wants to know who created math problems. And if we needed to know how to do math as humans, especially as you say, as we started to have communities and use money or barter for things. But maybe Lele is asking more like who created the study of math or this idea that we teach people math and do math problems, not just learn how to count because we have to know how to count. Well, what happened is that the moment we are faced with a situation like, okay, I need to get to school, but first I need to have breakfast. I need to wake up. I need to brush my teeth. So then you start thinking, okay, how much time I'm going to take for breakfast and how much time do I need to get from here to school. So natural events that happened to us, and these are problems that we solve in order to be able to deal with some realities in life. So who created problems? Well, yes, sometimes you have your teacher creating tons of problems so that you suffer through them and stuff like that. But math problems come from the world. When we're starting to wonder, you know, the Egyptians is like, okay, how do I build these pyramids so that it doesn't fall down or it doesn't crumble over a bridge as well and engineer? How do I build this bridge so that it will resist trucks going on top? Or how if this young girl likes chocolate and she has to divide it equally with siblings, how do I divide it in a way that is fair for everybody? You know, or I strategize perhaps, how do I do it so that I can get more chocolate than others? So this is where math, where really math problems come from. Now that sometimes we create ridiculous problems like my mother bought 300 watermelons and divided between my aunt and my siblings. Well, those are weird problems that sometimes I make for school. But real math problems really come from the world. Lele also wonders why does one plus one equal two and not eleven? We have this system of writing numbers that is called place value. So it depends where the number is. So one one means that the one to your right, the first one is a one, but the next one is not a one. It's a ten. You see? So for example, the number 245. In that number, the two is a 200, the four is a 40, and the five is five. So it depends where you position the numbers that it changes. So one plus one is two, and one one does not represent two. That one represents a ten, and then a one, so ten plus one is eleven. Yeah, it's just interesting to think about we've created these systems that are supposed to make it easier for us and easier for us to do these kinds of problems with other people. So that your brain and my brain can match up and we both understand what one plus one equals. I think I see where Lele is coming from in that it can be really interesting. It can kind of blow your mind when you start to think about like, oh, we had to make this work for all of our brains. My name is Kai. I live in California and I'm four years old. Why is there so many numbers in math? Oh! The Japanese, as I said, when counting started, we had very few numbers. It was one, two, three, many, and then somebody instead of having three sheep now, tomorrow they have four sheep or five sheep, and then they have to add that. So we needed a system that the more we have, the more needed to be accounted for. And we have a very, very nice system where we just basically can go on forever and ever and ever and ever and ever. Well, some of the kids want to know why. My name is Lily. I'm nine years old and I live in Portland, Oregon. Why don't numbers end? Hi, I'm Isa. I live in Clearwater. And why do numbers never stop? My name is Nicholas. I'm five years old. I live in Washington, D.C. Why do numbers go on forever and ever? Why don't numbers end? Why do we never stop adding numbers? Is there really infinity numbers? Yes. Yes. So if you give me a number and I can add one to that number, then now you have more numbers. For example, there's the Google which has a one and a hundred zeros afterwards, right? That's right. Before we all knew what the internet was, Google was just a number. That's Google spelled G-O-O-G-O-L. Google the internet search engine is G-O-O-G-L-E. Google the number, as Melania said, is a one followed by a hundred zeros. It's a huge number. And then there's the Googleplex, which is even larger than that. And you say, so there's the Googleplex and I can add one to that and it's bigger than the Googleplex. And then I can add one to that one and I can keep going on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on. And I just go on. You see? But also infinity can be kind of also small. Like for example, I have a mile to go. And so then I can go half a mile and then I go half of half of the mile and then I get half and half and half of that and that. Do I ever get there? No, never. And I can go infinitely going and the steps are smaller and smaller and smaller. Eventually I'll end in real life we get there. But mathematically, we just can be stuck there trying to get there. But if you always do half, half, half, half, half, half, we will not get there. This is what is amazing about mathematics is that you can go on with your imagination and math is a great companion for that. And it shows you ways that you never thought that were possible. And that's what is so wonderful about it. It can kind of make your brain hurt when you try to think, think, you know, all the way out on those things, but hurt in a good way. I mean, it's just cool. So it is true. You talk about the hurt and about the struggle and all of that. What happens when you are able to solve a problem that is really, really hard? How do you feel about that? Really good. Proud of myself. Really good. Yeah, like I figured it out. You get this big high, isn't it? You get like, wow, I'm really smart. I'm at the top of the world. You know, that's what we mathematicians live for. You know, we're working, we struggle. And then when you finally solve it, I'm not just solving it. It's the beauty sometimes of those solutions that are just like, how can this be so perfect? And that's why. And there are mathematicians that spend a year, two years, eight years, you know, ten years trying to solve a problem, but they think that is worth it. So that's another thing. You don't need to be fast to be a good mathematician. Many kids think that they have to be really fast problem solvers to be really good mathematicians. That's not true. You know, you can take your time. Hi, my name is Triffin. I'm nine years old and I live in Winnipeg, Manitoba, Canada. Why do people hate math so much? Why do people hate math so much? And we should say, certainly not everybody, but math has a reputation and people sometimes seem to feel comfortable saying, oh, I'm not good at math or I hate math in ways that you wouldn't say about other things. That's right. Many times is the way that math is presented to us. It's just like a series of rules and you have to solve this problem and that's it. And that's not math, actually. That's just something that we call practice. Real math is not that. You need to know the tools. You need to know how to add and subtract and all of that. Yes, but that is like you need a hammer and you need nails to build a house. So that's what that is. But math is thinking. Math is strategizing. Math is not just the solution. It's the way to get there and how you're thinking to get there. So many times is how math, if it is just road learning and just memorizing all the time, which we have to do sometimes. But if that's the only thing that we learn and the only thing that we do, then it's really boring. I'm telling you, if that was math, there wouldn't be professional mathematicians because, no, come on. We're not that boring people. We really like explorers. That's what it is. Math is about exploration. It's about questioning. It's about doing all that. If you start to dislike math, and this is also something that happens, is perhaps along the way, and I find that many people say, I like mathematics, but at some point I start disliking it because I got lost. So what I tell kids is this. If you are in class and you understand everything and all of a sudden you don't understand something. Go and ask your teacher. But soon, don't wait a month or two months afterwards. Go immediately and ask your teacher, hey, I didn't get this. Could you explain it to me again? Because math builds on top. It's something that is a structure. So if you miss the first floor, then the rest of the floors are going to be a wobbly and you're not going to understand. So don't be embarrassed about asking. And if you are embarrassed in front of the class, then ask after class. But don't leave something that you don't understand and see what later on I'll catch up. No, no, no, no. So don't get lost. Go for help as soon as possible. That's always good practice. If you don't understand something, ask a question. Get some help. Math is complicated. And if one explanation of a math concept isn't working for you and your brain, you can always say, could you describe it to me a different way? Or maybe you need someone to write it out for you. Or help you work backwards from the answer back to the original question. You can ask for different kinds of help to make sure you understand the math you're working on in school or at home. Coming up, why are the numbers in the order they are? And is there really math in everything? And of course, I still have to solve that puzzle Melania gave me about the chicken farmer. Stay with us. This is But Why, a podcast for curious kids. I'm Jane Lindholm. Today we're talking about numbers and math with mathematician Melania Alvarez. We're going to solve that puzzle about the chicken farmer in just a little while. But first, some of your questions about how numbers are ordered and how they help us count. I'm Kai. And I'm six years old. And I live in St. Paul, Minnesota. Why are the numbers in order? Why are they in one, two, three, four, five, six, seven, eight, nine, ten? Why can't they just be like in different order? Well, so numbers are like a step ladder. We make one number and then we go to the next. And when we go to the next and then we go to the next. So that's what keeps an order. And that order helps us to count. If the numbers were all over the place, imagine we have here one and then comes 25 and then comes 36. And how can we count with that? We can't. So it is like a ladder. We go step by step by step and we gave them numbers, those names, right? Because we need them to track things. We need them to trade. We need them for things in real life. And if we didn't have that order, we wouldn't be able to do that. We'll be lost in confusion in the jungle of numbers. So that's why there's a rule why we have an order. You know, it's like you would say, why don't you build a house upside down? Because then it wouldn't make sense. So that's exactly the same thing with this. I'm Miles and I'm five years old. I live in Quebec, Canada. Why are numbers for counting? Why are numbers for counting? Well, the numbers are counting because actually there's where math began. Math began with counting long, long, long, long time ago, over 20,000 years ago. So this is something that helped people to survive. And you can think about, let's say you had to get through a winter and you needed to have enough crops for your whole family to get through the winter. Yes. Well, you have to know how many people are there that I'm trying to feed. So let's say there are four people in my family. How much do we eat every day? How many days do we need to get through to get through the winter before we can grow more food? So you need to be able to count and add and multiply to know how much food you need to store for the winter. Which will take you to how much you need to grow in the summer, which will take you back to how much you need to plant. And how many plants you think the animals are going to eat before you get to have them. So how much more do you actually need to plant to be able to have enough to harvest? And, uh-oh, there's a new baby in the family. Now you have to do that, but for five people. So you have to be able to do that math in order to survive. And even if we're not thinking about growing all of our own food now, as families, we have to figure out how to budget, how much money we need, how much money we need if we also want to go on vacation to the beach at some point. So math is really important. And we do like it because it helps us get the things that we want and need. Even if we think, or some people think, they don't like math in school. Yeah, I absolutely right. Zoe lives in California and is seven and wonders, why do you need to do math? We already said math has helped people survive, but what are some of the other ways math is needed? Well, you need to do math for so many things. You need to do math to go to the supermarket. You need to do math to trade with people. You need to do math to build a house, to build a pyramid, to study chemistry, to read graphs about who's going to win the presidential election. So we also need to know, like, for example, if you are in class and you want to go to recess and you want to know how many minutes are there to recess so you can count them. Oh, it's almost five minutes to recess. I want to go there. Also, if you like to trade cards, how many cards should I trade for this card? That card is worth three of these cards. And now, for example, all this technology, the phones, the TV, everything, all of that was created thanks to math. My name is Sunmi. I'm 10 years old and I live in Bathill, Washington. Is there math in everything? Math is not just in everything. Math is also a way to see everything. We can see it in patterns from nature, flowers. There's a sequence called the Fibonacci sequence that goes one, one. And then what is one plus one is two. And then one plus two is three. And then if I add two and three, so I take the last two numbers and add them up and then I get the next sequence. And what's interesting is that that sequence represents a lot of things that happen in nature. The petals in flowers, they are usually their Fibonacci number. So you really math is like this invisible thread that connects everything around you. And it is the spiral in the shell. We have the rhythm in music when you bounce a basketball to the trees in the branches. But the secret about this is you can see this if you are curious. You have to be curious, OK, to see it. So math doesn't necessarily scream for attention. It whispers to you, it says, hey, hey, come check it out. But you have to be curious. You can notice a lot more if you are curious. And you can have a great time if you're curious. Well, you came to the right place because anybody who's listening to this podcast is a curious kid. It's in the name of our show. So all of the kids who are listening, that's something that we all have in common all around the world. We are curious kids who want to know more about the world. So if you have us convinced, let's wrap up with Alistair's question. Hi, my name is Alistair. How do you become a mathematician? How do you become a mathematician? We all want to do it now, Melania. How do we become mathematicians? So first of all, we are all mathematicians. You know, babies, they immediately can recognize patterns. When we are playing and we're putting cubes on top of each other and trying to measure if it's going to fall or not fall, you know, and how to build things when we're little. We are all mathematicians, all of us. When we like to say how many cookies I need to bake for everybody in my family, I look at cool patterns and I say, oh, how does that grow? How can I continue this pattern? All of that. Now, mathematicians, every mathematician not just answer the questions, they also ask questions. A mathematician is always asking questions about how things work and then tries to answer it. So this is what it is. Everybody, you know, everybody can do math and we all can be mathematicians. Now, if what you want asking is how I become a professional mathematician, usually most mathematicians, I mean, there are some who don't, but most of them go to university and they become undergraduates in math or math related thing. And then they go for a PhD in mathematics and they solve problems now. There are two types of mathematicians, mainly they apply mathematician and the pure mathematician. So I am an applied mathematician and my husband is a pure mathematician. So an applied mathematician, people comes with problems to me. Like I have worked in problems in anthropology, I have worked with problems in engineering. So engineers come with a problem and they want, you know, they want someone who does all the calculations and who creates a model of what they're seeing. So I do that. So people comes with their problems and I take care of their math problems, only their math problems. That's it. So that's what I do. The pure mathematicians, they ask questions if some really abstract thing can work or not work, you know, and then they start, they start working on the, on these abstract mathematics that it looks like they are useless. That who cares doing this math that it doesn't seem to be a real application. And lo and behold, 10 years from now, 200 years from now, 3000 years from now, all of a sudden we find the application. It's like magic. And that's what is so excited about math. That is so cool. Okay. So before we end, I want to go back to the problem, the puzzle you gave us at the beginning. And let's recap it. So the question was, there's a farmer who goes to three farmers markets and he has chickens for sale. And at the first farmers market, he sells half his chickens plus half a chicken. Yes. And at the second farmers market, he sells half his chickens plus half a chicken. And at the third farmers market, he sells half his chickens plus half a chicken. Yes. And he has no more chickens. And you gave me a really great clue, which is that no chickens were harmed in these transactions. They were all alive. They were all alive. So how many chickens did he originally have? So I want anybody who's listening now who wants to solve it to pause the episode and see if you can figure it out. Can we go through the answer and how one way that we might be able to solve it? Because I was thinking about it while you were talking and I think I have an answer. Okay. Why don't you tell me what you think it about? Okay. I think he had seven chickens at the start. How did you solve that? When you said all the chickens were alive and at the end he had no chickens, it made me realize that when he at the very end, at the last market, he sold half of his chickens plus half a chicken. He would have to have one chicken to sell because no chickens were harmed. Yes. So then I sort of went from the very end to the beginning by sort of adding and multiplying rather than subtracting and dividing. And so I think he had one chicken at the beginning. Yes. Three chickens in the middle and seven chickens at the start. And you got it absolutely correct. Wow. Phew. And that's actually that's the way working backwards, you see. So you work backwards. You said, okay, I think that the first one is one and then the next one will be three because you calculate what's half double of that and then you calculate what will be sold and then that. So you got it absolutely right. So in the first market, he has seven chickens and half of those chickens is three and a half plus half a chicken is four chickens. So seven minus four is three. So we're left with three chickens. He goes to the second market. Half of those three chickens is one and a half chickens and then plus half a chicken. That's two chickens to three minus two is one. So we're left with one chicken and the last market is one chicken and then is half of a chicken is half and then the other half is one. And there we are. And oh, there were no chickens hurt in this. Also, I was so as you said, I was so pleased when I realized, oh, I can figure this out. And get to the answer. So there are many ways that you can solve a math problem. You can you can guess and you can do a systematic guess, not just random numbers, but little by little that guesses that will give you some information. So you go on, you can start backwards. You can draw a diagram to sometimes you can draw a picture and that will help you. There are many ways and that's what mathematicians use. They have the different ways of approaching and see what will work. And sometimes it works. And if it doesn't work, then you start again. And that's all there is. Let's end this episode there. Did you figure out the answer to the puzzle? I will admit it took me a while and I had to write myself some notes. And I did start to get really worried at one point that I wasn't going to get the answer right. And then my mind started to go blank. And then I thought of all of you listening and I thought, oh, no, you'll all be so disappointed in me or think I'm not very smart. But as Melania was talking, I realized two things. The first was that I just needed to take a deep breath and start working backwards and I could probably figure it out. And number two, that if I couldn't figure it out, that's OK. No one is supposed to just automatically know all the answers to things. And when we're learning math, part of what we're doing is learning how to solve problems. So I knew I could ask Melania for help if I got stuck and she would steer me to the right strategy. Thanks to Dr. Melania Alvarez of the University of British Columbia and the Pacific Institute for the Mathematical Sciences for answering all of our math questions today. We're going to add some math puzzles and resources in the show notes if you want more. As always, if you have a question about anything, have an adult record you asking it on a smartphone using an app like VoiceMemos. Then have your adult email the file to questionsatbutwhykids.org. But why is produced by Melody Baudette, Sarah Bake, and me, Jane Lindholm, at Vermont Public and distributed by PRX. Our video producer is Joey Palumbo and our theme music is by Luke Reynolds. If you like our show, please have your adults help you give us a thumbs up or a review on whatever podcast platform you use. We'll be back in two weeks with an all new episode. Until then, stay curious.