Edit: check out the link in the description to the original video I watched. Original text: Sorry, it took a while to upload, things got really busy with work. Hopefully, it can help some people out! ^^; On the plus side, it's over a month since I filmed this and I'm SUPER comfortable and able to do mental arithmetic (at least with whole numbers). And when I can't, I can quickly work through a problem by writing it out. :D
As a very math-y person who got recommended this video, I'll say this: You're exactly right that this is what mathematicians mean when they say that an equation is beautiful. It's all about the surprising simplicity of the logical patterns behind things. I wonder what you'd make of Paul Lockhart's famous essay "A Mathematician's Lament". It's an excellent (and very approachable!) critique of conventional math education from a mathematician's perspective.
Yay! I'm glad I interpreted that phrasing correctly! That essay sounds interesting (as a teacher, I also 'enjoy' lamenting the education system), I'll put it on my TBR list 😊
I was coming here to say almost the exact same thing - and also, it's always a bittersweet feeling seeing something like this, someone discovering beauty in math and having things *finally* click ... but after a long painful while of having school failing to be good it feels that in most cases, it tends to be a failure to provide the necessary resources for the person, rather than the person's "inherent incompetence" in a field, or whatever crap - no, nearly anyone can do nearly anything if you've got the resources and motivation for it, but getting the resources is tricky, and so people lose motivation...
Another math major here who watches both math and furry content separately and was randomly recommended this video. I had not really seen this way of memorizing the times table before! I saw you asking elsewhere in the comments about what people learn during a math degree. I am currently studying undergraduate pure math in the US and hope to eventually get a PhD in pure math and pursue a career in mathematics research and education. I think that math is one of the most interesting subjects out there, and the sheer breadth and depth to which mathematics has been explored over the millenia is just amazing to me. Here are some highlights of the higher math curriculum: - To vastly oversimplify, calculus is a way of turning physics and geometry problems into algebra problems. For example, in your first calculus class, you will learn a very general method for finding the area under basically any curve. For example, you will be able to prove the formula for the area of a circle. In later calculus classes, you'll learn how to think about motion in space (and even higher-dimensional space) algebraically, and how to compute the surface area of weird 3d objects like donuts. - Abstract algebra is a generalization of the concepts of algebra and arithmetic to all sorts of objects that behave differently from numbers. Modular arithmetic, which is deeply related to what you're doing here, fits under abstract algebra as it is the algebra of a number line that is wrapped up on itself to form a circle. You can also do algebra with things like motions and symmetries. - Set theory is a very abstract subject that builds on the most fundamental principles of logic to precisely and formally define everything we do in mathematics from the ground up. - Topology is like geometry, but squishy. Instead of measuring lengths and angles, you study more elusive properties of shapes like how many holes they have, how many dimensions they have, or whether or not one can be squished and bent to look like the other (Turns out a straw has one hole! We figured this out back in the late 1800s). I hope you're not intimidated by the vastness of mathematics! It's exciting, isn't it? :3
Wow! Thanks for such an in-depth comment! I've heard of some of those topics, but didn't really know what they were! ^w^ I'm not intimidated, per se, by the scale of everything to learn. Maybe cos I don't have to learn it for school/ uni, haha. I'll just go at my own pace, and get as far as I get ^w^ Best of luck with your own Maths journey as well! It sounds exciting and I hope it all goes well for you! :D
I'm just wrapping up my degree (got an exam in 8 hours and then one in 32 hours then I'm done with exams forever!) it's a bsc in maths and stats in the UK (so I do at least one stats module a year) my favourite modules I've done are graph theory you have a collection of vertices and edges that can connect any two vertices (vertices do not have to be connected, but an edge must start and end at a vertex) it's really useful for modelling things in the real world, like roads for example combinatorics counting how many ways there are to arrange something, it can go pretty in depth and can be used to model real things like if you have people who can do certain jobs is it possible to get every job done with no person (or team) doing more than one job game theory hello internet, game theory creates a "game" where each player has a set of strategies and each outcome gives a "utility" (how good the outcome is), and you try to find the strategy that guarantees the highest utility (prisoners dilemma is the most commonly known example of a game theory problem) other notable ones are quantum theory (my exam for this starts in 8 hours lol), complex analysis was really cool but I sucked at it, and I enjoyed set theory a lot which was mentioned in the parent comment oh I have also done knots and surfaces which I believe is related to topology, some rather interesting stuff although I didn't study it as much as I'd have liked due to stressing about the other modules lol
@@rambleswolf thank you! I think it went okay, I spent 20 minutes trying to integrate the wrong function but I finished with 5 minutes to spare so at least I didn't lose marks by running out of time. final one is tomorrow and also my birthday!
i think you're just looking at the final digit and if I'm right you can do this kind of cycle in any base and it's called the modulo, it basically looks at the remainder after dividing by some number if we take multiples of 3 modulo 5 for example you get 3, 1, 4, 2, 0 which are the remainders from 3 6 9 12 15 when divided by 5, it repeats itself in a cycle like with the circle in the video we count in base 10 typically and you can use those cycles and some clever little tricks to work out stuff like what the final digit of 3 to the power of 1851 is by taking modulo 10 (I'm not gonna do it cuz it's awkward but i have done it in the past)
@@rambleswolf specifically to reduce it by a modulo, but it's quite a lot of busy work and isn't really worth learning unless you have a number theory exam coming up lol
Yep! This is why modular arithmetic is called clock arithmetic. It loops! Math is best learned with your favorite proofs❤ Good luck with your maths! I was randomly recommended this... I have a math degree... and watch furry content....
Oh, that's cool! Never heard of clock/ modular arithmetic before! :D Did you study pure or applied mathematics? I'm kinda interested in what people learn during a maths degree, and what kind of work people get into afterwards. If I get comfortable enough, I might try and get an A-Level in Maths (for fun), since all my A-Levels were in Humanities. (In the UK, A-Levels are 3 subjects you take between the age of 16-18 at a sixth form college after finishing high school (age 11-16), and getting your GCSEs. A-Level grades are what you use when applying to university.)
@@rambleswolf I hope you take on calculus down the line. The way everything comes together is just so beautiful. The first time I learned it my mind was changed forever.
@@Luingus Hopefully one day! I want to be able read stuff with the big ʃ in it! XD (I think they're called integrals? No clue what they actually are though, LOL) Still, I need to polish up my Pre-Algebraic Arithmetic first - just gotten up to dealing with fractions, haha. Soon to go on to Decimals and Percentages. Since filming this, I've become pretty confident with multiplication. But, I'm finding dividing by two or more digit divisors quite tricky...^^; It's sort of coming back to me that fractions were actually something I really struggled with in school. And I kinda get how to deal with them now, which is cool! Just need to practise them some more! :D
Check out the link in the description, as he's an actual teacher who explains it more in depth. But basically, each of the number wheels are the same; the shapes are just to help you visualise the pattern of the multiplication. :3
Of course there are patterns lol, by many measures, maths is the *study of patterns* But yes, it's rather stupid that we're largely forced to memorize these things without ever expecting there might be a pattern. The kids who realize anyway get a massive boost straight off the bat and the others already start to get left behind.
this is how people did math before calculus was invented. the ancient greeks would just draw a bunch of triangles and circles on the ground and then land 20 headshots. math is magic, it's the reason we have the trope of wizards
there's nothing shameful in not knowing. you can always learn. and learning and sharing your experience is anything but shameful. if it helped you, you are helping someone just by sharing! ps when u hold the paper up close to read it it looks like ur tryna figure out what's going on through sniffing it and it looks funny
Aww, thank you! ^w^ That's sorta why I started this channel - to measure and share my learning journey with different topics! Also, LOL, I hadn't noticed that, but you're right! XD
oh oh oh mr interupting bear here calculus is advance spiral art with oh whatcha call it again? spiral graph, eh? had to learn a few tricks also on certain numbers 7x8
Edit: check out the link in the description to the original video I watched.
Original text:
Sorry, it took a while to upload, things got really busy with work. Hopefully, it can help some people out! ^^;
On the plus side, it's over a month since I filmed this and I'm SUPER comfortable and able to do mental arithmetic (at least with whole numbers). And when I can't, I can quickly work through a problem by writing it out. :D
when i saw 'math' 'magic' and a wolf furry holding up a pentagram you better believe i clicked this video SO FAST
The unholy trinity! xD
Honestly, same
wish i had a big wolf to teach me math tricks when i was in school
Me too! x3
As a very math-y person who got recommended this video, I'll say this: You're exactly right that this is what mathematicians mean when they say that an equation is beautiful. It's all about the surprising simplicity of the logical patterns behind things. I wonder what you'd make of Paul Lockhart's famous essay "A Mathematician's Lament". It's an excellent (and very approachable!) critique of conventional math education from a mathematician's perspective.
Yay! I'm glad I interpreted that phrasing correctly!
That essay sounds interesting (as a teacher, I also 'enjoy' lamenting the education system), I'll put it on my TBR list 😊
I was coming here to say almost the exact same thing - and also, it's always a bittersweet feeling seeing something like this, someone discovering beauty in math and having things *finally* click ... but after a long painful while of having school failing to be good
it feels that in most cases, it tends to be a failure to provide the necessary resources for the person, rather than the person's "inherent incompetence" in a field, or whatever crap - no, nearly anyone can do nearly anything if you've got the resources and motivation for it, but getting the resources is tricky, and so people lose motivation...
Another math major here who watches both math and furry content separately and was randomly recommended this video. I had not really seen this way of memorizing the times table before!
I saw you asking elsewhere in the comments about what people learn during a math degree. I am currently studying undergraduate pure math in the US and hope to eventually get a PhD in pure math and pursue a career in mathematics research and education. I think that math is one of the most interesting subjects out there, and the sheer breadth and depth to which mathematics has been explored over the millenia is just amazing to me. Here are some highlights of the higher math curriculum:
- To vastly oversimplify, calculus is a way of turning physics and geometry problems into algebra problems. For example, in your first calculus class, you will learn a very general method for finding the area under basically any curve. For example, you will be able to prove the formula for the area of a circle. In later calculus classes, you'll learn how to think about motion in space (and even higher-dimensional space) algebraically, and how to compute the surface area of weird 3d objects like donuts.
- Abstract algebra is a generalization of the concepts of algebra and arithmetic to all sorts of objects that behave differently from numbers. Modular arithmetic, which is deeply related to what you're doing here, fits under abstract algebra as it is the algebra of a number line that is wrapped up on itself to form a circle. You can also do algebra with things like motions and symmetries.
- Set theory is a very abstract subject that builds on the most fundamental principles of logic to precisely and formally define everything we do in mathematics from the ground up.
- Topology is like geometry, but squishy. Instead of measuring lengths and angles, you study more elusive properties of shapes like how many holes they have, how many dimensions they have, or whether or not one can be squished and bent to look like the other (Turns out a straw has one hole! We figured this out back in the late 1800s).
I hope you're not intimidated by the vastness of mathematics! It's exciting, isn't it? :3
Wow! Thanks for such an in-depth comment! I've heard of some of those topics, but didn't really know what they were! ^w^
I'm not intimidated, per se, by the scale of everything to learn. Maybe cos I don't have to learn it for school/ uni, haha. I'll just go at my own pace, and get as far as I get ^w^
Best of luck with your own Maths journey as well! It sounds exciting and I hope it all goes well for you! :D
I'm just wrapping up my degree (got an exam in 8 hours and then one in 32 hours then I'm done with exams forever!) it's a bsc in maths and stats in the UK (so I do at least one stats module a year)
my favourite modules I've done are
graph theory
you have a collection of vertices and edges that can connect any two vertices (vertices do not have to be connected, but an edge must start and end at a vertex) it's really useful for modelling things in the real world, like roads for example
combinatorics
counting how many ways there are to arrange something, it can go pretty in depth and can be used to model real things like if you have people who can do certain jobs is it possible to get every job done with no person (or team) doing more than one job
game theory
hello internet, game theory creates a "game" where each player has a set of strategies and each outcome gives a "utility" (how good the outcome is), and you try to find the strategy that guarantees the highest utility (prisoners dilemma is the most commonly known example of a game theory problem)
other notable ones are quantum theory (my exam for this starts in 8 hours lol), complex analysis was really cool but I sucked at it, and I enjoyed set theory a lot which was mentioned in the parent comment
oh I have also done knots and surfaces which I believe is related to topology, some rather interesting stuff although I didn't study it as much as I'd have liked due to stressing about the other modules lol
@@EggZu_ Those all sound really interesting, but also super complicated XD Thanks for sharing! I hope your exam went well! ^^
@@rambleswolf thank you! I think it went okay, I spent 20 minutes trying to integrate the wrong function but I finished with 5 minutes to spare so at least I didn't lose marks by running out of time. final one is tomorrow and also my birthday!
how did i get here
You clicked on the thumbnail? 🤔 You must either be watching maths or furry stuff too, cos those are the only tags, LOL
@@rambleswolf the former, sure, and i think you can blame my gf for the latter part
@@kornsuwin LMAO
Yyyyeah.. I was hoping this would be satire
you have just unlocked a part of my brain that i did not know existed, thank you rambles the wolf
i think you're just looking at the final digit and if I'm right you can do this kind of cycle in any base and it's called the modulo, it basically looks at the remainder after dividing by some number
if we take multiples of 3 modulo 5 for example you get
3, 1, 4, 2, 0 which are the remainders from 3 6 9 12 15 when divided by 5, it repeats itself in a cycle like with the circle in the video
we count in base 10 typically and you can use those cycles and some clever little tricks to work out stuff like what the final digit of 3 to the power of 1851 is by taking modulo 10 (I'm not gonna do it cuz it's awkward but i have done it in the past)
Wait... there's a hack for learning powers?? I NEED this information 🤣
@@rambleswolf specifically to reduce it by a modulo, but it's quite a lot of busy work and isn't really worth learning unless you have a number theory exam coming up lol
@@EggZu_ So, what you're saying is: I'd be better off just using a calculator? XD
@@rambleswolf hahaha yes
Yep! This is why modular arithmetic is called clock arithmetic. It loops!
Math is best learned with your favorite proofs❤
Good luck with your maths!
I was randomly recommended this... I have a math degree... and watch furry content....
Oh, that's cool! Never heard of clock/ modular arithmetic before! :D
Did you study pure or applied mathematics? I'm kinda interested in what people learn during a maths degree, and what kind of work people get into afterwards.
If I get comfortable enough, I might try and get an A-Level in Maths (for fun), since all my A-Levels were in Humanities. (In the UK, A-Levels are 3 subjects you take between the age of 16-18 at a sixth form college after finishing high school (age 11-16), and getting your GCSEs. A-Level grades are what you use when applying to university.)
@@rambleswolf I studied computational mathematics and computer science and statistics, so more towards the applied side.
Was going to mention this, it looks like modulo 10 arithmetic. This is also used in cryptography as well
Were passing the final with this one boys
You can do it! Coming from someone who sucked at math and is now acing a CS&MATH degree, if you put your mind to it, you can accomplish anything.
Thank you so much! And well done on your degree! That's awesome! You must've put in a lot of hard work! ^_^
@@rambleswolf I hope you take on calculus down the line. The way everything comes together is just so beautiful. The first time I learned it my mind was changed forever.
@@Luingus Hopefully one day! I want to be able read stuff with the big ʃ in it! XD (I think they're called integrals? No clue what they actually are though, LOL)
Still, I need to polish up my Pre-Algebraic Arithmetic first - just gotten up to dealing with fractions, haha. Soon to go on to Decimals and Percentages.
Since filming this, I've become pretty confident with multiplication. But, I'm finding dividing by two or more digit divisors quite tricky...^^;
It's sort of coming back to me that fractions were actually something I really struggled with in school. And I kinda get how to deal with them now, which is cool! Just need to practise them some more! :D
@@rambleswolf If it makes you feel any better, once you get to higher maths, most division is done by calculator anyways 🤣.
I don't understand how drawing numbers on the corners of shapes help? Where is the logical correspondence between 0-2-4-6-8 and a pentagram?
Check out the link in the description, as he's an actual teacher who explains it more in depth. But basically, each of the number wheels are the same; the shapes are just to help you visualise the pattern of the multiplication. :3
Of course there are patterns lol, by many measures, maths is the *study of patterns*
But yes, it's rather stupid that we're largely forced to memorize these things without ever expecting there might be a pattern. The kids who realize anyway get a massive boost straight off the bat and the others already start to get left behind.
Math is gorgeous how it work.
Yeah! The more I learn about it, the more I'm surprised at how cool it is, haha.
Magic, also known as Geometry
this is how people did math before calculus was invented. the ancient greeks would just draw a bunch of triangles and circles on the ground and then land 20 headshots.
math is magic, it's the reason we have the trope of wizards
Oh my, your video certainly blown up, how do you feel about it? Personally, this wolfer thinks your method is pretty funs :3c
I felt a mixture of pride and panic! XD
Yeah, I like this method! Steiner schools are quite interesting in their pedagogy.
@@rambleswolf Well, your ramblings are worth listening to in this wolfer's perked ears, ya got yourself a new floofl-
Greetings from Vietnam!
@@sufferingrin3886 Aww, thank you! ^^
there's nothing shameful in not knowing. you can always learn. and learning and sharing your experience is anything but shameful. if it helped you, you are helping someone just by sharing!
ps when u hold the paper up close to read it it looks like ur tryna figure out what's going on through sniffing it and it looks funny
Aww, thank you! ^w^ That's sorta why I started this channel - to measure and share my learning journey with different topics!
Also, LOL, I hadn't noticed that, but you're right! XD
hi cute British wolf guy
is this a cult thing?
no it isnt
Yeah no, i cant see.
oh oh oh
mr interupting bear here
calculus is advance spiral art with oh whatcha call it again?
spiral graph, eh? had to learn a few tricks also on certain numbers 7x8
english majors outside their domain tacking maths