Mathematicians on Smogon

[Diophantine]

Hey! I seem to remember a thread by Blazade that unfortunately did not last very long and did not have much participation. Having spoken to many Smogon users, I find that there seems to be quite a few maths students, graduates, or people simply interested in maths, so I thought why not remake this thread :) I want to hear all about your experiences with maths, whether you're a PhD student or a middle/high schooler with an interest in it. Talk about whatever you want.

Here are some questions to help break the ice:
Why are you interested in maths? Do you have any stories that sparked your inspiration? I was always interested in maths without really knowing it. Naturally, I liked things like chess, card games, football statistics and tactics, and the London Underground map, but I found my "maths classes" quite boring unless competition was involved. I thought maths was just something I was lucky to be good at so that I'd be able to get a decent job in the future. There isn't much inspiration for maths around you when you're a child/teenager in an inner city comprehensive school. I always thought I'd be an accountant because "lololol good with numbers". However, when I was 14, my new maths teacher, who was appropriately named Mr. Lemma, inspired me like I never had been before. He introduced me to more interesting things like tricky problems, getting me to come up with proofs of things I had taken for granted like Pythagoras' theorem, and showed me many applications of high level maths in the real world. From then, I dove deep down into the rabbit hole and I am about to start my postgraduate degree this September!

What field of maths interests you? When I was younger, I was interested in Number Theory, Combinatorics and Geometry. The former two were topics that you'd only ever see in competition maths, and so felt as though they had more of a prestige than things like stats and calculus, which everyone did in the classroom. These days, I'm very interested in Stats! I only realised I liked stats because I dislike how people use stats lol. I am really interested in Financial Maths too, after reading about how Jim Simons and co. began the quant revolution, and after working in the industry myself.

Have you competed in maths competitions? I competed in the UK Maths Challenge each year at school, and was invited to the British Mathematical Olympiad several times, which is the following round. I had a lot of fun doing that. I got to the finals a couple of times but was never good enough to get onto the national team. The standards are insane. I always felt that it favoured rich students who went to schools that had the best teachers in the world, whereas students at schools like mine had to grind it out for themselves. I didn't do any at university because I was more focused on internship stuff (and getting wasted)

Can you recommend any books or videos? Solving Mathematical Problems by Terrance Tao is great if you want to try your hand at competition stuff. Physics of Finance by James Owen Weatherall had me interested in Financial Maths. I'm currently reading Chaos by James Gleick. Numberphile have many really good videos on their Youtube channel. Michael Penn, Flammable Maths, and blackpenredpen have loads of good videos too.

I hope to foster a kind of community here, so if you need help with any maths problems or want advice in general, feel free to ask someone here! If there's enough interest maybe we can set up a discord server to help each other out.

Discord server: https://discord.gg/Yv5FvYH

Weekly challenge 1

 

[billymills]

I've been interested in number theory and complex analysis for a while. Something about going around in circles and actually getting somewhere is pretty cool.

Can definitely relate to liking random sports statistics and subway maps. When I was younger I'd used to read the sports page in the newspaper every day just to look for weird statistical anomalies, and I had basically the whole city transport map memorized.

Used to do some minor math competitions, but that fizzled out when I was competing with people who actually trained for the competition and I couldn't be bothered.

 

[Voltage]

I'm an engineering and applied maths major, and I'm always a big fan of trying to relate concepts from life and media to math, science and engineering and whatnot. Scion is hugely important and I really want to make silly videos about mons and relate them to math, i.e. using the Heat Equation PDE to explain why Heat Wave isn't a super accurate move (lol). Sophomore year of undergrad, I basically modelled a portion of Twitch Plays Pokemon Red as a stochastic process to determine the time it would take the player to cross "the ledge" section.

Otherwise, a lot of my interests are in the applied region, so a lot of linear algebra and Differential Equations (ODEs, PDEs, etc.). Haven't done any math competitions, though they don't interest me as much as real world examples.

 

[CaffeineBoost]

Your name is Diophantine so you're clearly looking for integer answers to all these questions...

 

[willempju]

I am currently finishing my PhD thesis in Mathematics. My main field of interest is differential equation, specifically those posed on discrete lattices, such as the set of integers. I also have a major interest in functional analysis (my Master's thesis and my first published paper were in the field of partially ordered vector spaces). I am definitely more on the abstract side of things, although I am not too fond of fields like algebra or number theory. However, the interplay between abstract results and applications can also be very interesting.

 

[Orange DBJ]

Hey, I'm a high school student from France. I got interested into Mathematics 4 years ago while i was watching some videos of MicMaths, a french youtuber. There was especially this particular video about multiplication that i found really beautiful. So i thought : "I'm really good at maths at school and it looks really cool when you go deep into it". I love helping people bout Maths and Physics and i keep watching videos from 3blue1brown and blackpenredpen. I really like geometry, algebra and statistics. Now, i'm on to study maths and engineering.

 

[Hiro']

If things go well, I should be starting my first year of a Master's degree in fundamental mathematics real soon.

I was always interested in maths without really knowing it. [...]
I thought maths was just something I was lucky to be good at so that I'd be able to get a decent job in the future. There isn't much inspiration for maths around you when you're a child/teenager in an inner city comprehensive school. I always thought I'd be an accountant because "lololol good with numbers".

That's basically how I felt too. In France, maths are pretty boring until you reach further studies unfortunately. It also appears that the "level" we're asked for is declining with time, so I really felt like "okay it seems i'm quite good at it but it's not that great so i'll just do what's needed".
[Warning: the following is kinda hard to translate for me as we don't have the same educational system, pardon me if that's not so clear]
Then, I started what's called "preparatory classes". Basically, it's a two (sometimes three) year course / training to take a competitive exam. In my case, it was a math/physics course so we get to join engineering schools, but it can be humanities or business.
It didn't go that well, I had a very hard time with physics, my first year teacher didn't like me very much so it ended with me just dropping it. Of course, the competitive exam didn't go that well.
Finally, I ended up going to Paris XI University, apparently one of the best in the world in math, where I earned a bachelor's degree recently.

Maybe it's too abstract for me, but I'm really not much into Algebra for some reason. I'm more of an Analysis enthusiast. I felt like Complex Analysis is far less restrictive compared to Real Analysis. Let's be honest, it's also way more gracious.
I didn't have the chance to study Number Theory yet but that's a field that has be attracting me for a while. I really like Combinatorics, Arithmetic too but that can become very difficult with not so many things (hi olympiads).
Even if I'm not that big of an Algebra fan, I must say I really like the spectral theorem...

Graph theory is also a very, very attractive field. I realized how versatile it could be when we learned how to calculate Wallis' integrals using cycle graphs. I don't actually have a link for this because I couldn't find any English paper but if I have some time, I could explain it to anyone's interested.
I'm sure there is so much more you can do with graph theory, that's just so exciting!

I can't say I really have competed in some math competitions, I find 'em very difficult and that needs a lot of training, that would not satisfy me and that's not how I want to do math either. Sometimes I challenge myself on some problems but when it needs tricky solutions, it becomes quite unpleasant. I don't believe I have any book or video to recommend for now, as I read n watch a very little amount of it.

Don't have much else to say 'bout me but I sorta knew there were some math enthusiasts here when I saw some dude talking about Dedekind.
Cheers!

 

[teal6]

Great thread, and great idea for a little community. I bug the hell out of a few guys on discord nonstop, as over the last few months, I've taken a real deep dive into learning maths on my own, having no real formal training (I stopped at Calc I in college). The area that interest me most, though I'm a bit haphazard in my interests, jumping from topic to topic (and I can honestly say I study probably daily at this point) would be Abstract Algebra, just when I found a series of lectures and realized how I could really back away from the rote concept of numbers I had been introduced to my whole life, the entire concepts of mathematics truly exploded to me.

Realizing, though, that I kinda had to build up from there, I've been working my way up a bit more over the last 2-3 months, rn going through a Calc II course while still poking around and trying to get the gist on some Real Analysis / Number Theory proofs that sound interesting to me. Here's my favorite YTer atm:

https://www.youtube.com/channel/UC6jM0RFkr4eSkzT5Gx0HOAw

 

[Diophantine]

When I was younger I'd used to read the sports page in the newspaper every day just to look for weird statistical anomalies.

I started taking an interest in stats because I felt that raw stats like goals and assists didn't do justice to some of my favourite football (soccer) players, and felt that there were more refined methods of approaching it.

I really want to make silly videos about mons and relate them to math, i.e. using the Heat Equation PDE to explain why Heat Wave isn't a super accurate move (lol).

Do it! Sounds fun :)

I basically modelled a portion of Twitch Plays Pokemon Red as a stochastic process to determine the time it would take the player to cross "the ledge" section.

This is really cool. Care to elaborate?

I am currently finishing my PhD thesis in Mathematics. My main field of interest is differential equation, specifically those posed on discrete lattices, such as the set of integers. I also have a major interest in functional analysis (my Master's thesis and my first published paper were in the field of partially ordered vector spaces). I am definitely more on the abstract side of things, although I am not too fond of fields like algebra or number theory. However, the interplay between abstract results and applications can also be very interesting.

Congrats on your journey :) I've been reading about Jim Simons and RenTec, and I found it really cool how a bunch of pure mathematicians conquered Wall St. Care to share a bit more about what your masters thesis was like?

If things go well, I should be starting my first year of a Master's degree in fundamental mathematics real soon.

Sounds amazing. Good luck!

I didn't have the chance to study Number Theory yet but that's a field that has be attracting me for a while. I really like Combinatorics, Arithmetic too but that can become very difficult with not so many things (hi olympiads).

They're worth a look into for sure. I studied them, so you can PM me for help/advice if you need it.

Here's my favorite YTer atm:

https://www.youtube.com/channel/UC6jM0RFkr4eSkzT5Gx0HOAw

I fking love this guy lmao

 

[Voltage]

This is really cool. Care to elaborate?

Essentially I was working on a MATLAB course that had a "bug-hopping" problem which involved assigning specific positions on a 1D bar for where the bug could go at any given time interval. This is just a random walk on a 1-D space, and I'm an applied guy, so this wasn't too hard to wrap my head around. Essentially I just ended up making a probability matrix for the given bar and went about my business. As one might expect, the transition from 1-D to 2-D was really easy as all I had to do was just assign more numeric positions. It was still a very sparse matrix, but it wasn't too hard to do by hand (I'm a terrible programmer).

I figured I had something for my University's Math club (of which I was the Vice President that year, so I had to represent well) that was basically a "share your cool math research or project" event, so I just did that. Essentially I found the number movements from any general starting point on a 4 x 13 terrain where you had to hit like 8 consecutive "right" commands in a row to make it to the exit. Then from there I just vaguely estimated the input time between accepted commands to estimate the amount of time it might take to get from the start point to the end point in the actual stream. Ultimately my answers were pretty accurate to the stream, so I'm very pleased with it.

Unfortunately I lost the code, but honestly it wouldn't be too hard to recreate I think. Maybe when I've got a little more time on my hands.

 

[Legitimate Username]

Can you recommend any books or videos?

How To Not Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg was a pretty interesting read that I had to pick up for a college course (Humans are Underrated by Geoff Colvin is another that's a bit less relevant but still a really cool analysis of the humans vs. machines issues). I read a pretty good amount of math-intensive fiction in my highschool years but can't remember any titles since it's been so long.

Numberphile has amazing content as always but my personal favorite is Vihart, she has a really charming and funny way of sharing a lot of interesting ideas in ways that are extremely entertaining. Everyone knows Vsauce too of course but whenever he puts out a math-intensive video it's always a treat.

 

[willempju]

Congrats on your journey :) I've been reading about Jim Simons and RenTec, and I found it really cool how a bunch of pure mathematicians conquered Wall St. Care to share a bit more about what your masters thesis was like?

I will try to not get into too much detail;) If you have a partially ordered vector space (POV) (i.e. a vector space with a partial order that respects the linear structure) then a vector x is positive if x=>0. In many POVs you can write any vector x as the difference of two positive vectors (for example for R^n with the componentwise partial order we have that (x1,....,xn) is positive if and only if all of x1,....,xn are positive scalars). Typically, there are many ways to write a vector as the difference of two positive vectors. In certain POVs you can define the positive part x+ and negative part x- of a vector x as follows: x= x+ - x-, x+ and x- are positive and there are no 0<=y<x+ and 0<=z<x- with x=y-z (in R^n you have x+=(max(x1,0),....,max(xn,0))). Next, you can also turn the space of linear operators between two POVs into a POV by saying that S<=T if and only if T-S is a positive operator, that is, if T-S maps positive vectors into positive vectors. My master's thesis concerned itself with the question if, and how, you can compute the positive part and negative part of such a linear operator between two POVs. For very 'nice' POVs this is given by the socalled Riesz-Kantorovich formula. My main result extended this formula to a more general class of POVs (but still far from all of them).

 

[teal6]

If everyone had to pick a favorite theorem, what would it be?

 

[Diophantine]

If everyone had to pick a favorite theorem, what would it be?

I don't really think I have a favourite one, there are many hat could qualify, but I feel quite nostalgic about Fermat's Little Theorem - not to be confused with the Last theorem.

 

[Style_Dota]

How To Not Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg was a pretty interesting read that I had to pick up for a college course (Humans are Underrated by Geoff Colvin is another that's a bit less relevant but still a really cool analysis of the humans vs. machines issues). I read a pretty good amount of math-intensive fiction in my highschool years but can't remember any titles since it's been so long.

Got this book as a gift from a student one year. Can confirm it’s pretty good.

Also read flat land if you want mathematical fiction. You’ll appreciate it if you’re a mathematician. Then watch the movie, because it’s hilariously awful.

Also, writing mathematical statements on this without LaTeX seems pretty rough lol.

 

[Sir Isaac Mewton]

hah imagine liking stats, we call it machine learning in 2020 sir

 

[Voltage]

hah imagine liking stats, we call it machine learning in 2020 sir

Explains why you could be banned.

As for Theorems, I really like the Chinese Remainder Theorem, if only because of how it just has a bad habit of showing up in some strange and unexpected places.

 

[IQMathlete]

ah i've been waiting for this thread!
i've loved math for as long as i could walk and talk, and in elementary school started competing in math contests, which remain a huge part of my life to this day. i would estimate 90% of my current circle of friends were people i met in a math contest or summer camp setting, and it's something i definitely want to pursue in college. my favorite math subjects are algebra and number theory, though i despise combinatorics. i qualified for the american math olympiad program this year which was super fun despite being virtual!
i was always pretty advanced in terms of school math; my school was super liberal in letting me pick higher classes, so i cleared out multivariable/linear algebra by my first year of high school. currently i'm doing statistics just to clean the bucket, and i actually don't see why it deserves all the flack it gets? i found it pretty fun and interesting.
i like Euclidean Geometry in Math Olympiads for books
i think my favorite theorem is probably the Shoelace Theorem for cartesian coordinates; i have a bit of a reputation for using coordinates to solve 90% of the geometry problems (including olympiad problems) that come my way and hey, if it ain't broke don't fix it! much love also for Stewart's Theorem for having the best mnemonic of any math formula :P

 

[Diophantine]

Was learning about Mandelbrot's work recently. Fractal dimensions blew my mind lol. Turns out the border of the British coastline has a dimension of 1.25. Chaos theory in general is some pretty dank shit. It tells us why some systems are simply unpredictable, despite being deterministic.

Regarding going forwards, I was thinking this could be a community to help each other retain or develop interest in maths. Perhaps we could have a discord server, some fun weekly problems or simply just share interesting things with each other. Love react or PM me if you're interested.

 

[Diophantine]

https://discord.gg/Yv5FvYH
We now have a discord server! Will be edited into the OP. Have fun!

 

[Diophantine]

Hello everyone!
I've decided to host a weekly challenge! I'll be finding a set of problems for you all to answer throughout the week.
This week's theme is number theory :)
PM me your solutions (on the forums, not Discord, for convenience) before next Monday and have fun! :D
I will be posting solutions this time next week.

Problems

 

[Diophantine]

If you are unsatisfied with 10) not necessarily being a number theory question, then prove this: F(n) divides F(m) if, and only if, n divides m.

 

[Diophantine]

Solutions 1-5:

Hide

Solution 6

Hide

Solution 7

Hide

(note*, not not)

Solutions 8-11

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For some reason, my LATEX wouldn't let me include the second half of solution (11), so have it in text form (thanks vapicuno for writing it out)

Hide

Now we prove the only if statement. Since F(n)>F(m) iff m>n, if F(n) > F(m) then n does not divide m. Only need to consider F(n) <= F(m). Trivially true for n=m since F is bijective. Lemma 2: gcd(F(n),F(n-1)) = 1. Proof (sketch) by induction using the Euclidean algorithm; gcd(F(n),F(n-1)) = gcd(F(n)-F(n-1),F(n-1)) = gcd(F(n-2),F(n-1)) ... = gcd(F(2),F(1)) = 1. We prove the only if statement by induction. It is trivially true for m=n. Suppose only if statement is true for all m<n+k, for some k>=0. From Lemma 1, F(n+k) = F(k)F(n-1) mod F(n). Iff F(n)|F(n+k), F(n) divides F(k)F(n-1). By Lemma 2, F(n) divides F(k)F(n-1) iff F(n) divides F(k). Since only if statement is true for m<n+k and k<n+k, F(n) divides F(k) iff n divides k iff n divides k+n. Thus, the only if statement is also true for all m<=n+k. By induction, the only if statement is true for all m.

I will post new questions tomorrow.

 

[Diophantine]

I did a thing :)

 

[Hiro']

If everyone had to pick a favorite theorem, what would it be?

I've studied algebraic topology for a semester and I must say it might be my favorite class ever.
van Kampen's theorem is both useful and beautiful, and it comes with a similar result in homology with Mayer-Vietoris' sequence which I used quite a lot for an essay at the end of the year.
I don't know if it's my favorite one but I guess I would pick the classification theorem of closed surfaces.