What are some of the biggest flaws that you see in how math is currently taught in the US?

That's a tough question, that a lot of people have thought about for a lot longer than I have. But I think one of the biggest flaws of math being taught in the school is too much of a focus on memorization, and not enough of a focus on original quantitative thinking.

What was your favorite class at PSU?

I took Theatre 100 (I think that was the number) and I loved it. Seeing actors perform in the class was very entertaining and quite different than anything I ever took.

Context: I studied computer science and now at 32 started a company in machine learning after working for 3 years. Also I am going back to university to to study mathematics and I have to manage a full course load and my company.

Question: I was wondering how you managed the training AND your course load. What was your typically daily routine like as an undergrad / a grad student? (I listened to the Freakonomics podcast where you explained this a bit but I would like some more details regarding undergrad/grad in specific :-))

Okay, so going into my schedule is going to take a little bit too much time, but I gave up a lot of things, socially and romantically.

Is Joe Flacco a Elite Quarterback?

The age old question! I know Trump stated his opinion. https://www.si.com/extra-mustard/2015/09/21/donald-trump-joe-flacco-elite-baltimore-ravens

So if you think Trump is brilliant and knows everything, Flacco must be elite. But if you think Trump is a fool and knows nothing, then I guess Flacco isn't really that elite after all :)

I feel like you're saying Joe Flacco is sub par on the down low haha

Noooooo. Joe is awesome. Seriously. Plus once he bought me Hagoromo chalk for Xmas. If that isn't elite, I don't know what is.

We might have an entire cabinet with a secret stash of Hagoromo chalk at MSRI - a mathematician's dream!

WHAT!?!

In your opinion, who was the smartest player you played with or against in the NFL?

Duvernay-Tardif is a pretty smart guy, and I'm happy to call him a friend. If you don't know him, look him and his accomplishments up!

John,

1. As a Penn State alum, Harvard student, & mod of /r/PennStateUniversity, I just want to say:
   You're my hero.
   You—more than any other player I can think off—embody Success with Honor. You do our great university proud, will always be my favorite cfb player, and frankly, I hope to run into you in Cambridge!

2. Q:

   Who are your heroes?

3. also:

   WE ARE!

Janet,

Thanks a lot! I've found that heroes don't need to be people who you see in the media, but often are just people around you. After all, we're all people. My hero is my mother. She made so many sacrifices when I was young to make sure I had every opportunity to become whatever I wanted to be.

Hi John!

I have a more mathematical interest. I understand that you research spectral graph theory. I wonder: why spectral graph theory? When you applied to MIT's math program, did you already know you were interested in spectral graph theory (or perhaps just in numerical analysis)?

I did do spectral graph theory before MIT, but I picked MIT because I saw a lot of brilliant people doing a lot of things that I thought were pretty cool. I wanted to broaden my horizons.

Are you actually a mad scientist who used football as a way to fund your Doomsday device? But really you are an inspiration to anyone keep being a genius.

How'd you know? But first Musk and I gotta get off this planet.

What offensive thing did you say to become an offensive lineman?

Fries actually do taste good with mayo.

Hi John, did the timing of your NFL retirement have anything to do with the NY Times CTE article? I recall it was the day after. Thanks

Hey, I more or less already talked about this in a USA today article and Freakonomics podcast this week. I think the podcast was pretty fun, and you should check it out.

Do you feel like you need to challenge the stereotype of what people think the typical math student is? Do you feel the urge to represent us and how diverse we are?

I don't feel the need, but I am proud to be one example of many that mathematicians come in all different forms.

Obviously you're great at Math, but were there any subjects you struggled with in high school or college? If so, how did you overcome those struggles and get through those classes?

I really really struggled with things like History and Biology, where a lot of memorization is required. I tried my best, made lots of flash cards, but at the end of the day, I'm just much better at things that value understanding over memorization.

Hi John, who was the hardest defensive lineman to block? College or NFL.

Suh

John what are your favorite white and black chess openings? Are you building a repertoire and/or how seriously will you pursue chess? Any more chess.com videos?

My favorite white opening is certainly the Catalan, and as black I'd have to say the Berlin. I don't like studying openings too much, and spend most of my time working on endings though. And yes, Danny and I are going to do Amateur Hour weekly on chess.com/tv

John, it is nothing short of impressive to balance pursuing an advanced degree at one of the nation's top institutions as well as playing a popular sport at the highest level. My question would be, if you had to pick one, do you think you're better at football or at math?

I'm so much better at math than football. I wouldn't consider myself extremely athletic or gifted. I spent so many hours working to improve as a football player. Even though I've had to work to improve as a mathematician, I started with a lot more natural ability.

What linkages, if any, have you seen between math patterns/sequences and football strategy/playing?

I think you can look at a lot of football decision making, especially from the coaches' perspective in game theoretic terms. My dad actually wrote a paper on something related

http://www.eng.buffalo.edu/~jzhuang/Papers/JQAS_NFL_2011.pdf

What's your favorite meme?

I have no clue why, but this one... http://media-cache-ec0.pinimg.com/736x/e9/db/43/e9db43ba7048e055bf943e7e52d691be.jpg

What's your favorite theorem (and/or favorite proof)?

Riemann rearrangement theorem is one of my favorites. It can be very shocking to a lot of people.

What would you say to a young person who feels discouraged by how long it takes them to work through a math problem?

I would say that the more problems you solve, the better you get at it. And also that sometimes it takes me a really really long time to work through one. The best part is when you solve it though. Maybe focus on the joy of solving instead of the stress of the amount of time it took?

Hey John, Penn State alum here!

I heard you speak when you were a senior, just two months away from being drafted into the NFL and talk about your past hardships. During your time at State, you went through a huge culture shock with the sudden departure of Paterno and the exit of many of your teammates to other schools. Are there any lessons from your five years playing PSU football that are relevant to your tenure with the Ravens or your docterate candidacy at MIT??

I think the biggest thing I learned was to keep things in perspective. Sure, my teammates and I faced hardships, but it paled in comparison to the hardships that the victims faced.

Hi John!

At what age did you discover that you like mathematics? Did you participate in math competitions when you were young?

I always knew I liked puzzles, but I didn't fall in love with math fully until I got to college, and then it started to come together. I did compete in MathCounts when I was a kid. I wasn't very good though. I never made it out of NY State. I'm a slow thinker...

What made you pursue pure mathematics over an applied field such as physics or engineering?

So I actually think that the things I do have a happy medium between pure and applied. Everything I do I like doing from a theoretical perspective, but I do a lot of things that have many applications, like numerical analysis, machine learning, and combinatorial optimization. I think it's pretty cool to solve fun problems, even if there aren't any applications, but if there are, it's that much more satisfying!

Can you honestly say you gave the Ravens your all? Especially last season when you were also taking classes?

Yes. I only did math the evening after the game and the off day. It more or less replaced relaxing and catching up on movies.

Hey John,

I coach youth football offensive line, what would you say is the biggest thing that I need to stress to them at a young age?

See what they hit.

Has anybody ever messed your last name and confused it with Steve Urkel?

More than you know...

Can you "explain like I am 5" your math research?

I like solving puzzles. The harder, and the more beautiful, the better.

Hey John, huge Ravens fan here.

Just wondering what you'll miss the most about the NFL/Ravens, and what you'll miss the least :)

I think I'll really miss the comradery. It's hard to find outside of football. I definitely won't miss the feeling when I wake up Monday morning.

What changes do you think will be made and/or need to be made in football (particularly at the youth through college levels), given recent research on the dangers of head injuries?

I think the biggest thing is pushing flag football for young kids. Give them time for their bodies to develop properly first. They'll have plenty of time to play when they hit middle or high school.

What kind of dinosaur would you be?

When I was young, I actually wanted to be a dinosaur when I grew up. I wanted to be a T-Rex.

http://memecrunch.com/meme/SSFU/dino-step-brothers/image.png

Just listened to the Freakonomics podcast where you were interviewed extensively. Great job, really enjoyed hearing what you had to say.

How do you feel about the news stories linking your retirement so publicly to the CTE study? Are you comfortable being seen so publicly as an NFL player taking these concerns to heart? And with the attention you've brought to this matter? Or would you rather have just been able to retire quietly?

I think a quiet retirement would've been greatly preferred. It was a little too much attention for my liking.

Hey John, I'm a Ravens fan, so I have followed your career fairly closely over the past few years.

One of your interviews really struck me when you said that you were ready to play after about 3 weeks, but it took longer until your mind was working the way it normally does. It made me think that NFL may not know half of what they should know about head injuries, and it could be just because it's a very complex subject.

What do you think about the NFL's attempts to reduce these injuries, and do you think the league is getting safer each year? And do you believe the NFL is truly doing all they can to make the league safer?

I think the NFL truly is going in the right direction. Every year I was in the league, practices were being changed to try to help player safety.

How much sleep do you recommend per day?

I sleep seven. But I think eight doesn't hurt.

Hey John,

PSU alum and current doctoral student in econ. I actually met with you when you gave a talk at my university in July of 2016. Unfortunately I had to take off to unpack, so I didnt get to hear your talk (my bad). Mathematics is closely linked to economics and its not uncommon for many economists to be infatuated with math. Are there any other fields that you find yourself admiring or fascinated with?

Thanks for being an all around down to earth guy and ambassador for math.

I really love physics. I started out in mathematical physics, and almost ended up working in quantum mechanics research for a time. My first paper was on a three body problem.

Hey John, I am a former o-lineman at western Illinois university and current equipment manager for them! Do you have any good stories about Ty Howel or coach fisher?

I do, but none that I can put on reddit (at least without Ty getting mad at me). I'll be there for the game on the 30th, so we can talk then.

Hello John, I have been following you since training days on ESPN. What kind of music do you listen to prepare you for an important mathematical equation?

Fiona Apple is always a solid choice. My musical preferences are pretty wide. Lately, one of my chess buddies introduced me to EDM, and it's not bad. I've been playing one of Solomun's remix albums lately. I like Late Night a lot.

which fellow pro football players struck you as having underrated intellectual potential, and given the concussion risks, might have been better off if they were given incentives to pursue something else?

I think the better off conversation is a tough one to have. For example, I fully believe that I'm better off for having played in the NFL.

Hey John, big fan! Congrats (or sorry?) on your retirement. I know you have the answer to this one.. does P=NP?? On another note, since it says on your page you are working on machine learning, what is your opinion on neural networks as taking the lead for many applications, given that it has the "more of an art-form" reputation? Thanks!

I think one of the toughest things in machine learning right now from a theoretical perspective is trying to justify rigorously why neural nets work so well, and why some parameters work better than others.

Whose the smarter ex-Raven: Matt Birk or yourself?

I don't know who's smarter, but in my opinion MIT is awesome. Definitely the best school in Cambridge ;)

Hello John, I enjoyed meeting you at the Mathnasium convention a few year back. Will you ever return to the DMV area?

My mother lives in the DMV. So if I didn't, I think I'd be in some real trouble!

What made you interested in mathematics?

I think one of my favorite things early on was the clarity of it. Either something is true or not (more or less).

Hi John, huge Ravens fan here..

Just wondering what you'll miss the most about the NFL/Ravens? And what you'll miss the least?

Bonus question: What was your routine when you were mid-season AND doing your PhD? It seems like it would be crazy!

So I think I more or less answered this above. In season it wasn't too bad. I was able to get my work done on my off day.

Hi John,

Do you use MCMC in your work? If so do you know of a good textbook?

I don't, but my favorite MC book is the one by Yuval. There's a good amount of MCMC in there, and other really cool stuff.

Hi John, have you been to the Muddy Charles yet? That place is great. Gonna try to get your Pirate's License?

Yes, I have frequented the Muddy. It's been a while though.

Are you interested in an academic career after your PhD or do you think you will try industry, government, or something else?

I think academics is the way to go, for me at least. But who knows.

The news that you were also taking full-time courses even during the regular season has not gone down well with some of us Ravens fans, including the ones at r/Ravens, given the inconsistency of the interior line over the season.

How did the organization react to it ? Was there ever a discussion about it after you retired ?

I think the biggest thing is what I do on my off day is largely my business. If somehow doing math on my off day is much worse than players who volunteer on their off day, or play video games, or just watch tv, then I guess it's a thing.