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Christopher: You know, for kids may maybe, maybe try to show how math is present in like, you know, baking or, or, you know, in sports or other things, just, just, and, and, you know, try to sort of integrate that, that math into their life. Okay. Another thing for kids that, that are really interested in math, you know, to get them to love it even more is, is to give them somewhat like challenging problems, like maybe like contest problems or stuff like that. And for me, that’s, that’s kind of where Dragos came in. Like he, he gave kids in, in this math program, like challenging problems, and then he showed how you can, you know, use reason to solve these challenging, like contest level problems in that it’s kind of like a puzzle, a puzzle or a detective process. And, and for me, that’s kind of what dragged me in a little bit into this, into this whole thing. Yeah. So, so, so kind of basically just to present math as something that’s kind of a creative or, or kind of a detective game rather than something that’s just like methodical or mechanical and dry. Yeah. Right. Yeah.

Yeah. That makes sense. And it seems that you went far beyond the bounds of the curriculum in your early years. Is that something that you recommend for kids to just, just go for it, go for the advanced, challenging math, not just to do the homework

Yeah. For kids that are interested in that are capable. Certainly I, I would suggest going beyond the, beyond the curriculum, but, but, but first of course you should kind of master the, the curriculum level first it’s, it’s only when, when, when you’re sort of comfortable with the, the curriculum level and then, and then you want something extra, then certainly go for it. Right. Cause the, the, the Ontario curriculum is, is certainly limited. Like, I, I guess like if, if, if you kind of look at the, the curriculum that, that, that was taught, let’s say in Eastern Europe or something, or, or like modern day Europe, it was, it was much more expensive than, than, than like the, the current Ontario curriculum. So, so certainly there’s, there’s much more to learn and outside of the UN the, the regular curriculum and, and kids that age are, are, are able to learn much more than, than the many kids I should say, are able to learn much more than the regular Ontario curriculum. Yeah. Certainly if, if, if a child is like capable and willing, then certainly I think it’s a good idea to, to try to expand the balance of the curriculum. Yeah.

Do you on that topic, do you have any advice for parents who you’ve got kids in, let’s say middle school and they’re struggling with the Ontario curriculum or right. Any, any standard of school and the, the kids are kind of struggling and there’s a sentiment of, well, like I’m not good at math, that kind of thing. Do you have any advice for those parents?

Yeah. Yeah. So, first of all, I would suggest to sort of sit down with, with, with the student and try to understand, you know, what’s the core cause of, of the students struggling. Like it could be something in, in their lifestyle or, or routine that has to be changed, you know, maybe they’re, they’re hanging out with the wrong group of friends that are negatively impacting their views towards math, negatively impacting their, you know, school performance. Right. So, so just sit down with them and try to identify some, some possible causes to why they’re struggling and then try to eliminate that. Okay. And then maybe also plan sort of a regular study schedule where you can like sit down with your child and, you know, try to go through their homework and, and then try to sort of build up their confidence with the material. You know, for example, you could also watch some math videos on YouTube with your child, you know, on, on subjects that they’re struggling with, but, but just, just try to, you know, do things that build their confidence and, and perhaps reduce their fear of math and, and, you know, focus on those points on, on, on, on those particular things that they’re struggling with.

And then, and then I would also suggest in conjunction with those two to, to perhaps get a tutor as well. I think a tutor could, could certainly help with that. Yeah.

Yeah. I think what you’re saying is that just to make it fun right. To, to just, yeah, for sure. Let, let go of the pressure and negativity saying, well, I’m bad at it. And so on, just, just to have fun with it, start with, start where you are and, and just go for it. So

Yeah, certainly yes.

I think that’s, that’s what you’re saying. So moving on, I mean, are there any like particular study habits that like somebody could, let’s say copy or swipe from you to get more success in their school,

Right. Yeah. So in terms of study habits, I think it depends on the individual, first of all. So, so people have, you know, different study styles and there there’s not one study sort of habit or, or, you know, study method that works for everyone. But I think a couple of methods that, that were useful to me were writing things down. So, so oftentimes I would, after my lectures, I would kind of go through my notes and then write down sort of a brief summary in, in, in, in my own words. Okay. And, and, and, and the, the summary can be as short as just saying, like, as just writing down three main points, for example, like you just go through your notes and then you try to identify, okay, what are three key things from this lecture, for example, and, and then you write those, write those down, and then you can sort of elaborate on those in, in a little bit more detail in your summary notes.

That’s something that I found helped me a lot, just to write things out in your own words and, and, and, you know, to try to keep a log of those kind of condensed summary notes. That’s one thing, another thing is, is well repetition as well. So like regularly reviewing things. Okay. Like, I, I, I sort of think of an analogy in terms of a, a paint roller. Like if, if you have kind of a bad paint roller, and then you’re trying to paint a wall, you know, if, if you kind of go through it once there’s there, it doesn’t like cover everything uniform, if there are a bunch of gaps, but then if you go through it down again, it covers it a little bit better, but maybe there are still some gaps. And as you go up and down, a bunch of times it gets you get a uniform layer.

Okay. So that’s, that’s, that’s, that’s kind of, for me, how, how it felt sometimes to review my notes sometimes when I’m studying for an exam or something, I’ll review my notes. And then I feel like, oh, there’s still a bunch of gaps that are missing. Okay. So I go through it again, there are less gaps, but still some gaps that are missing and I just keep going through it until there are no gaps. So, so I think that’s repetition. That’s, that’s, that’s something that, that, that is useful. And, yeah. And in doing that repetition together, like together with, you know, your, your short summary notes,

I love that.

Yeah. And then a third thing is to, to also get a study part, because as one of my professors used to say the best way to learn a, a subject is to teach it to somebody else. So if you can find a study partner, and then if you can sort of teach things to each other, like teach the, the content of the class to each other, that can also be tremendously helpful to, to learn the material and, and to study. Yeah. Yeah. So those, those are some studies study habits that, that, that I think are useful.

Yeah. And that ties in nicely with, you know, getting away from the negativity and to the positivity, like finding friends who yeah. Are super friends in a way. I mean, if it’s not too cheesy to say super friends, but you know, somebody who you can use as a sounding board to explain concepts to someone to study with.


That’s great. So I have some fun questions. If you could do anything without failure, like if you were, I know you’re smart, but imagine 10 times smart, or if you could not fail at anything, like what would you do?

Well, I mean, I, I, I would probably just continue with my current mathematics, I guess, like, if, you know, if, if, if, if you can be a mathematician who never fails, then I guess you’d, you’d pretty much be the best math mission who whoever existed. Right. So, I mean, to some extent, it’s not a really realistic question cause it’s like a super power. Right. So, yeah. But, but if, if, if I could never fail, I guess then, then I would, you know, I would do mathematics without failure.

That’s right. So you would unify theories in, in physics

Or I guess so. Yeah. I mean, I would probably focus on mathematics cuz that’s, that’s sort of been my, my main interest. Yeah. But I suppose physics, like coming up with this grand unified theory of physics might, might be more useful to, to society as a whole, I suppose. Yeah. But I would probably still stick with math.



What are your interests like specifically in, in math?

Yeah, so, so my interest in math center around algebra and geometry and their interaction. So I work with these objects called groups, which are algebraic objects in the sense that you have some algebraic operation where you can sort of take two things in the group and you can in a sense, multiply them together to get something else. And so that’s, that’s, that’s called an algebraic object. It’s a group and I’m interested in studying this through a geometric lens. So it turns out that groups kind of in contrast with many other objects, they have a, a really, really, really neat and, and kind of strong geometric description that isn’t really present with other objects. And so I study these, these objects groups through this geometric lens. Okay. And yeah, so, so my, my work sort of, kind of, it’s, it’s, it’s sort of an in interplay between the algebraic aspects of groups and, and their geometric and sort of combinatorial aspects.

So it’s kind of going between those two and seeing how each one complement the other and, and, and, and how both of those can, can tell you interesting results about, about groups about these structures that you’re studying. Yeah. So that’s, that’s, that’s kind of my specific interest in, in physics. I’m, I’m interested mainly in like astrophysics. I think that’s, that’s, that’s my favorite branch of physics. Yeah. My sort of first exposure into science was, was into actually astronomy. I remember around like summer of 2010, I was, I, I watched this documentary from the history channel about space and I was like, absolutely captivated by it. I thought this is like the coolest thing ever. And so since then, I would say astronomy has been my favorite branch of physics. Yeah.

That’s great. And what was it about the documentary that, that, you know, captured your, your attention and interest?

I guess it, it was, it was the kind of existence of, of this whole other universe that sets outside of ours. Like what, what I mean by that is that we kind of go about our day to day lives here on earth. And then we, we don’t really think about what’s happening in the stars, you know, but there’s so much that’s happening, you know, even in just, just in our solar system, you know, one, one thing in, in, in, in that documentary was they, they, they went to different, you know, planets in our solar system and then kind of told the story of each planet and, you know, just, just, you know, for kind of a, a regular person here on earth, you know, you don’t really see that, you know, we’re just kind of focused with our lives, you know, just going, you know, day in, day out. But there’s, there’s, there’s like so much rich structure out there in, in, in, in, in the universe waiting to be discovered. And, and to me that’s said something that like really opened my eyes and really got me interested into science. Yeah.

So you had to learn the language of the universe.

Exactly. Yeah. Yeah. And that’s what led me to mathematics actually. Yeah. So, so I was originally in interested in physics and then I realized, well, to do, to be any good at physics, I, I gotta have to learn some math and then eventually kind of the math took over and that’s where I am today.

Very good. Are there any common myths about mathematicians or math in general?

Yeah, certainly. Yeah. So, so one common myth is that mathematicians are kind of an isolated breed of people. You, you know, you have this kind of stereotypical image of a mathematician, just kind of like sitting at their desk kind of isolated from everyone and just like working on their own stuff. And nobody knows what they’re doing. That couldn’t be further from the truth, from my experience, at least mathematics is a very collaborative field. Okay. And there’s a lot of emphasis on communication. So it’s it’s so, yeah, so, so mathematicians work on stuff and they, they often communicate their ideas to others and things like conferences, or they also often, you know, work on things jointly. So, so you might have like 10 people working on the same thing. Okay. And they sort of publish their, their work. And then other people look at it and then ask questions and then, you know, connect with them.

And so math is really this, you know, doing work in mathematics is kind of a, a, a big network where, you know, many people are, are, are connected and they, they share ideas. They, they share methods. They work together. It’s, it’s, it’s, it’s very far from, from being just like each person just kind of grinding away on, on, on, you know, their own stuff. Just, just isolated. There are, there are of course mathematicians like that, that, that are just kind of isolated, but, but it’s quite rare. I think from my experience to, to see that, you know, mathematics is, is really a collaborative field where, you know, communication is, is essential. Yeah. And yeah, yeah. I was gonna say another myth about mathematics is that mathematics is really about numbers. That’s not, that’s, that’s not true in general. So, so most of mathematics is, does not have to do with numbers.

A better way to describe mathematics, I would say is, is the study of abstract structures. Cause a lot of the things that you do in math is you define abstract structures like groups, for example, which I study, you define those. And then you’re interested in sort of discovering some of their properties and how they interact with other structures. So you can kind of think about mathematics as a universe of abstract structures and how each of them sort of interacts with each other and, you know, properties of, of, of these structures. It has very little to do with, of course there are areas of mathematics that do involve numbers, but these are, this is just a small part of mathematics. Yeah.

I love that. Yeah. It’s, it’s so true. You know, it’s not just about being a numbers person or a words person.

Yeah, exactly. Yeah. It’s

It’s how much creativity, how much can you imagine? Like in your mind, you know yes. At what level, like how much abstraction can you handle Before you lose your mind? That’s true. But no, it’s, it’s true that, you know, it’s not ISOL, it’s not working in isolation, it’s collaborating. Absolutely. People are not, well, what’s funny is that it sounds like it’s not competitive at that level because people are exchanging ideas. Is that, is that fair?

There, there is still competition to, to some level, I guess you can also have competition between sort of different groups of people like, so, so that’s, you, you might have kind of one, one sort of group of people that’s, that’s sort of working on a result and then you have another group of people that are, you know, working on something independently and then sometimes kind of compete to see like who, who, who, who can get the best results first. Yeah. And so there definitely still is competition in, in, in mathematics, but I would say sort of collaboration forms a, a larger part than just sort of competition. Yeah. I would say that

That’s right. So the, the, the competition aspect, it’s very positive people. Wouldn’t withhold inform Absolut from each other in order to yes, yes. Get an advantage.

Yeah. Yeah. For the most part. Yeah.

Very good. Have you had any unexpected outcomes from your recent adventures in math?

Yes. Yeah. So, so actually last fall, I did have an unexpected outcome on, on the, on the project that I’m working on for my master’s actually. So there was one sort of object that, that, that I was working on that I was working with. And in, in, in, in one sort of, you know, base case, this, this object turned out to be finite. And I was working on a bit of a more general case and my supervisor and I expected this to be infinite. We, you know, there was no reason to believe initially that, that this object was actually finite and, and, and, and we were, we were expecting it to be infinite. And then we, we were trying to like, think about ways, how to sort of, you know, incorporate the infiniteness of this object, you know, it like, you know, we’re basically assuming that it’s gonna be infinite, but it turned out that quite surprisingly, that, that this object was actually finite.

Okay. So, so, so I guess my successful venture was that I was able to sort of generalize this previous about this finite object. And we thought that it was gonna be that this generalization would be infinite, but it was actually finite. And then that, that really surprised us. And so that simplified a lot of things that this object was actually finite and made everything work out much nicer than, than we imagined. So, so that was something the very surprising and, and quite nice that, that, that, that it was very simple and, and, and it worked out.

Wow. And are you, what’s the biggest challenge that you’re facing right now in your research, Chris?

Yeah. So, so the, the challenges is to sort of generalize this further. Okay. So, so, so, so as, as I just discussed, I, I, I generalized sort of one aspect of this starting case to, to one thing, but now I’m trying to generalize it to an even larger case and that even larger case I’ve been working on it for a couple months and I’m like basically stuck on, on, on a bunch of things. So right now that’s, that’s the biggest challenge that, that I’m facing right now is generalizing it just to this even larger case. But how am I trying to overcome that challenge? I’m trying to kind of throw different ideas at it, basically, you know, just, just try to think of whatever I can and, and, you know, try to see if, if I can make any progress also looking at, you know, different papers that I can find online and seeing, is there anything useful that I can apply to this and make any progress, and also having regular meetings with my supervisor to kind of bounce ideas back and forth and, you know, try, try to get some progress to try to, you know, move things forward.

Yeah. And it is kind of moving forward incrementally, but, but it’s still like a lot of work to do. And, and a lot of things to, to be discovered.

Yes. So back to the collaboration you need, you need a helping hand maybe absolutely need to give you a novel idea.

Absolutely. Yeah. Yeah. My supervisor has been tremendously helpful and I, I, I don’t think I would be able to, you know, solve this completely on my own. Yeah. So definitely collaboration is, is, is quite useful in this case for me

And your supervisor, does he supervise you individually or within a group

Individually? For me, yeah. For me, I’m, I’m, I’m the only student that’s working. I’m the only of his students that’s working on geometric group theory. So he has a bunch of other students, but they work on different things like common torics and something called descriptive set theory and stuff like that. So I’m the only student that’s working on geometric group three.

Yeah. So in a way, supervisor is tutoring you in a way.

Absolutely. Yeah. Yeah. That’s, that’s a great description. Yeah.

And speaking of tutors, you’ve, you’ve been approved to be a tutor on tutor ocean.

So congratulations. I have you, I’m excited. Thank you. Yeah. I’m, I’m excited to join to ocean.

So if there’s some students out there who want to get tutored by, by you, how would they do that? I guess they’ll find you on the website, you know, tutor, Yeah,

Yeah, yeah, exactly. If you just search up my name, Chris Garske can find my, my profile. Yeah. And yeah, if, if, if you’re interested, then, then you can get in touch through tutor ocean, and I would be happy to, to meet you and to work with you.

What subjects do you specialize in teaching Chris?

Yeah. So I’ll, I’ll be teaching mathematics at the, from the middle school level up to undergraduate level. So, so all, all subjects of mathematics, they are algebra pre-algebra calculus, precalculus, you know, anything. And then for physics also, I’m, I’m also tutoring, but, but at the high school level. Okay. Yeah. So, so physics at, at the high school level and potentially also at the, at the undergraduate level, if, if, if, if there’s demand

And why do you enjoy tutoring, Chris?

Yeah. So, so for a couple reasons, first of all, you know, tutoring someone is, is, is, you know, helping them quite a bit. You know, if, if, if someone needs tutoring, then you know, they’re, they’re obviously struggling with the subject and it’s, it’s, it’s always nice to, to help somebody, you know, in a moment that, that they’re struggling. I think every human feels joy in helping another human with something that they’re struggling with. So, you know, when I, when you tutor someone, you you’re helping them in that regard and, and, you know, bring that brings joy. But, but also, you know, it’s, it’s not only helping somebody with, with, with something that they’re struggling with, but, but also, you know, doing something that, that I like, which is mathematics, and I’m always happy to talk about mathematics or physics with anybody. And so if I can help somebody, but also, you know, talk about them with mathematics, talk about, talk with them about mathematics or physics, then that that’s also an extra plus for me. Yeah. So it’s that, you know, those two things of, you know, just, just helping them and then also, you know, helping them through mathematics and, and physics, which are my passions. Yeah.

That’s great. Well, there’s certainly a lot of people looking for math help these days. Yes. I guess I, I wonder why do you think that kids struggle with math as opposed to any other subject?

I think it ultimately boils down to the, to, to kind of our, our evolutionary upbringing because human beings are not really sort of hardwired to do math, you know, and, and same with physics as well. Same with other sciences, you know, evolutionary speaking, evolutionarily speaking, you know, mathematics is mathematics and physics are, are, are sort of, you know, we’re, we’re not programmed to do mathematics and physics. And so it feels oftentimes so unnatural and so alien to us. And I, I think that’s the fundamental reason why a lot of kids and, and a lot of people in general struggle so much with math and science. Yeah. But, but, but of, of course these, these struggles can be overcome by, by, you know, hard work I think. And, and perseverance. Yeah.

And to quote Mary Poppins to find the element of fun.

Yes, of course. Yeah.

So those are all the, the questions that I have. But is there anything that you would like to say before before we, you know, say goodbye here?

No, I don’t think I have anything else to, to add to our discussion.

Great. So if there are any parents listening, you can certainly find help with, for your kids through a excellent tutor of quality like Chris Kapinsky. So anyway, thank you very much for being on the show. Yeah.

Thank you. Cameron. Never stop learning. It was, it was a pleasure. Yeah, for sure.

Okay. Take care now.

Take care. Bye


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