 So the first thing I just wanted to say is thank you. Thanks for the invitation. Thanks to the organizers. It's a lot of work to pull off a conference like this. And every participant I've spoken to has said, I got so much out of the sessions I was in yesterday. You were in workshops. That's probably the right way to learn anything. And so being a very workshop-oriented person, it's intimidating to come give a plenary where you're supposed to talk at people instead of talking with people. So I'll try to talk with you as much as possible. But apologies for any of the ways in which I'm talking at you. And I hope we'll continue the conversation afterwards. All right. So those are my thank yous. And that's my 14-year-old self who arrived here in 1983, who is also really thankful for the education that I got here and the ways that it's really launched my professional career and my friendships and my marriage and lots of things. So you've been doing workshops. And now we're going to extend this idea of how mathematical modeling might have impact as you make a transition from school mathematics into the workplace. So that's what we're thinking about. So take a minute. We're going to do some think share because you've been pairing a lot and you hopefully have established yesterday trust in each other enough to speak up without always the pair part. But just take a minute and think, how do you imagine that what you do with your students is different from what they might do if they went to go work at Google or Yelp or Microsoft or Bristol Myers or the post office, American Airlines? And then think about how that may be the same or different from if you asked your students, how is what we're doing right now, today, yesterday, last week, last year, related to what you would do if you worked at and name any company that they know? What would they say? When you go back, ask them. And then email me and tell me what they said. Even better, if you can, audio record them and send it to me. What did they say? I'm curious. Have you had time to think? I think there may be a disconnect between, I mean, when I taught high school, I had no idea what it would be like to work as a mathematician in industry. And I think there's more awareness now. But I wouldn't even have known how to get that perspective when I was teaching high school. There's more on the internet. There is an internet now that we all have access to. And there's more ways to get this information, so that's great. But there still might be a disconnect. So tell me what your students would say. So what I would say, a take home message to your students is getting a math job, take skill, which they're developing every day. And it also takes guts. So here's a math problem for you. A job application lists eight desired, eight qualifications, which some people will read as minimum requirements. And some people will read as maximum requirements or desired requirements. How many should you have before you're willing to apply for the job? Hold up your fingers. How many would you expect yourself to have? Hold up your fingers. OK. So I've got a 10. I got a seven. I got a five, a five, a five, an eight, a four, a five. From the person who works in industry, Helen, raise your hand, really hide. Everybody look at Helen's fingers. That's the message you need to take home to your students. Three, she knows she's applied to these jobs. Women and people in our culture, in our country, who have been told you have to be more than perfect, people from underrepresented groups who have been told you have to be more than perfect to get a job are certainly going to say, often, eight, if not 10, because you never feel quite good enough. And you don't want to be embarrassed. And you don't want to misrepresent your people, whoever they are. When you don't want to embarrass, I don't want to embarrass all women when I go into an interview, so I better have 10. Or else, if I mess up, then the next woman who comes along is going to have a harder time in an interview. So it's not just me I feel responsible for. It's like all the people like me that I feel responsible for. And that prevents people from having the courage to go get jobs, OK? So that's your take home message for your students. And tell them, if you mess up an interview, fine. If there's something you don't know, go learn it and go interview again. Because unlike a class, there is no shame in applying twice to the same job, especially if you can say what you did in between. And I absolutely have heard stories from people in industry who said, someone came, they messed up an interview, they followed up, they figured out what they needed to know. They learned it, they recontacted, they said, I learned it now, I'm ready. I still really want to work for you. That's the person you want to hire. All right. So we often go to job fairs and we ask, what do you want students to be able to do? We want them to be able to solve problems and learn stuff. Those are the big messages. And I hear it over and over. Why are mathematicians important in industry? Because they like solving problems. And they're good at it. They can see to the bottom of an issue. It doesn't matter what I throw at them. They'll go learn stuff. So what I've been thinking a lot about is the whole continuum of experiences from Dan mentioned immersion, where this year I worked with kindergarten teachers, special ed teachers, dual language immersion teachers, and language specialists. That was my little group. To think about how mathematical modeling can help them, their students learn to communicate, learn to problem solve from the kindergarten level, all the way through, there's the high MCM, there's the Moody's Mega Math Challenge, there's other mathematical modeling opportunities. The students who lose these competitions right into the competition and say, I don't care that I lost, I know what I want to do with my life. These are really fantastic opportunities for students to engage in problems. So if you aren't familiar, I'm going to refer to M3 today. That's the Moody's Mega Math competition, which happens to be what my math societies I am helps organize and sponsored by Moody's. Okay, the clinic program, I'll talk about a little bit at Harvey Mudd College, where I work, that's a capstone experience for senior undergraduates, where they work in a team of four for a year for a company. And I'm not going to be able to tell you a lot of those stories, because a lot of it's proprietary, right? But I'll kind of talk around those experiences that my students have had in industry. And then most recently, I've been working on the Big Math Network, which is a cooperation between the mathematical societies, there's 20 or more of us, and we don't always all get together on the same page, but we're all interested in our students getting jobs. And so we're all working towards communicating, disseminating information about career preparation and opportunities in business industry and government, which just is a nice acronym thing, but it includes lots of things. And Dan mentioned game. And then we also have a national mathematical modeling repository and online hub that we're creating. So we've just gotten funding from Siam and Comap, and we've approached several other organizations. And CTM was really a instigator of thinking about the need for such a place for high school teachers and college teachers, and all of us to get together all the way from K. They say K to Gray now. I know it's not sure if I like that or not. I'm in the Gray's camp now. All the way from K to Gray, I don't know. To think about, to basically have conversations and get stuff you might need. Okay, so this is another bottom line. You can't these days get very far and very many jobs without computation, or at least computation is such this powerful tool to use in addition to the other things you do, but if you can't communicate, forget it. Not useful. All right, so when I talk to people who work in industry about their work and what their answers to their problems need to look like, here's what I see. Here's what I hear. The first one's interesting because if you think about metacognition around a mathematics problem, in a job you would want to be very, very careful about how you decide you're gonna go about solving a problem. And you would spend a lot of time thinking of all the ways that I could solve this problem. How are we gonna do it? Does that make sense? I mean, that would just be a significant, and then actually going about doing that thing that you decide to do is probably a whole lot easier than the process of deciding what to do. And I think a lot about my students and the tasks that I have them do. Like, how much do I value the time in which they are deciding how they're gonna go about solving the problem? Versus, like, what's the proportion between that and the time they actually spend solving the problem? And I think I need to rethink that and I need to re-communicate with them about that. Because I think a lot of times if I perceive that they're taking a lot of time figuring out how to do the problem, it's because they didn't understand something that I already told them how to do the problem and they just didn't get it somehow. As opposed to there was really significant cognitive work in making that decision. Does that make sense? I mean, I teach a differential equations class where I have to, they have to take the next class. They need to use it in physics, they need to use it in engineering. It's a bunch of techniques and if they come out of my class and are not able to do those things, they aren't as useful in the next class where they get to apply them. And so how do I somehow communicate that this? And there are only, like, I can count the techniques they have to learn on one hand. And once you know what kind of differential equation you've got, you already know which solution technique you're supposed to use. It's not a very significant cognitive task to make that decision if you already have the differential equation. So the hard part is really the development of the differential equation or even the decision to use a differential equation in the first place, which in the real world would be a big decision based on a lot of assumptions. And again, how often do your students get to give you good enough answers? And this whole idea that your answers have to be really, really good. And then your answer to the question, how many of these qualifications do you have for the job has to be really, really good. And what is really, really good, right? It's like 90 to 95 to 98 to 100%, which Helen's answer to the question, it's not three eighths, right? If they get three eighths on an exam, that's not such a good score. Right, and so we set them up to think three eighths isn't good enough. So when I think about these things about math at work, it reminds me of mathematical modeling. It's very consistent with a modeling task where you're not just trying to use somebody else's model, but you're actually trying to develop your own model. Do you see any inconsistencies? When you give a student a mathematical modeling task, is there anything here you do not want them to do? I can't think of anything, but I'd be interested because maybe you have some ideas. All right, so I have an affliction or a wonderful privilege, whichever way you wanna look at it, of having resting friend face. And what that means is that every time I ride on an airplane, by the time I'm done with my airplane ride, I've seen all the pictures in someone's iPhone, I know where they've traveled to. And most recently, I was sitting next to a US Army special ops command sergeant major, and I had that list and I said, and I'm always asking people like, what's your biggest problem in your job? And he said, well, in addition to that list, what I see missing is that you're constantly building the aircraft in flight, and your right answer is only good until the problem set changes. So that led me to think, okay, and so I wrote it down and I was like, is this what you just said? And he said, yeah, yeah. Can I take a picture of you and quote you, no? Like, can I put your name on it, no? Can I say you said it, yeah, okay. But in mathematical modeling terms, I started thinking, okay, maybe we can make up problems where you are trying to demonstrate that you know if this constraint or this thing changes, this is what I'm gonna have to change, or I can keep the same model, or I'm gonna have to have a different model. Is it gonna break the model that in flight this parameter and the problem changed and that this solution better be flexible? So I tried to make up some analogies to what's going on in mathematical modeling. So raise your hand if you've tried a task where you've had the students change an assumption. Moody's often asks you to do this, right? In the second problem it'll say, okay, now imagine you have a dollar less. How is your solution gonna change? So a subcontractor is delivered a model. You could take an answer from a modeling competition and have your students identify an assumption in the model and then demonstrate mathematically how it impacts the conclusion and maybe even whether you can even use the same model. And bonus points of the assumption your students find is one that was made in the model but wasn't identified by the writers of the answer to the solution. So raise your hand if you've done anything sort of like this with your students. All right, so it was worth bringing up as a possibility because that's not half of you guys, okay? So I encourage you to do this because this is real. If you don't get this, then you don't really get your model. All right, and then another idea might be this flexibility question. You could give a solution and either you or your students could generate, right? Three ways that in-flight the situation's gonna change and then have the students, right? Mathematically justify whether it breaks the model. Can you still use the model if this changes, right? Can you still use the model if that changes? And then you could, an extension could be how would you have to change the model if you can't still use the model? But to me in some ways, the nice thing about this is that you get to skip the time it takes to develop the model. And the truth is in your job, you're often handed a model somebody else already started. The real issue is, or that someone else developed. And the real issue is, is it gonna pertain to my current situation? And is it gonna be flexible enough to deal with my current situation in the next number of years? And all of these slides will be available to you guys. Okay, so how can you find mathematical modeling problems all around you? And how can your students do that? So like I said, I'm always going around and asking people who their biggest problem is. When I was with Immersion, I had to go to Montana, so I check into the hotel, why are you here? I'm here to talk to elementary school teachers about mathematical modeling. Oh, I hate mathematics, you've never heard that before. Oh, I hate mathematics, it's very scary. I hear there's a thing called Common Core. Seems like nobody likes it, seems really scary. Now nobody can help anybody or their kids with their math. And so, and we really don't like math. And I said, oh, well what's your biggest problem here at the Lark? And they said, oh. Well first they were like, I don't know. And then I looked around and there was a coffee carafe. And I said, tell me about that coffee carafe. They were like, ah, let me tell you about the coffee carafe. Okay, and then they started to speak and I was like, wait, let me get my phone, because I have my phone. I was like, okay, I'm gonna videotape you. Like I wanna hear what you say. Okay, so here's what they said. I think. So maybe some kids were to think about that with you with that beat that you still saw. Cause it does sound like you're trying to solve that. I was like, thank you so much. Okay, so she was like, and I kinda like math. Like I kinda used to like math until this horrible thing happened, which you've also heard. Okay, but this one was like, I really don't do math. But then when she got so excited, she got in on it. So she was like, no, no, turn that back on again. I have something I have to tell you. So now we got this lady. I think there's two minds to every take out. So let me show you guys some cards. The monster beaver, the copster beaver. The copster beaver. Oh, okay, can you show me your card? Yes, it does, it absolutely does. Thank you. But the students, like now they wanna solve the problem, right? So this is sort of for me how I try to be an ambassador for mathematical modeling, and it's really simple. You say, what's your biggest problem today? And then if they're like, I don't know, just look around you. Like what looks like their biggest problem today? Cause you can often identify what is very likely a biggest problem in a business in about three seconds, right? And then say, well, tell me about that problem. And then that was all I did. Okay, and you can do that in any business. All right, so talking to businesses made me think about my own family. This is my grandparents and my mama, my uncle Aaron, and my mom always told me, my grandparents were very successful in business and my grandmother always, my mother always told me that the most important thing to them was education. Neither of them, my grandfather didn't get to go to college because all the brothers and sisters sent one sibling to college who then became a New York Supreme Court judge. And my grandmother went to college but didn't finish. And so they started a watch repair business and I named after, it used to be called Ray Jewelers and then it was later called Levy Jewelers. So they had this business and I worked in it as a kid which I think was really great to work in a business and learn the work ethic of what it means to get up and go to work every day even as a middle schooler or a high school student. So when I think about my family business and things that they experienced, they lived in Savannah, Georgia, which is still in some ways a very segregated town. And in about 1950, when this picture was taken, no African-American person had ever worked, everyone who worked in a store, especially downtown was a cleaner of the store. That was really the only job that was accessible. Maybe wrapping room where you'd be upstairs and no one would ever see you. And my mom told me this story as a kid where there were dinner table conversations about whether or not to have people selling who were from the African-American community in town. And so my grandparents at the dinner table were talking with their kids about this risky decision. So let's imagine now you have been hired as a consultant for my family's company to model the impact. So they had a cleaner at one store and they were considering moving her downtown as a salesperson because they really, people were already, she had strong ties in the community, she was a wonderful person and they just thought she had a lot of potential. But this was a very risky thing, the schools aren't desegregated yet. So what would you consider in the model? So just take a minute and talk to your neighbor about what are, you know, try to come up with three factors you would need to consider in this model. Talk about this for a long time, right? I mean, we could work on it for an hour and we could each come up with a model and it would be interesting. But I would just love to hear what are some of the factors you came up with? So could you share an idea that another person in your group said that was really interesting to you? Yeah. With the potential backlash or drop in business, how much reserve do you have to be able to handle, to handle that potential loss in revenue? Other factors, yeah. Right, right, what are the risks to Ms. Solomon if she takes the job? And you mentioned some factors. Herself, her, so how might her increased salary offset the risks she would be taking to her own person and potentially her family? Mm-hmm, yeah. Right, so would there be flight to another store and what would happen there? Yeah. There could be a real economic benefit. If she's a great sales person, then they could increase sales because they've moved her into a position where she's bringing a lot of value to the company. Is there a huge untapped market in the African-American community in Savannah that might come to the store to offset, to A, benefit the store and B, offset any flight from the store? Yeah, in the back. Yeah, so what would be the various impacts with your suppliers? And you can think of lots of, would you need to somehow, are there, if you have, yeah, I can think of lots of supply issues, right? Like, yeah. And sort of all of those other issues play into the, the supplier is a person or it's a company. At that point it was probably more like a person as much as a company, right? And so how does that impact that relationship with the people that you need as your suppliers, as well as perhaps what you're, what you're getting. Okay, so then you get the point. There are a lot of factors to consider. Okay, so for example, these things that you already mentioned, right? And then if you wanted to model, you gotta think in some places, when I was thinking about this problem, it's like, is it a plus or a minus, or is it both, right? So, and even just thinking about the impact on the Solomon, is it, you know, I think for her there's pluses and minuses. And then how do you get data to try to think about this problem if no one's ever done it before? And you know, maybe your town is like some other town where it's happened, and maybe it isn't. Maybe your relationship in that town is like it is other places, maybe it isn't. Because things were in such a personal level at that time. So how do you get data? Do you have any ideas? Like where would you get data, right? Feel out your customers? What else? So in some sense some informal survey could be a formal survey, probably informal. It might be tough to figure out the impact on customers because it hasn't been, maybe this question hasn't been considered as, you know, within your context or maybe in other contexts. Because it really was on the forefront of this, right? And because in the South, in some ways Savannah is very progressive and in other ways it's not progressive. And so this was an interesting test place because there was sort of this mix of progressiveness and lack of progressiveness. Yeah. Yeah, yeah. And my uncle has really interesting stories that come later in the story about those interactions with companies in other places. Because they did have groups of stores that weren't competitors. Because in those days if you were geographically not in the same place you weren't a competitor, that's a little different now with the internet. Okay, so nobody asked, your client is my family, right? So remember as a modeler you need to get data from these people. What do you need to understand from these people? If you go to a financial consultant what's one thing they ask you? Is this just a business decision? What else? Yeah. What's your appetite for risk? That's a very common question if you want to make an investment, right? They'll say, are you, you know, put yourself on the scale from risk averse to risk-seeky. What's your goal? What are you trying to accomplish here? Okay, so nobody mentioned before that you can get data from the client and in some sense this is really important because this helps you set up the weights in your model so that you're meeting your client's objective. And my students, I think, you know, this is a very typical mathematicians thing to do. You're given an interesting problem, then you go away and now it's your problem and you're gonna solve it with all your machinery and you're gonna put on, you know, you're gonna be the one who gets to decide the weights and do all this stuff. And a real difference between school mathematics and work mathematics is you, first of all, the airplane's changing in the air. So you have to constantly be checking back with your client to make sure that what they told you last week is still what they think this week because priorities change fast in a company. And you need to make sure that you aren't getting so excited about the problem that you're failing to deliver what the client needs that's good enough in a reasonable amount of time, not what you think would be the best, interesting, most interesting solution. And that's really different. Okay, so a lot of businesses assess risk, okay? It would probably be hard to think of a business that hadn't, in some way, whether it's through insurance or some other kind of part of the company had to assess risk. And you can think about, you know, the police department, probably a police officer is assessing risk all the time, right? When they go out in their job because they would really like to come home from their job. And it's certainly a risky job, a fire department. We're working on sensors that can go into buildings so that people don't have to go into the building to decide whether people can go into the building because robots can go into a fiery building and sense things that can't usually bring a kid out at this point. And so often, if you're gonna save a person, you have to send a person in, but maybe a robot can help you decide that. So an interesting modeling task might be to analyze the disaster resilience of your school. And you could define that lots and lots of ways. When I got to Harvey Mudd College, I'm used to hurricanes. If you live in hurricane country, you are always thinking about what's gonna happen in next year's disaster. I'm from Wilmington, North Carolina. But in California, when you know there's gonna be a really bad earthquake, but you think it could be anywhere from like next minute to next 100 years, it's easy to not worry about it in the moment. Plus it's sunny every day, which is a problem because we need rain, right? But I got to my college and said, where's the water? Where's the food? Where are the disaster supplies? So for me, who always has lots of water in the house was just really interesting and worked with my own college to assist, to think more about our risk and try to make sure we had enough water for our students. Okay, back to the story. So what happened? What do you think happened? So I interviewed my uncle and I said, so my mom always told this story, right? But she sort of, but my uncle's the one who actually took over the business. So my uncle said, well, we decided, my parents decided to hire Queenie and I knew her as Queenie and Evelyn Brown. We always called her Evelyn Brown because there are two Evelyn's in the store. Because it was the right thing to do. And I think my own family's history, this wasn't so long after World War II when most of my family that wasn't in the US perished wasn't so long after a time that my family understood what and we still remember what it's like to be undesirable and not have opportunities, maybe even for life. So it was the right thing to do. Ultimately, my uncle, the way he remembers it and you know everyone remembers things differently but the way he remembers it was like, well, they had to talk to us about what might happen but ultimately that wasn't, all of those things weren't a factor. The most important thing was that it was the right thing to do. Okay, so how do you encode doing the right thing in an algorithm? This is a very important question. How many people in the company have been hired to make sure that the algorithms that are being written by my students when they graduate are doing the right thing? And how do you even get to define that? These are ethical questions. These are questions of equity. Mathematicians are pretty good at equity. We learn equals really, really early in our mathematical training so we should understand equity and we should understand fair division but fair is an interesting question. I have three five-year-olds in a whole cake. Fair division is not dividing the cake into thirds. And so then you have a question of how much cake is an appropriate portion size and kindergarteners can talk about that, right? How many pieces of candy should a kid eat on the night of Halloween and all the nights thereafter? Kindergarteners can talk about what's fair and fair division is still a really important question at all aspects of society. All right, so if you're reading business news kinds of things, the cool thing is that the word is that to some degree every company is gonna have to become a math house. Love that quote. Your house is a math house company. That means we get to work there. That's a lot of jobs for people who are mathematically trained. Their job won't be called mathematician. That's the hard part, right? So you gotta figure out who the people who are trained in the mathematical sciences, what their job's actually called and it's often like senior research associate or sometimes it's called now math modeler but more likely it's something that sounds like it could be almost anything. And so that's a hard thing about trying to get a job. And we have a lot of cautionary words from long ago about what will happen if machines and computers and profit motives and property rights are considered more important than people. What's important is being encoded in algorithms that decide who gets a loan. The same people who are encoding the algorithms may or may not be interested in the question of equity. They have a job to do. They have a goal that they've been given and the goal of the company is to make money. That's appropriate, right? So who pays attention? How in our culture do we pay attention to the issues of equity? Where does that come from? Does it come from the legal system? Does it come from social responsibility in companies where you get a good rating? How do we do that? I think that's a really, really hard question. One person who's really trying hard to think about this question is Kathy O'Neill and I had the pleasure of interviewing her a week ago. This is a hardcover book right now. It's coming out in softcover in September. It's very accessible at probably middle school level. And it raises some important questions about the ways in which algorithms can be just and fair and equitable and ways in which sometimes they're not. And sort of she's trying to work us towards what would the characteristic be of an algorithm that's fair and just. All right, so some of her ideas are you need to be continuously revising that model based on the data that come in. And those data need to be as open and accessible as possible so that anybody could see how your algorithm's working and how you're updating the data. And she uses sports stats as an example. Like you know the rules of the game. You get, lots of people get to watch the game. You can yell at the refs or not but everybody kind of sees the same thing. And then the person, the player's stats get updated based on their performance that everybody got to see. And we know basically what the rules are and how the points are calculated, those kinds of things. And so as sort of decision based on data goes, Kathy at least thinks that that's a decent way to think about things. Okay, so the assumptions need to be laid out clearly. There need to be a greed upon definition of success, right? And that might include fairness, it might not. And it should be, and she's really insistent that algorithms should be designed and used to help the people that are the least lucky and that are suffering the most. Right? That the help is getting to those who need it. That these algorithms are working towards equity, not against it. That's an interesting premise. And she notes that the algorithm itself probably isn't good or bad. A hammer isn't good or bad, it's a tool. You can build a house, you can bash someone's head in. Right? I mean, it's a tool. And algorithms are the same. So the mathematicians who are developing new algorithms, new mathematical ideas, along with people in all through, when I say mathematicians, I mean mathematical scientists, right? Because that includes statistics, it includes operations research and certainly includes our partners in computer science, lots of other fields, our partner disciplines, our subject matter experts, right? She claims that these moral decisions probably should be made separately from the act of encoding them, right? That those are really different jobs. And that probably they require different skill sets and expertise and ways of thinking. But at least if it's in the same job, you should be aware that these two things need to be happening. It's interesting. So I enjoyed reading this book. So I thought, well, how could we have our students try something with respect to this? And I thought, well, maybe students could try to model the question of how does my behavior in a social media environment impact what I see? Timely question. You could even say in a computer game, right? How does the gender of the character I picked does that impact? Is there any way of probing a video game to see if the gender of the character I picked impacts that character's experience in the game? I don't know. The interesting question. And could you do simulations that say, oh, well, if I give, so maybe you make a fake social media environment and if I give it this rule, look, now the information is sort of distributed amongst everybody. And if I make this other social media rule, we really see silos in the environment. And there's some very cool agent-based modeling kinds of programs. I think NetLogo, there's ways of doing this that would be really, I think, interesting to students and connect to their own experiences. Okay, so my students do these capstones. And I would say, when I think back over the last 10 years, here's the kinds of problems that our students are facing. They are asked, what's the best? An optimization problem. That shouldn't be surprising, right? What's the best estimate of something? We've done routing problems. We've done pricing schemes. We've done container mixes. I've got crops coming in. I don't know. I need to buy containers. They're so big, they have to last me for 10 years. I have lots of different kinds of things coming in. So I need a mix of sizes, right? And if they're not all the way, if I buy big containers, it's cheaper. But if they're not all the way full, then the oxygen in the container makes the stuff in the container poorer quality. So the smaller containers have the higher quality stuff and the bigger containers end up with the lower quality stuff. So how do you manage that in a company? Very complicated problems. Very real problems. Very related to operations research as a field. If you don't know what field that is, sort of the people who do the air traffic control, that's also an operations research, classic operations research type problem. Another problem that so many of our, I can't start naming companies, but you name a company, I'll tell you what their anomaly detection problem is. Basically, I got a lot of data coming in, real time or not real time. How do I know when something's wonky? How do I know when something's off? How do I know when I should wake somebody up in the middle of the night in another part of the world to fix something? And how do I know when it's just the Super Bowl and so everything is a little different than usual in terms of traffic of all kinds? Does that make sense? How do I know when I'm doing, I want to do things faster. How do I know, and I want to do them safely, how, what are the signals that I can't go faster because it wouldn't be safe? That's a really typical question we get asked to solve. And then depending on the type of data, the type of mathematics changes. And then decisions, under what conditions should we go for plan A versus plan B? Should we pursue a drug, right, that will be extremely expensive and risky and might not work, right? Should we invest all that money because if we succeed, it has huge societal impact and huge financial reward to the company or should we choose this other drug to pursue, right? And these decisions are being made every day and will have impact on society. So the takeaway lesson is that these problems, these real problems are really messy and my students are really ambitious and they always want to solve the big problem first. And you may see this when your students are doing modeling competitions, they want to do the whole thing at once because they just figure it's more efficient that way. Then when we're done, we're done. But it's possible the problem that they choose has too many variables and they never will be able in the time that they have. They will never be able to solve the big problem and they're gonna have to make some simplifying assumptions. And so I have absolutely had teams work on something for a year and at the end of the year, they'd said program won't run or it won't run in my lifetime. Like, we've got a program and it has all the variables but it's not gonna return an answer until 2065. Not useful, okay? So to me, it's like, how do you help someone learn that lesson without failing? I don't know. Cause sometimes if you're just hard headed about it, you gotta, so how can you give them a problem that can give them that intuition before you get to the problem they have to solve for the company so they don't get an egg on their face? Cause they didn't, they did everything the company asked them for but that was impossible. Right? And so a lot of, when we work with companies it's sort of reevaluating expectations. And so giving them problems where they wouldn't be able to solve the whole problem but if you redefine the expectations, it would be a very solvable problem and whatever amount of time you give them that's a very useful skill in the workplace. What problem can you solve in the amount of time you have? And get a good enough answer. All right, so here are some closing thoughts. What you do will heavily influence what happens when I walk into the lark and say, I'm here to do math. It's all of our jobs to try to figure out how to help people understand the value and the impact and the excitement and the beauty and the power of what we do. And I know you know that, that's why you're here. But how can we help our colleagues that aren't here? Right? How can we help our colleagues at schools that could never ever afford to send anybody anywhere? Right, how can we have impact globally? You know, this is not just a problem in the US. I spent, I spent summers in Korea teaching mathematical modeling. And you know, worldwide everyone's trying to figure out how to have better attitudes about mathematics. And if we don't get it right, on the left is a group that was the President's Council of Advisors on Science and Technology and they were supposed to figure out how to produce one million additional college graduates with degrees in science, technology, engineering and mathematics. Guess who wasn't at the table? A single mathematician. Why? Clearly, they thought they could spell STEM without an M. Okay, and that's a problem because we have a bad reputation in terms of communication. They don't really, you know, they, whoever they is, we are sometimes not wanted at the table because the perception is it's not gonna be better if we're there, it might be worse. Right, and what does their conclusion say? It says math teachers in colleges really shouldn't be the ones teaching math. Let's just have the biologists teach the math or the physicists teach the math. Let's have the partner disciplines teach the math because the math teachers are pretty awful at it. That's, that endangers the profession of everyone who comes after me. Okay, so we gotta get at the table and we gotta play and we gotta be valuable. Okay, so I'm really thinking about how to bridge schools and work. So how many minutes do we have now? Zero, negative three, two, seven, two? Okay, all right. So I'm gonna leave this with you and I hope that you will communicate with me about it. So this is sort of like new thoughts, current work of the last, I don't know, 36 hours. So this is what I thought about on the plane flight here. So you're the first people besides the antique. I was willing to look at it. I was like, am I crazy to show this to people? He's like, no, no, no, it's all right. All right, so on the plane flight here, I was thinking when I taught at high school, what did my students really care about? They really cared about whether they were gonna make their car payment and whether they're sweetie like them and whether their friends hated them and what was gonna happen to them in the future? And maybe you can help me by adding to this list. Okay, what do your students care about? That's what my students cared about when I taught high school. All right, what did my school care about? We really wanted to make sure the students were doing what we asked them to do. We wanted to make sure that they were doing it well and we wanted to make sure that they were, that their presence at the school made the school a better place. And I really tried to think about like, what else, what other categories are there? So let me know what I forget here, okay? And then what did jobs really care about? Jobs care about can you get up to speed and be useful? They care about, again, did you do your work well and in a reasonable amount of time? Do you do what you say you're gonna do? And then can you thrive? Can you work with others? Can you communicate? If you quit tomorrow, will somebody be able to pick up where you left off, right? Or if I need to move you to another project, can you pass it off? Have you documented your work well enough, okay? So I think that the student concerns should motivate the contexts for our problems often. Because that's what they care about. And if they care about the environment, then that's a context that they care about, right? But whatever it is, to me that has to do with sort of future concerns, right? Or community. And then school concerns, it's sort of like the more that we could get students to self-assess, so that they're answering the question, am I doing what my school and I hope I could be doing? Like am I meeting the expectations? The more I'm responsible for that, the more I'm accountable for that. And the more I can set goals and try to reach those goals. So the same is in the workplace where you would wanna set a goal and then be held accountable to that goal and then it should be an individual goal. I think students should have, like every student should have individual goals for the year. And then somebody to check back with them and say, how are you doing? What do you need? If you're not meeting those goals or exceeding those goals, what are you not getting that you need? Because you're capable. So you set this goal. You believed in yourself a month ago. What's going on now, right? What do you need? And the job concerns I think could, we could think more about just like I was trying to convert what the US Army person was saying into the type of task that you would be doing in a modeling problem. I think that the types of behaviors that we need in the workplace could better be connected to the types of tasks that we're giving students that we could make a direct connection to them for something that might happen in the future. Like if you worked for this company and the more you connect with companies to say, hey company, what do you need? What's your biggest problem? The more you can really point to somewhere in your community and say, company, this factory or this company or this prison or this post office has this issue yesterday, right? And they need people who can do this. All right, and then we can think about like my problems and my classes deal with health. I know there were some sort of policy talks here. I don't know, I don't deal really with fairness or security in my classes and security, whether that means cyber security or privacy are really, really important mathematical questions right now. Okay, so the good news is this list I showed you really can find this stuff at work. Okay, so the good news is you've come to a conference where you're learning a lot about mathematical modeling and how to engage in mathematical modeling and you really, those are directly applicable to the workplace. Okay, so I'll leave you with Robin, one of my kindergarten teachers who said if you have a job to do, she's like I always just get into my day and I forget to do the modeling part of the day. So I think if I have a job to do and I can't remember to do it, I'll give it to my kids. So she told the kids that the driving question is all day long, where is the math? And then if one of them anytime of the day sees any math, they get to yell, Booyah, I see the math. So when I observed her one day, there was something that was going on and Robin got excited and she was like, Booyah, I see the math and the kid was like, Booyah, I see the math and the teacher was like, no, no, no, I saw the math first and the kid was like, no, no, no, I saw it, I saw it. And now the teacher and the student are having an argument about who saw the math first and I was like, oh, kindergarten. That's how I want the world to be. All right, so thank you.