 It's so nice to see so many people here tonight. Thanks for coming out to America's Only Museum of Mathematics. And I'm glad people are applauding. Hold on now. Go again. I think John is not happy with that response. Thanks for coming out to America's Only Museum of Mathematics. I think we need John at War Mo Mathematics. So I am so delighted to have John here. I first met John a number of years ago. He was doing some work with another company and happened to come through War Math as part of that work. And he became an immediate friend. It's wonderful that somebody who is such a talent on the football field, the athletic field, also turns out to be so talented in mathematics. Not only is that an unusual combination, but it's a great combination for us to get kids excited and delighted about mathematics. I see that these two things do not have to be mutually exclusive. So John is at MIT pursuing Ph.D. in mathematics. He's recently retired from the Baltimore Ravens, so he can go to university. And he's also a new father. So I'm delighted. And I know you will be delighted to hear what John has to say. So without further ado, I give John your show. All right. How's everyone doing? Doing well? Good. So today, what am I here for? So there's something going on in a couple of days. Does anyone know what it is? It's like a mild event. High day. High day is coming up, exactly. No, we have a Super Bowl. This is naturally a thing. And I couldn't help but notice that some people have already, you know, have picked their sides and made this quite known. I'm not going to pick sides because, well, like she said, I'm in Penn State. I know many Eagles fans. And I currently am getting my Ph.D. at MIT. And, of course, I know many Patriots fans. So I want to fold you guys real quick before we get started. How many of you guys have taken high school math? Okay, your hands up. How many of you guys have taken calculus? How many of you guys have gotten a college degree in a quantitative field? And how many of you guys have gotten an advanced degree in a quantitative field? Okay, perfect. So my goal tonight is for all of us to be together on this journey. We're talking math. We're talking football. I'm not going to lie to you. It's really a lot of math. I'm not going to lead you guys astray. And I guess the way I want to start this is to tell you a little bit about myself and to talk about, you know, the strange dichotomy, the strange dichotomy between the world of mathematics and the world of football and these things that are seemingly disjoint. And for many years, I lived in both these worlds and I went back and forth. And I have to tell you, you'd be surprised, but the great feeling you feel on the football field after you fought your heart out for 60 minutes, play after play, drive after drive to get that victory, that amazing feeling is not that much different than the amazing feeling that I feel when I've been grinding on a math problem. And I'm not talking like, you know, the math problem you get for, you know, problem 17 out of your calculus textbook. I'm talking, I've been working on this math problem for maybe weeks, maybe months, maybe a couple years. And I've been trying as hard as I can to try to make progress. I've been fighting with this thing day in and day out to try to just learn something, to try to face this problem that no one else in the world has ever solved and try to just glean a little glimpse of the unknown and try to fight against that in the moment when it becomes clear to you when you've figured this thing out and you are the first person in the entire world to ever solve this problem and to be able to share this with others so that no one else ever has to struggle with this and they can, you know, more or less stand on your shoulders. That moment is just as amazing, if not more amazing than that moment you feel at the end of a football game when you're just spent, in my opinion. And so to start us off, I'm going to start us off with a little bit of a bang. I'm going to tell you guys a story. So the first thing I'm going to do is I'm going to put up one of my papers if you will allow me. And I want to talk about it for a second. So this paper is titled On the Characterization and Uniqueness of Centroidal Vornure Tessellations. Under it you see an author, John Urschel, that's me. I want to make sure we're all in the right place. And the story behind this paper, this came out last year and this paper was the product of years of work. I kid you not, this project took me a full two years and I thought it was going to take me longer and I thought this was going to be much more difficult and I didn't know if I was going to be able to solve it at all. And you might ask, why am I telling you about this? Why am I putting this paper up here? Could I possibly explain to you guys what a centroidal vornure tessellation is and all this complicated math in here and what does it have to do with anything other than what's in this paper? This is a reasonable question to ask. And so, I'm going to put this aside for a second but there might be some mild foreshadowing here. We are going to go to the paper and now we are going to talk some quote unquote football. I have a question for you guys. And the way we're going to do this is by poll. Here's the game we're going to play. I'm going to draw a football field for you. Here's a football field. Please excuse my drawing. This is the end zone. And now here's the game we're going to play. I tell you there's a player on this field with the football and I will mark him with an X. Now he's trying to score but the issue is there's defenders in his way trying to stop him, trying to tackle him. And now what I want to ask you guys simply put, with perfect play all the athletes run at the exact same speed can this person score? Where the defenders are, what do we think? Yes? Who says yes? Given where defenders are. Okay, so I'm just going to start off by saying here I think it seems somewhat straightforward to a football player that this guy doesn't have a very good chance of scoring. I mean listen, there's a defender right in front of him there's defenders to the side and there's no place, no route this person can take that a defender can't get to quicker than him to get to this end zone. So this is the test case. I'm going to give you guys a harder one and I'm going to pull you guys to see what you think. Doesn't it depend who the runner is? So yes, does it depend who the runner is? Where's the rest of the office? Where's the rest of the office? This is a good point. Third runner. Everyone is running at the same speed. Can this person with the ball score? Who thinks yes? Yes. Who thinks no? And now I'm going to ask you a third question who can come up with a good way to tell for sure? Yes. Well, the three, the defense, I tried to score over there if they tried to tackle him I think he would get a pretty good chance of actually scoring because if he tries to walk down, run down that field the other two people can try to get him but I don't think they'll get him. Okay, this is a good idea. And also let's say for these instances if the defender can touch him, they can tackle him. How would you mathematically tell if this runner has some route that he can use to get to the end zone without being touched? How would you try to tell quantitatively? I can't in a pure sense, but let me ask you a question. Yes. Are there now or later mathematics that would allow for the runner to do a juky-juk? Yes. Run, batter, stop, fake left, go right. There are no juky-juk. Next here, I'm sorry to say. Can I defer to another person? Yes, please defer, but I appreciate it. Yes. There we are. I would assume that the guy who's behind him is out of the line. So I would measure the distance between the two defenders below him. Okay, we're measuring distance. This is going to be quantitative. Take the center point and measure the distance between the X and one of the defenders if the X is shorter, then X is going to make it shorter. Oh, you have an idea? Yes. Tell me. Okay. All right. Let's say you connected the two circles with the X. Okay. Obviously, as mathematicians, we know that the shortest distance will point to a line. No, no. Yeah, correct that. The shortest distance from a point to a line is along the perpendicular. So let's say this X guy starts running towards the line that would connect the two defenders. Okay. He will reach halfway between the two defenders faster than the defender will reach him because he has to, because if you draw the perpendicular from X down to the base of that triangle, you'll have a leg of a right triangle because the two guys are running along the hypotenuse. I like where we're thinking. We're getting quantitative. I want to hear one more opinion. Yes, you, ma'am. I don't know what I said. Yes. Yes. Okay. If the two players are running at him, and they're going to the same place because he's going downhill, and you said they're on the same speed. So if the person in the back is running the same speed as him and he's coming down, the person in the back is out of place. So if they go together to tackle the person that's running downhill, he could quickly turn to either corner because they leave that space open when they come together to get the person that's running downhill. And since NFL players have a lot of legs very quick and agile, they could go to the corner. I like it. Okay, these are all fantastic ideas. And we've gone from just guessing yes or no to coming up with quantitative ideas. Ideas about drawing lines between the circle and the X. Ideas about perpendicular lines. And now let's take a look. Suppose we just look at X and this defender on the left. And we ask ourselves, what areas of the field can X get to before the circle on the left? And what areas of the field can the circle on the left get to before X? The way we're going to do this mathematically is we take this line between them, we bisect it, and now we are going to draw a line perpendicular to it. And now, if you look, it becomes very immediately obvious that every point on the left side of the line, the circle can get to before X can. Every single point on the right side of the line, X can get to before the circle. And now we can do this exact same procedure for every single line connecting X with the circle. And very simply, you can decide mathematically whether or not this X can score by just looking at this polygon that we've made from these lines. So X is contained in this polygon. And the simple question to decide can X score reduces to what here? What about this polygon? The interior? So this polygon represents all the points that X can get to before any of the other circles. What would we need out of this polygon for X to be able to score? Yes. If X could get to the two points, if it's enclosing this polygon and all the chains are before it, X would then not run outside of the line because by your polygon he knows he can't get there because the circle could get there before X. But if he runs straight to the middle and the two circles on the bottom run down at the X point, if they run down at the X point where X could get there right before, if they get there a little bit down under the same P, K, D. Okay, so this is a good explanation. And I think the takeaway here is that we look at these lines that connect different points or different players. We bisect them and we look at these perpendicular lines and these induce polygons. And this is actually a partition of this given space. And the answer, go ahead. Are you assuming that the circles know that path X intends to take? No, they don't need to know. So can they react instantaneously? Yes. This is somewhat of a derived example, but I promise we are getting somewhere quickly. So because this polygon doesn't touch the end zone, we can immediately say this player can't score. And in fact, if we continue making these lines, not just for X, but for these other circles together, we are going to end up with something very interesting. We're actually going to end up with a partition of the field into four parts, each containing one of the players, and each region is saying this is all of the space in this field that X can get to the fastest, or you can say that X is closest to. This whole region is all of the space on the field that the circles closest to and that this circle is closest to and that this circle is closest to. You might be asking me, why are you showing me this? Do you want to know what these things are called? These are called Voronoi tessellations. And these aren't just things that show up in math papers of has-been football players getting their PhD at MIT. It's true. These things also show up in the intersection between math and sports. I admit, the sample I just gave you was somewhat derived. But I did that to warm you up to things like this. So, you say, well, one of the uses of Voronoi diagrams is to really connect to sports. And I'll actually have you know that the majority of sort of spatial-based research in sports analytics, in the NBA, whether it be in, you know, so-called European football, the real football, as many people say, or whether it be in NFL football, specifically, I know by second spectrum, Voronoi diagrams tell you something about how defensive players cover space and how well they're stopping their opponent from scoring. And so, for instance, these sorts of things are used extensively in the NBA. This here is a diagram of a given play, a given NBA play. And now, below, what you will see is the Voronoi diagram induced by every single frame of this play. And as the offensive players move, you can track how well the blue dots or the defense is covering space and also spreading themselves out to maximize the amount of this court space, particularly within the three-point line that they are covering, that they are actually closest to. And this is a great way to measure analytically how well a defense is staying spread and is not being not being distorted through some sort of trickery of the offense. And this is just a warm-up to show you that even the advanced math things that you see, your math professor doing at MIT, that I might be writing papers for, these are things that sit in the real world. These are things that have applications. And yes, applications like basketball or cool, these things have applications in, you know, advanced things and computational geometry and so many different applied fields. Do you have a question? Yeah. What's up? I guess we're like an NBA team or something. Yeah. It's on. But how is this that useful when it's not taking into account, say, the speed of one player versus, like, how are they, like, I guess in some sense, it's like you're spreading your defense out well enough so that you're able to grow this amount of space. Would you want to take that into account as well? Are you, like, is this really that useful in that sense as well? You can modify this to take that into account to some extent, but this is, I know for a fact this is extremely useful and actually used by a large number of NBA analytics departments. At least, you know, people I know in the sports analytics world. And one of the best ways that this becomes really interesting is it's a really easy way to scout it upon. You take this, you input it, and all of a sudden you pull out plays where your opponent's defense seems to be out of place. You pull that playoff like that and you say, what about this play caused that? And you say, let's do that. This is one simple example. You've done these two-dimensionally. Can I assume it could also be done three-dimensionally? These could be done in any dimension in my papers, actually, in our, it's in n-dimensions, general dimensions. But, yes, this is for sports, it's used in two-dimensions. If it's a basketball, you imagine you can get that height coming out of it. They mainly just use it in two-dimensions, but for a lot of things in computational geometry, they mainly do three-dimensions. Yes. Okay. I was just thinking, because it's not proposed at these times, what about on the battlefield when you have an enemy and then you have your own soldiers and they're trying to either stay away from the enemy or go toward him? I... What will the gen loss if he did this? That's a good question. I don't know because I have to admit, I tend to try to limit myself to, you know, boasting applications that I know for sure are actively being used. And so it's possible, but I don't know for sure because I actually don't have one of any friends who do those sorts of things. I have to admit. And... We'll hook you up because our son was at the analyst. Yeah, yeah. So we'll connect you. Yes. So when you were playing football, were you actively thinking this way on the field? When you were playing football, were you actively thinking this way on the field? So sadly, I have to admit... Are you framing your roommate, your teammate, as well? I have to admit if I tried to think about these types of things on the field, I would get murdered. This would not be too good for my health. But let's move on and also know that at the end, I hopefully intend to have at least 15 minutes of question and answer for whatever questions you guys may have about what I'm talking about or perhaps not. And so, given that that means I have about 15 minutes left, I'm about to move into the second half of this talk. So, this is something that we can really sink our teeth into and feels a little closer to what we might see on Sunday. So, what I want to look at is a certain decision. Suppose it's some play in the game in, say, middle of the first quarter. The offense has gotten down to say the one yard line. It's third down. It's fourth down. They get no other chances. This offensive coordinator has to decide what play am I going to call. And equivalently, across the field from him, this defensive coordinator has to decide what type of play am I going to call. Even though football is indeed this battle of brawn and strength on the field between coaches, this is a battle of minds. And so, who knows a little bit about game theory? Anyone? Okay. So, we are going to get into this deeply, but what I want to illustrate to you guys, and those of you who know buzzwords, I'm going to quickly illustrate mixed strategy. Equal agreement. So, suppose we have our offensive coordinator, we have our defensive coordinator, and the offensive coordinator, to be simple, let's say he can choose between a run or a pass. And we'll say it's perhaps a play-act. And the defensive coordinator can choose a defense that either focuses on stopping the run, say, let's run heavy, or a more modest defense that focuses on coverage. And suppose the offensive coordinator, if he runs the ball, and the defensive coordinator indeed blitzes and plays a run-type defense. Perhaps the offensive coordinator, the offensive coordinator has a 30% chance of scoring. If they play coverage, suppose it's 70%. If they call a play-action pass, and it's a run, if it's 80%, and now they call a play-action pass, and the defense drops in the coverage, let's say it's 20%. I just pulled these numbers out of a hat. We could pick different numbers, but now my question to you is, if you're this offensive coordinator, and you are trying to, you're trying to score, you want to score badly, how do you decide what to do in this situation? How do you decide? What would be the best option for you to do? What would you pick, and what do you think is best? I think he said, you should have looked at film. We're in the heat of it, and we're trying to decide what we should call. How would we think about this quantitatively? Yes? Okay. I would choose a run-play, because even if the defense blitzes, there's a better chance of scoring than if you choose a play-action play, and the defense goes coverage. So you would have a higher chance of scoring, even if you guess wrong. Gotcha. Anyone else have any opinions? Would it depend on conditionalizing those probabilities, if you will, based on what you think the defensive coordinator thinks you're going to do? Now we're getting somewhere. Right? And even further. Yes? Bring me up, you want to have the possibility of the offensive coordinator and the coordinator to each one by the percentage. Okay. We're starting to think quantitatively here. I like it. And the main takeaway I want us to see from this is that you can't say that there's one say, fixed, best answer. You can't say running the ball is 100% best here, because what if the defensive coordinator is picking coverage and he's decided he is doing coverage, no question. And also, this play-action pass, what if the defensive coordinator is deciding he's going to blitz and it's going to be run heavy 100% and you can't know these things. So, what I'm trying to tell you here is that in these types of situations it's not yes, run 100% is the right answer or yes, pass 100% is the right answer. What I'm telling you is that there's a distribution. There is a distribution and there's a certain percentage where you say I should run here with say let me just look and guess. I should run here 50% of the time and I should pass here 50% of the time. And that way no matter what my opponent does I know I'm playing optimally. In fact, in these types of situations you should ask yourself if my opponent even knows the strategy I'm doing can he actually do any better than just the best strategy not knowing what I'm doing. And in these cases where there's no clear situation where you have a best strategy no matter what your opponent does where you wouldn't go back and say man I would have preferred to do that strategy this is where the concept of game theory mixed strategy equilibria come into play. And now the last question I'm going to leave you guys with and the last exercise we're going to do involves the question that all of a sudden when the decision making you need to make in a football game as a coach somehow needs to not just be okay we have to call a run here or decide we have to call a pass but you have to have some distribution between the two to be optimal how do you try to be somewhat random during the game. For example every single play as an offensive coordinator you have to decide is it going to be a run play or is it going to be a pass play and the problem is if you're predictable and your opponent knows yes sometimes you can just run the ball down their throat but in general at the NFL at a high level if your opponent knows what you're doing because you're too predictable this is not good for you and your chances of winning they severely, severely go down and so it's important even in football for football decision making to be able to make decisions between things with distributions and to try to simulate some sort of randomness in college football and the NFL I've witnessed this first hand from the offensive side offensive coordinators trying to balance run and pass trying to make sure that they aren't giving away tendencies making sure that they're balanced so that when their opponent looks at the things they do they can't get some advantage out of it and so yes so would on less important plays would they be willing to go for a lower percentage just to play with the other coach to sacrifice that so that they can do some things more unexpected when the game comes up that's actually very astute and this actually happens in the NFL so you see this all the time you'll have coaches call plays in garbage time to break tendencies so that if you have another team that's analyzing your game and isn't really being careful about it they'll lump in these garbage time plays and this will sort of hide tendencies and give the other team an advantage in the opposite case I've been on offenses where we will do something specifically to build a tendency on purpose just for us to break it at an opportune moment so let me follow up could the other team correct for that by coming up with some weight for the value of the play and this is something that's very common but also the idea of building a tendency so that you can break it when you really need to is also a very common thing and what I'm going to leave you guys with before we get to what I consider to often be the best part of these sort of talks being with you guys is where we have interactive questions where we can talk about things that you guys really want to know about but before we do that I have one last exercise I need one brave soul to attempt to be an offensive coordinator one brave soul you're brave? so here's what we're going to do you're an offensive coordinator and I'm going to make your life simple there's nothing complicated here you're going to have to tell me run or pass and I'm going to have a defensive coordinator trying to, he doesn't need the mic actually trying to guess whether or not you're running the ball or passing the ball if they guess right they get a point you get a point and now if you're random they shouldn't be able to guess any better than 50% right their scores should be the same at the end of this so I am going to put up a nice little app the so-called mind reader can computers read your mind? does anyone know who Shannon is? a lot of Shannon does anyone know the Shannon mind reading machine? wait does someone know the Shannon mind reading machine? you have homework when you get home but this is a modern variant of it see and now here's what I want you to do you are going to have to tell me you run or pass and this computer is going to try to guess which one you're going to say every time a guess is wrong, you get a point every time a guess is right it gets a point don't let this thing beat you you should be able to, on average you should beat it half the time what I want you to do I want you to raise your right hand left hand for run left hand for pass let's test it out give me a fled and another one and another one there we go we are going to try this out we are going to see how he does is everyone ready? we are going to start the game yes we are ready, set oh you are doing well is the one who wins you do need to speed this up so give it to me quickly there we go we will open this up to questions well done sir observations about that experiment more data that the computer had the better it was at predicting ok what else do we think what's the computer notices a pattern in his movement the computer or bot is more likely to predict where where which hand the player will pick up and why why are there patterns in what he is doing the system makes it like they think exactly what you are going to do with how you put up your hand so most of the time you haven't done most of it you put your hand up and they won't know what you are going to do so they won't read the play but for most of it when they see a pattern of what you have been doing they realize how to guess the right play and not have you get good yardage the main takeaway from this app I have done many times and I've seen many people do many times is that humans are awful at being random or downright it is something that is hardwired into our just nature we think we are giving random answers or not and I encourage you guys I encourage you when you get home you can type in this on your phone type in this web page mindreaderpro.appspot.com try the hard difficulty and yes it seemed like when he was going much faster it went much it went much faster as well yeah it gained ground because he went fast but it also gained ground because it was it gained ground because it went faster so he was just going on instinct because he was going faster and also at that point it had much more data on it and if you we did it for like I think it was 50 was it first to 50 if you make it 100 or 200 this just gets more and more obscene and these are the sorts of things that yes and you had it binary I guess it would be the same thing if there were multiple choices yeah same thing if there were multiple choices so this probably goes outside of mathematics but is there an evolutionary reason is there no this is a good question that is a legitimate question that I don't have a good answer to but I do have a question for you and then I will open it up to questions for all of you I have beaten this thing I've beaten it many times inputting things fairly quickly how have I beaten it how would you beat it flipping a coin is a good answer another another answer of how to beat it half the time you don't look at the results of the that doesn't because it sees your results you could start off with a pattern so the computer thinks that it knows what you're going to do then you could go on on a different path so it has to restart all the data that is an interesting idea and I like where your head's at mathematically this is not fully going to work just based off how this algorithm here that the computer uses fully random and the point of being fully random to an extent I mean it you know it recognizes things but the point of being just about fully random with tweaks is that no one strategy will beat it it's not some strategy that you could come up with a fixed strategy where you do that strategy every time and you're going to beat it higher than 50% if you just do it over and over again and that's sort of something very complex about the algorithm that's guessing what you're doing but I'll give you my favorite way to beat it half the time what is someone's favorite like irrational number pie and now how would you use pie to try to beat this half the time odd left odd left even right unless it says oh it's pie you were unless it says it's pie which thankfully this thing does not recognize pie but there has been some meandering tonight but I hope that through the things I've shown you you can see that some of the advanced we only had a 40 minute snapshot some of the advanced things that appear in fields like computational geometry advanced things where this computer little toy this toy was made by world leading machine learning experts and I can assure you the applications of these types of things are abundant and these are the types of things that people are actively researching at places like MIT and these are the things that tie into decision-making in games these are the things that tie into the sports we love the games we play and also the decisions we make in life and things that are core to our human structure in particular here the inability to be random and now for our last 15 minutes I am taking any and all questions you take the lead on choosing you run the show I will this when you're done with your degree this is a good question so that Penn State I was playing football but I was also getting my degree in mathematics and I got my degree in three years and I had a beautiful opportunity my last few years at Penn State I got to teach and not TA, I got to teach my own college courses and prior to that I knew I loved research I knew I wanted to be a researcher but after that experience I truly recognized I don't just want to be a researcher I love teaching I love trying to inspire young people not just in mathematics but inspire young people through mathematics to be a professor and while there are many many great sort of employers of mathematicians I know that the professor is 100% for me this is where I'll be going would that work for like a different sport like soccer or something yes so the same sort of idea of working for soccer and the same concept of picking some defensive structure that covers space on say a soccer field well I actually saw a talk either a talk and a paper at the premier sports analytics conference the Sloan sports analytics conference that's MIT and I saw it three years ago and it was exclusively on that it was exclusively on ordinary diagrams applied to European football so know that these things are active and play a lot oh sorry I can't pick also referring back to the football player thing with the circles in the X yeah if you put science into it a straight line isn't the shortest distance between two points so wait what now everyone a straight line isn't the shortest distance between two points can you expand on that well it's kind of confusing but in physics it's something about using the fourth dimension and so you can go to another point quicker than you can do it in a straight line if you're running towards it you mean instead of like drawing a line between two dots on a piece of paper taking the two dots and putting them on top of it because if you have like a string and an ant on it and the ant was crawling to one of your hands all you needed to do was this and the ants already there so that is possible well not right now it's very true and this is something for us to hope for in the future and no sadly my model doesn't take this into account but I don't know I'm kind of looking forward to the point where we can just like let's just bend space time and like you know I want to go hop to I don't know where do I want to go right now Mars I like Hawaii a little bit we can do two of them I will go to Mars and I will go to Hawaii can you also give us a little bit how you got your love of math what was the point sort of of when you sort of discovered math and you discovered how did you get started I had a strange relationship with math I'm always embarrassed to say this in front of people I didn't like math when I was little I didn't like it in middle school I didn't like it in high school and I really didn't like math class and it wasn't until college that I really fell in love with math and it was when I finally felt like like the world was open to me there was no one you know sort of standing over my shoulder telling me John this is the next math class you have to take because you just took this and this follows that and there wasn't anyone to tell me John you're a freshman you can't take a fourth level senior year math class when you're a freshman with no prerequisites and thankfully no one was there to tell me because this is what I did and it was this sort of freedom where I really started to see math as it was and the higher you go in math the more you get to see the true elegance and beauty and some of the most beautiful things about math and in particular math courses in college for me was that I was never told something I was never you know shown something and been told this is the formula I had never been told something and shown this is how it works and now let's use it it works like this let's use it there's something that really that really spoke to me about the need to verify the need for proof the need for understanding and that was something that really really caught my attention and that was really what made me fall in love with mathematics since you're both in athletics and mathematics do you believe in momentum in sports because some people say there is no momentum like say basketball shooter he's on a hot street but is he really over time oh that what's that famous paper it's the disproving the hot hand yeah it's the what was it the 44% what was the percentage anyway that's a tangent I completely believe in momentum in the sense that not necessarily in shooting but I believe in any competition yes there's a huge physical component to things but also up here affects how you perform and how you handle things mentally affects what happens next and if what's come before has some impact on you mentally yes there is there is an influence hi so I wanted to go back to the question about the academic history I think it's very important for young adults and students to understand this so could you speak to this question you talked about you were a freshman and you started doing that senior level math class in your opinion where did getting grades in terms of getting the grades that you got a grade that senior level course where would you say you placed importance of getting the grades versus the passion for math oh yeah that's a great question and also I think I kind of did sort of like kind of half it was a very average answer I gave to that previous question and I want to talk about time is limited I would say that it was really sort of my fault for those years middle school to high school for not sort of truly understanding the sort of relationship math had in my life and actually the person I have most to thank for where I am today and my mathematical maturity is my mother because she's the person who after I had a day at school where I'd be in math class and I'd be sleeping or I'd be reading a book like some random book for some other subject and I'd be paying attention I would come home and we would have fun and we would solve puzzles together and we would do math workbooks together and we would challenge each other together and we would get to get me math workbooks and we would do something really fun we would not read the instructions we would just go to the problems and we would try to figure it out for ourselves and we would try to figure out how can we approach this and I remember these are like some of my fondest memories in childhood I love this stuff I remember I got allowance by at first being able to tell my mom the amount of change she was going to get back at the grocery store and when that sort of got a little too pricey for her and I could calculate the tax before the register put it in I would get the change so we did these were times where people at least my mom back then she mainly used cash which I was quite happy about and your question was the importance of grades or the lack of importance I would say so I have to in full disclosure I was a 4-0 student when I was at Penn State but I didn't really care too much about grades because and also when I taught I don't really care too much about grades I care to the extent that if you understand the material I will pass you and I don't care too much about your grade if you don't understand, yes I have to fail you but the point of taking a class isn't to get a grade so that you can take the follow up class to get another grade so you can go somewhere for someone to hire you the point of taking a class the point of college is about learning the whole idea is you want to take this class because you want to learn so that you can go and learn other things and yes you get this piece of paper this piece of paper you have at the end of the day is worthless without you having the skills and the ability that this piece of paper represents and in my opinion I would rather have someone with the abilities and not the piece of paper than someone with the piece of paper and not the abilities this is something that people always ask me with respect to math I will take a student who really understands math but maybe he didn't get a 4.0 over a 4.0 student who just crammed things and then doesn't remember it a week later it's truly about learning build upon the question that was just asked and it's great to see so many youths in this audience and I'm here with my 10 year old son so my question is of course there are programs like this to get them interested and excited about math I was also just thinking as you were talking about the sports analytics we have some professional teams here like the NICS that's something that I'll look into but do you know off the top of maybe a few programs out there that cater to not so much internships but to kids this age to really spark their interest in applied mathematics and you know rewarding the love that they're developing for the subject yes so applied mathematics I think it's a little tougher for applied mathematics I know there's a bunch of contests for both middle middle school, high school and college students where you have some problem that they release and then you try to do some modeling to come up with the best solution also for middle school kids something I highly recommend to sort of get your puzzle solving juices going I am a big fan of math counts so if you're a middle school aged kid and you like solving puzzles you like solving problems I would encourage you ask your parents to get you some old math count workbooks I think you can even print them for free online and this is sort of one of a bunch of amazing different sort of resources for kids to really challenge themselves and to really see math in this fun and sort of almost sport like light because I feel that a lot of times young people, at least I know when I was a kid my mom my mom knew this all of a sudden when competition is involved sometimes kids get a little a little more interested at least I did yeah I guess people do going back to the where it was fourth down one yard line what would happen if the offensive coordinator decided to do a pass play but the defensive coordinator did a blitz run heavy but then they saw that the offense was spreading out wide achievers on the sides would they eventually go back to coverage that's a good question and that is a quite applied question but actually in practice yes they often do they often do but then you have to watch out for draws what so did you feel intellectually isolated in the locker room if you guys if anyone I know that this was supposed to go until seven if anyone has to leave promptly you will not offend me feel free to just get up and go at any point but I will try to take like three or four more if I'm allowed to be here a little longer did you feel intellectually isolated in football no not at all I find that you'd be surprised that there are quite a good amount of smart people in football it's just that people have very different interests and just because someone might have a different set of interests than you doesn't mean one person is smarter than the other some such thing many of some of the smartest people I know were never mathematically inclined people and you know it's a shame but you know how it comes in all shapes and forms how would you define being a great mathematician to an elementary school child yes so I've thought about this a lot in my opinion being a great mathematician involves three things four things one solving problems two sharing those problems and those solutions with the world three inspiring young people and being a resource for young people mathematically bringing the next generation along and fourth I believe historically and I think mathematics has gone away from this a little bit but historically mathematicians and mathematics has been a sort of a service field and what do I mean by service field when back in the day when a physicist had a problem that he really couldn't figure out he had some trouble he would come to a mathematician and mathematics historically has really serviced so many different fields whether it's physics or chemistry or biology or computer science and I think that is also an important part of being a mathematician being able to sort of help solve important problems and help blend your expertise to other people with expertise and things that you know are directly impacting the world okay so we have time for about two more questions but while those questions are happening I'm actually going to have one of the exhibits turned on which is the floor that John is standing on because what I want everyone to see is we actually have an exhibit here that we call my game and so as people are leaving if you come and step on the floor you will actually see a Voronoi pattern and hopefully after this talk you will understand exactly what you're seeing also I was in the gift shop earlier today I saw the coolest thing so some of you guys were like oh I might get something from the gift shop this is the thing you need to look at there's this there's this toy where it's a bunch of little small like marbles or some such thing it's down at the bottom and what you do is you flip them and they ping these little like metal I don't even know how to call it like little slots imagine like almost like what were those pin machines the what the chinko I think I think we're showing our our generation from the bell curve yes and it forms a bell curve at the bottom and it is one of the most beautiful little simple and you're there all day and it's just like fast you can see the marbles going down bouncing you see the randomness you see the binomial like distribution and the shop is open so if some of you guys are like oh I think I might get something that would be the thing because I think that looks really cool incidentally a friend and colleague of mine is coming out soon with a film about Claude Shannon so we'll let you know about that my question is you know the original the Shannon's mind-reading machine you know MXT still has it it's like in one of their storage so my question is on a little bit of a different direction but nothing new any thoughts on what football at all levels should do about brain injuries and injuries good I'm surprised we got this long okay so yeah I do have I have some strong opinions we'll see so my opinion is that football is a dangerous sport I don't think anyone's going to argue that maybe but I feel like football is a dangerous sport and I don't think I have a huge issue with you know professional football players playing football we I always I like to believe that we do understand there are risks involved in playing football it's a dangerous sport it's violent there are risks in many sports there's risks in boxing and kickboxing there's even risks in soccer or basketball or whatever sport it may be but the one thing that I am a hundred percent against I have no issue saying this to anyone is I am a hundred percent against like small little kids playing tackle football and it's there's no need to you know clap and it's to everyone's preference but for me personally I think that you know little kids could benefit a lot more things like seven on seven and if you want to play football I think you can wait I didn't play football till high school you can wait till high school play seven on seven until then when your body and brain is a little more developed my issue is just you know in pop more football you have kids whose brains aren't fully developed their necks aren't strong enough to support themselves and lots of times you have coaches who don't quite manage kids like they should be managed and I don't know I don't think there's a big difference between having like two kids banging heads on the line at like age seven or eight and like two kids getting in like a boxing ring and sparring at age seven or eight and so you'll be able to answer a couple of questions people can come up to you later okay perfect one more question yes we have one more person what's your favorite football moment my favorite football moment okay so I remember it was my senior year at Penn State where we are six and five and we haven't had the year we wanted to have we've gone through a lot of adversity and we're going to Wisconsin and Wisconsin is completely writing us off and they're talking about we deserve to be in a BCS bowl they're already locked up to go to the Big Ten championship we deserve to be in a BCS bowl they want to go to the Rose Bowl we're going to Wisconsin and we are 25 point underdogs and I remember this was my last game of college football which I love my time at Penn State in college football there's nothing like it and we went into that stadium and oh my lord was it a bloodbath we just dominated this team and any of you guys who do we have any badgers here okay good anyone who knows like Wisconsin football at the start of the fourth quarter they always play you know like jump around and they always have this you know tradition where the whole stadium they start jumping around and their whole sideline starts jumping around well fast forward to this fourth quarter and they're getting whooped their sideline is in disbelief their stadium is like emptying out before the fourth quarter that song comes on and would you believe it we looked like the biggest I can't even say the word we are jumping around on the Penn State sideline we are out on the field jumping around celebrating the raps are looking at us and laughing their sideline is just staring at us in disbelief no one on their sideline is doing anything the whole stadium is just like booing us while we are just dancing you would not believe and just like yeah and that was my best football memory on this floor you will actually see the Voronoi we need at least three to actually show it you'll see the Voronoi region's pop-up all the points closest to John are one color there we go closest to this young man or blue feel free to come up and ask questions hey how's it going yeah of course