This video is a pearl in the middle of the internet ocean. It's fascinating how you explain how some subjects of math are the abstraction of things we already use in Simple math. As a student of computer science i apreciate a lot this work
learning about lambda calculus is how the magic of abstraction "clicked" for me. Being able to define problems away is just mind-blowing to me still lol. "This function is a number now because I say it is" is just amazing
Instantly subbed, this is one of the most “eye” opening videos on mathematics that I’ve seen so far, you took an “abstract” concept and broke it down in a very digestible way, one could say you used abstraction to minimize the number of elements it takes to convey the underlying structure of “the utility of abstraction within mathematics” lol. Thank you for the video!
@@Eyesomorphic Please make a course where you teach Type theory but do it by simultaneously teaching ALL the prerequisites and building blocks that we need to know from logic and proof theory. I would be so happy paying for a course if you can make it just as intuitive and visual as this video.
tbh i thought my real weapon was a combination of logical reasoning and math theorems.. i used a lot of statistics and logic to check how likely a statement is to be true or not given for example, if the person claims that 10 rare conditions were simultanously true, that's probably bullshit. but if it was a smaller set of conditions, or there is proof that some of them are true, the situation changes. or for example, using advanced counting and probabilities to win card games and impress ppl
I’ve watched like 5 introductions to category theory, but your analogy of what algebra is to numbers is what category theory is to composition was the priming I needed. Heck! I learnt algebra before. And I know how I learnt algebra. For me learning algebra involved doing a lot of examples and then creating algorithms for it once I got a good grasp of the subject. So yesterday I started with an exercise heavy book to category theory (spivaks category theory for the sciences) and it’s exactly what I need to understand it. He introduces ologs that are the first real objects I studied seriously that don’t fulfill composition. Thanks a ton on getting me started!
That's great to hear! It took me at least 10 different books and lecture series to fully get to grips with the principles of category theory, and I guess this video is the culmination of that, and the progression that felt most intuitive to me. Good luck on your quest!
instant subscribe! i got my b.s. in mathematics last year, but real life hasn’t given me much time to keep up with reviewing what i learned in undergrad. this video made me feel like i was in one of my theory classes again! ❤
I dont regret a single second of watching this video, you completly changed my perception of not only mathematics, but the whole reality. Thank you for this amazing content, you defenitely deserve a sub! 👏
As a first-year Math Degree student, I can that almost all (if not all) Mathematics can be described by the art of Abstraction. For example, if you want to prove "The sum of even numbers is even" you could try to check one by one, but you'd just never end because there're infinity even numbers. Instead, you can consider work with only two objects "A" and "B", which are two representatives of all integers that verify the property of being even (formally, if we consider the universe "Ω" to be set of all intergers: "∃n(A=2n)" and "∃m(B=2m)"). In other words, we've just removed all particular characteristics of individual even integers to stay only with what characterizes an "even integer"; we've made abstraction. Where the magic lies is that if you manage to prove any property with "A" and "B" (such that "A+B" is even), you're proving it for any two even numbers (actually, "killing infinit many birds with one shot"). 🔥
Welcome to TH-cam, Eyesomorphic! Stunningly simple and accessible presentation that couls invite more people into this beautiful area of study. Hope you could go deeper into category theory and present useful results in a similarly accessible fashion. Looking forward to them!
Such an amazing video that explains category theory in a remarkable way. I have been looking for category theory videos but I never found any with this level of articulation and quality. Your hard work to put together explanations and graphics deserve great applause 👏
Wow, man, you're really really good at this, your approach to mathematics and your skill to teach in a simple way with many examples is amazing. Please, keep making videos, there's nothing like this on TH-cam.
Beautiful simple, clear explanation! Thank you for abstracting math education to its essence. I believe a ‘top down’ approach to math is as important as building a bottom up foundation - it helps to build motivation, and provides a framework to hang the whole of math. Would love to see your take on linear algebra, calculus, geometry, etc, and how they are different aspects of the same concepts.
Thank you for amazing video and especially for reference to a course by Bartosz Milewski! I tried to study Category Theory twice before, and gave up both times. Thanks to your video I found Bartosz' lectures (here on TH-cam) on Category Theory, and they are much more accessible than materials I used before - so I'll give it another try. This video was very inspirational for me. Thank you!
Apparently this is your very first video (on this channel). Obviously the algorithm knows what I like. The channel name is awesome. Isomorphism explains everything. Looking forward to the N+1 video.
Welcome, so glad to see a new and starting math channel :) I have to say, as an avid set theorist myself I absolutely love your presentation! Your discussion on the identity function was thorough. I'd love to see you do a video on set theory in detail or logical paradoxes (Russels and axiom of choice) or something on large cardinals (recursive functions and calls?) if you choose. Either way though, subscribed.
Great video. A young kid could understand this, and it would likely turn them into mathematicians! The world needs more mathematicians, especially now. Bravo.
This video has really helped me on a personal level, I've been undergoing changes in my thinking pattern recently, influnced by formal logic, and abstraction was a huge part of it. I've being trying to articulate my process of thinking, but I think this video on abstraction really hits the nail on the head. Thank you.
You caught my attention by just one video and you also made me impressed of this. I've never seen this topic before. I'll might use this in my journey in mathematics as a second year highschool student. Hope you can make more videos like this.
Beautiful presentation of category theory. I enjoyed how Alice and Bob's speech colors were mapped to a (for Alice) and b (for Bob) respectively as a way of abstraction which then allowed me to understand the rest of the video, as though you created a rhetorical category to be an analogy to mathematical categories.
Cool and thought-provoking. It would be nice with a follow-up that shows more concretely how abstraction and categories actually can help you solve problems or reach new insights!
I did my undergrad thesis on adjoint functors and my Master degree thesis on the homotopy theory of differential graded categories. Congratulations for the work and the views!
What a beautiful video. When something is presented simply enough, it’s truth is revealed in all forms. Your section on rationals and reals got me thinking of kolgomorov complexity in a whole new light. Your section on composing functions got me thinking of computable functions and how one can apply category theory to complexity theory. I imagine that was unintended, but welcome for sure. Cheers to you, this is inspiring work. You’ve won a new subscriber. I hope to see more of your videos in the future.
Really beautiful i loved it! Thanks a lot, can't wait to learn more! Would love to hear more about category theory if you want to consider it (but i see you provided an awesome list to learn more!). I wish you the best going forward ❤
My god. That's your very first video? It's amazing! I really would love to see many more content from you. If you want some ideas, you could make some videos on topology in a not far future, I'd love to see it that way!
Loved the “always has been” joke. Great video very well made ❤ I love the more philosophical approach to mathematical concepts. Can’t wait to see whatever you decide to do next
Really good video (and the perfect name for the channel), I hope you continue to post. That said, I would say that category theory is the abstraction of abstraction. Composition is what links an abstraction to another. Also, the functorial nature of the whole shebang should be a really good sequel.
Love it!!!!!! I will link your video as required on every first lecture of my courses. I have used Ring Theory to "obliterate" the Integer type in some programming languages (Java, JavaScript)... An Integer (concept) in a knowledge domain is not isomorphic in another domains Integer (construct) =P. Infinity points to a reference in memory in computers, LOL. infinity +1 is -infinity =)....
I really hope you make a category series! I feel like soft I teoduxtipns to CT are everywhere but it’s so hard to get gentle explanations of higher concepts like the yoneda lemma
This video brought me great joy. Reminded me of those many years ago when I first was introduced to linear algebra. ❤ "Like a field of roses, how closely does man walk to ultimate truth that but with a few slight shifts, he'd have realized his most profound question: what is this life?" - 'tuyi
This video is beautifully made Everything from starting to defining what abstraction means in mathematics and it's usefulness within the study of either numbers,orders,relationships and compositions I also admire the effort put into creating such video with very high quality Im looking forward to the next 😊
Hoping for more Category Theory content. I've been trying to grok it (without opening a textbook) for a while now. Haven't found anything as good as this yet.
WOW!!! What an amazing video I really hope you continue doing videos (no rush, just dont leave it please). As a personal opinions, the background music was a little bit loud for me (I like it anyway), also I love when people gives me non-examples, like "this is not this because of this". Keep it up!! I wish you a lot of luck 😊 P.D.: Also, as a personal demanding, I would love a video about series, convergence, how are they connected with other mathematical fields (if they are), etc
This is very good food for thought for those who work with visual programming languages. Without knowing the specifics on the history of the development of such languages, I'd imagine they started from these concepts in mathematics before they were what they are now.
this is my first time seeing this video and thinking of this topic. I understood things that I never thought of before or learned. I am taking functional programming class next semester and I will see how the small snippet of abstraction on functional programming here will help me. Thank you for the great content.
Beautiful... Awesome explanation, Thanks for sharing and for your efforts. I just know college level Mathematics but I love Maths and watch lots of Maths video, This was very well explained. Thanks
Now I want a 3B1B series about "The Essence of Category Theory", if only for the animations, because "Category Theory for Programmers" by Bartosz Milewski explains it well enough
Identity functions got me thinking. In a programming language I could define two different identity functions, one of them takes 10 times longer to return. Category theory views these functions as identical. So equivalency is not sensitive to the path a function takes, but purely whether the results are identical for arbitrary inputs.
I am good at social abstraction. I am a degreed mathematician. I thought they were not related. Thank you for connecting the dots making me feel whole.
Actually, unexpectedly beautiful and revealing initiating inspiration. Please make more of these! Even though at the end went above my head- but have to rewatch to regain the thread. But so nicely explained and abstracted- and delivered almost perfectly. Pun unintended. The music though, after some time becomes to generically tiresome- while the content is flabbergastingly exciting. I simply loved it- and felt so good, until I lost the thread and realized: wow, I guess I’m flagrantly meeting my limits. 😊 anyway: Awesome video! (Thanks!)
Hey, thanks for the great video man!!!! I believe there are few simple discrete rules exist in the nature like recursion, composition, categories and few others that I don't know, can be used to derive everything...
Welcome to TH-cam! I downloaded this before hopping on a flight and it was definitely worth every second! Just some feedback in case you decide to make more videos (which would be incredible!). I loved how you gradually built up from fundamental algebra but felt that it could have been sped up a bit. I imagine that it's a tough line knowing what's "trivial" and what's not, but as an undergraduate engineering student, I think the rational number example could have been a bit faster. The only other thing is as an engineer, I would have loved to see a slightly more complex example explored. I found the analogies wonderful and loved how the example you have crossed into many different domains (linear algebra, CS, etc. ) However, the final conclusion felt a little too obvious, to where I'm wondering if everything that was discussed is just mathematical boilerplate needed to prove something rigorously. I know nothing about this field so I'm not sure if there are any examples that are slightly more complex but still tractable for a video. In any case, this was an absolute gem. The animations, the characters, and the style was of a very high caliber. Thank you so much for your contribution to the community! 🙏
Thank you for such in-depth feedback! I completely agree with what you're saying, but of course it's an impossible task trying to cater towards those who have almost no formal mathematics experience and those with a lot of it, so when coming up with the examples I did find it incredibly difficult trying to think of something that would be approachable but also interesting. As for more complex examples, it is also rather difficult. Category theory has quite a steep learning curve, the definition is relatively simple, but to do anything profound requires quite a lot of new definitions. To combat this, I'll probably make another video covering these new topics, with some more obviously useful examples, both in pure maths and in the real world. Thanks again for your kind words and the feedback, it has been taken on board and I thoroughly agree with what you said, I'll take it into consideration moving forwards :)
This video is a pearl in the middle of the internet ocean. It's fascinating how you explain how some subjects of math are the abstraction of things we already use in Simple math. As a student of computer science i apreciate a lot this work
Thanks!
learning about lambda calculus is how the magic of abstraction "clicked" for me. Being able to define problems away is just mind-blowing to me still lol. "This function is a number now because I say it is" is just amazing
This is possibly the best intro category theory video in the category of intro category theory videos
Instantly subbed, this is one of the most “eye” opening videos on mathematics that I’ve seen so far, you took an “abstract” concept and broke it down in a very digestible way, one could say you used abstraction to minimize the number of elements it takes to convey the underlying structure of “the utility of abstraction within mathematics” lol. Thank you for the video!
Brilliant. Clean animations, thoughtful and clear exposition and a great topic. Can’t wait for more videos from Eyesomorphic.
I can't say it any better, so a great big DITTO!
Welcome to TH-cam! Fantastic presentation. Absolutely looking forward for a long and prosperous playlist, Eyesmorphic. Thank you for existing!
That means a lot! Thanks
@@Eyesomorphic Please make a course where you teach Type theory but do it by simultaneously teaching ALL the prerequisites and building blocks that we need to know from logic and proof theory. I would be so happy paying for a course if you can make it just as intuitive and visual as this video.
@@Eyesomorphichave a nice day and be wise ☕️🍰🍸
@@Eyesomorphicintuition is hugging you deeply, warmly and passionately
tbh i thought my real weapon was a combination of logical reasoning and math theorems.. i used a lot of statistics and logic to check how likely a statement is to be true or not given for example, if the person claims that 10 rare conditions were simultanously true, that's probably bullshit. but if it was a smaller set of conditions, or there is proof that some of them are true, the situation changes. or for example, using advanced counting and probabilities to win card games and impress ppl
I’ve watched like 5 introductions to category theory, but your analogy of what algebra is to numbers is what category theory is to composition was the priming I needed.
Heck! I learnt algebra before. And I know how I learnt algebra. For me learning algebra involved doing a lot of examples and then creating algorithms for it once I got a good grasp of the subject.
So yesterday I started with an exercise heavy book to category theory (spivaks category theory for the sciences) and it’s exactly what I need to understand it.
He introduces ologs that are the first real objects I studied seriously that don’t fulfill composition.
Thanks a ton on getting me started!
That's great to hear! It took me at least 10 different books and lecture series to fully get to grips with the principles of category theory, and I guess this video is the culmination of that, and the progression that felt most intuitive to me. Good luck on your quest!
do you have a CS/Software background? if yes can we expect some CS related videos to from you in the future besides pure mathematics? @@Eyesomorphic
@@YuruCampSupermacy My background is in mathematical foundations for CS, so you can definitely expect some more CS orientated content in the future!
instant subscribe! i got my b.s. in mathematics last year, but real life hasn’t given me much time to keep up with reviewing what i learned in undergrad. this video made me feel like i was in one of my theory classes again! ❤
That's great to hear!
I dont regret a single second of watching this video, you completly changed my perception of not only mathematics, but the whole reality. Thank you for this amazing content, you defenitely deserve a sub! 👏
As a first-year Math Degree student, I can that almost all (if not all) Mathematics can be described by the art of Abstraction.
For example, if you want to prove "The sum of even numbers is even" you could try to check one by one, but you'd just never end because there're infinity even numbers.
Instead, you can consider work with only two objects "A" and "B", which are two representatives of all integers that verify the property of being even (formally, if we consider the universe "Ω" to be set of all intergers: "∃n(A=2n)" and "∃m(B=2m)"). In other words, we've just removed all particular characteristics of individual even integers to stay only with what characterizes an "even integer"; we've made abstraction.
Where the magic lies is that if you manage to prove any property with "A" and "B" (such that "A+B" is even), you're proving it for any two even numbers (actually, "killing infinit many birds with one shot"). 🔥
I can see how thoroughly you planned this video! Both the visualisation and the topic are beautiful!
Welcome to TH-cam, Eyesomorphic! Stunningly simple and accessible presentation that couls invite more people into this beautiful area of study. Hope you could go deeper into category theory and present useful results in a similarly accessible fashion. Looking forward to them!
Such an amazing video that explains category theory in a remarkable way. I have been looking for category theory videos but I never found any with this level of articulation and quality.
Your hard work to put together explanations and graphics deserve great applause 👏
Wow, man, you're really really good at this, your approach to mathematics and your skill to teach in a simple way with many examples is amazing.
Please, keep making videos, there's nothing like this on TH-cam.
This was my very first exposure to category theory and it was beautiful!.....Thank you.
This is not only a great introduction to Category Theory, but also a great introduction to Mathematics in general. 🔥
Don't let this distract you from the fact that a monad is a monoid in the category of endofunctors.
Alas, Haskell Brutalism rears its ugly head again.
@@vonBottorffHaskell Brutalism may be ugly but still a beautiful phrase
beautifully reminiscent of 3Blue1Brown imo, looking forward to more! Gave me a really solidly improved understanding of category theory :)
I hope you're in top tier winners for #SoME3! Brilliant explanation . As a math student, absolutely fantastic work!! Would love to see more.
Beautiful simple, clear explanation! Thank you for abstracting math education to its essence. I believe a ‘top down’ approach to math is as important as building a bottom up foundation - it helps to build motivation, and provides a framework to hang the whole of math. Would love to see your take on linear algebra, calculus, geometry, etc, and how they are different aspects of the same concepts.
Thank you for amazing video and especially for reference to a course by Bartosz Milewski! I tried to study Category Theory twice before, and gave up both times. Thanks to your video I found Bartosz' lectures (here on TH-cam) on Category Theory, and they are much more accessible than materials I used before - so I'll give it another try. This video was very inspirational for me. Thank you!
I hope you're in top tier winners for #SoME3! Brilliant explanation 👏🏼
Gold!👌 Looking forward to following this series!
Apparently this is your very first video (on this channel). Obviously the algorithm knows what I like. The channel name is awesome. Isomorphism explains everything. Looking forward to the N+1 video.
such a great video, the best one i’ve seen so far on introducing category theory, i love it so much! also i love the channel profile picture and name
That's very kind, thanks!
This video is so well made, the best I've seen in a long while on pure maths. Amazing work!
This kind of math content is definetly worth a channel for!
A video with an agile structure and a lean data posture. A job well done!
Welcome, so glad to see a new and starting math channel :) I have to say, as an avid set theorist myself I absolutely love your presentation! Your discussion on the identity function was thorough. I'd love to see you do a video on set theory in detail or logical paradoxes (Russels and axiom of choice) or something on large cardinals (recursive functions and calls?) if you choose. Either way though, subscribed.
Great video. A young kid could understand this, and it would likely turn them into mathematicians! The world needs more mathematicians, especially now. Bravo.
Please make more videos! Im so lost learning abstract math and this was such a nice way around it
Beautifully simple overview of a difficult area of mathematics. I'm looking forward to a deeper dive in future videos.
I REALLY like your style, visuals are so perfect for following on
I have never subscribed and turned on notifications for a channel so fast.
Best category theory introduction I’ve come across thus far!
This video has really helped me on a personal level, I've been undergoing changes in my thinking pattern recently, influnced by formal logic, and abstraction was a huge part of it. I've being trying to articulate my process of thinking, but I think this video on abstraction really hits the nail on the head. Thank you.
This video blew my expectations. AWESOME. I hope to see many cool videos like this one from this channel now
Man, I'm still SO EAGER for another video! This video is absolutely beautiful, I can't wait for the next one, and the next ones!
This is the most exciting math related video i have ever seen!
Loved it. Subscribed. Looking forward to future videos, i can't believe your first video is of such high quality. kudos.
You caught my attention by just one video and you also made me impressed of this. I've never seen this topic before. I'll might use this in my journey in mathematics as a second year highschool student. Hope you can make more videos like this.
Beautiful presentation of category theory. I enjoyed how Alice and Bob's speech colors were mapped to a (for Alice) and b (for Bob) respectively as a way of abstraction which then allowed me to understand the rest of the video, as though you created a rhetorical category to be an analogy to mathematical categories.
Very clear and beginner friendly, waiting for More :)
Spanish: Este video es una maravilla, en serio, poder explicar algo tan "abstracto" de una forma tan digerible es todo un arte. FELICITACIONES!!
¡Eso significa mucho! Gracias :)
Cool and thought-provoking. It would be nice with a follow-up that shows more concretely how abstraction and categories actually can help you solve problems or reach new insights!
I did my undergrad thesis on adjoint functors and my Master degree thesis on the homotopy theory of differential graded categories.
Congratulations for the work and the views!
What a beautiful video. When something is presented simply enough, it’s truth is revealed in all forms. Your section on rationals and reals got me thinking of kolgomorov complexity in a whole new light. Your section on composing functions got me thinking of computable functions and how one can apply category theory to complexity theory. I imagine that was unintended, but welcome for sure. Cheers to you, this is inspiring work. You’ve won a new subscriber. I hope to see more of your videos in the future.
Really beautiful i loved it! Thanks a lot, can't wait to learn more! Would love to hear more about category theory if you want to consider it (but i see you provided an awesome list to learn more!). I wish you the best going forward ❤
My god. That's your very first video? It's amazing! I really would love to see many more content from you. If you want some ideas, you could make some videos on topology in a not far future, I'd love to see it that way!
Very nice and simple ! Thank you !!! Hopping There will be others videos !!!
Loved the “always has been” joke. Great video very well made ❤ I love the more philosophical approach to mathematical concepts. Can’t wait to see whatever you decide to do next
Best intro to category theory I've seen, you get an instant new subscription from me!
Really good video (and the perfect name for the channel), I hope you continue to post. That said, I would say that category theory is the abstraction of abstraction. Composition is what links an abstraction to another. Also, the functorial nature of the whole shebang should be a really good sequel.
First time I watch a video about category theory that actually makes sense. Thanks for this ❤
Love it!!!!!! I will link your video as required on every first lecture of my courses. I have used Ring Theory to "obliterate" the Integer type in some programming languages (Java, JavaScript)... An Integer (concept) in a knowledge domain is not isomorphic in another domains Integer (construct) =P. Infinity points to a reference in memory in computers, LOL. infinity +1 is -infinity =)....
That intro was sick af
Two minutes in and I know I'm gonna be watching every video you post :D
This is amazing, simple and comprehensive way to display explanation of the topic.
My god this was so eye opening and extremely thought out of. thank you for the effort brother.
I really hope you make a category series! I feel like soft I teoduxtipns to CT are everywhere but it’s so hard to get gentle explanations of higher concepts like the yoneda lemma
After watching so many videos on Category Theory, this one is hands down my favorite. I have watched at it least 3 times.
Thanks for the kind words!
This video brought me great joy. Reminded me of those many years ago when I first was introduced to linear algebra. ❤
"Like a field of roses, how closely does man walk to ultimate truth that but with a few slight shifts, he'd have realized his most profound question: what is this life?" - 'tuyi
I really like the visuals! The explanation was succinct as well! Please do continue!
The three first seconds of the video already made me subscribe. That intro has style, mate.
This video is beautifully made
Everything from starting to defining what abstraction means in mathematics and it's usefulness within the study of either numbers,orders,relationships and compositions
I also admire the effort put into creating such video with very high quality
Im looking forward to the next 😊
Amazing entry, I hope you win :).
abstraction is a relevant concept in Algebra as well as in mathemathics. Amusement
Hoping for more Category Theory content. I've been trying to grok it (without opening a textbook) for a while now. Haven't found anything as good as this yet.
WOW!!! What an amazing video
I really hope you continue doing videos (no rush, just dont leave it please).
As a personal opinions, the background music was a little bit loud for me (I like it anyway), also I love when people gives me non-examples, like "this is not this because of this".
Keep it up!! I wish you a lot of luck 😊
P.D.: Also, as a personal demanding, I would love a video about series, convergence, how are they connected with other mathematical fields (if they are), etc
Nice one! I am currently reading Sheaf Theory by Tennison - maybe this would be nice to be covered in a future video
awesome video! can’t wait to see the full potential of this channel
Wowie. I expect more interesting videos in the future, huhu ^,^
Beautifully done. Great content, good pace, lovely animations.
This is very good food for thought for those who work with visual programming languages. Without knowing the specifics on the history of the development of such languages, I'd imagine they started from these concepts in mathematics before they were what they are now.
Category theory and Lambda calculus do serve as inspiration for most functional programming languages, and even some imperative languages too!
What languages are you thinking of exactly? Other examples than just mentioning Haskell. @@Eyesomorphic
this is my first time seeing this video and thinking of this topic. I understood things that I never thought of before or learned. I am taking functional programming class next semester and I will see how the small snippet of abstraction on functional programming here will help me. Thank you for the great content.
What a nice channel, I know this is a gold mine. Please post more.
Beautiful... Awesome explanation, Thanks for sharing and for your efforts. I just know college level Mathematics but I love Maths and watch lots of Maths video, This was very well explained. Thanks
After watching this video, I'll abstract my comment into one word, "Beautiful"! :)
You have a very dry and subtle sense of humor that is perfect for math videos.
Now I want a 3B1B series about "The Essence of Category Theory", if only for the animations, because "Category Theory for Programmers" by Bartosz Milewski explains it well enough
Feynman technique at its finest. Thank you for this!
Dude got 2 thousand subscribers in just 4 days. That has to be a record of some sort
I'm as surprised as you are!
One of the best math videos I have yet seen
5:35 :D a talented educator and a meme lord. Hats off to you, good sir.
Nice clear video. Much more category theory, please!
Identity functions got me thinking. In a programming language I could define two different identity functions, one of them takes 10 times longer to return. Category theory views these functions as identical. So equivalency is not sensitive to the path a function takes, but purely whether the results are identical for arbitrary inputs.
Very nice video! I really appreciate how well made everything is here, keep it up ^^
One of the best video on category theory intro!
I am good at social abstraction. I am a degreed mathematician. I thought they were not related. Thank you for connecting the dots making me feel whole.
I absolutely loved every single second of the video. This was just amazing.
Great abstraction of Category Theory !
Thank you very much - this is a very interesting topic and I do hope that you can keep making videos like this.
Oh wow so beautiful...cannot wait to watch with my kid...wish you would create such beautiful, deep and simple videos more ❤
Actually, unexpectedly beautiful and revealing initiating inspiration. Please make more of these! Even though at the end went above my head- but have to rewatch to regain the thread. But so nicely explained and abstracted- and delivered almost perfectly. Pun unintended. The music though, after some time becomes to generically tiresome- while the content is flabbergastingly exciting. I simply loved it- and felt so good, until I lost the thread and realized: wow, I guess I’m flagrantly meeting my limits. 😊 anyway: Awesome video! (Thanks!)
Loved the content. Need great playlists containing such
Hey, thanks for the great video man!!!! I believe there are few simple discrete rules exist in the nature like recursion, composition, categories and few others that I don't know, can be used to derive everything...
i am learning how compiler works and i give up after learn this kind of diagram 14:23 thank you for simplified this
Wow, what a remarkable video and interesting content!
Welcome to TH-cam! I downloaded this before hopping on a flight and it was definitely worth every second!
Just some feedback in case you decide to make more videos (which would be incredible!). I loved how you gradually built up from fundamental algebra but felt that it could have been sped up a bit. I imagine that it's a tough line knowing what's "trivial" and what's not, but as an undergraduate engineering student, I think the rational number example could have been a bit faster.
The only other thing is as an engineer, I would have loved to see a slightly more complex example explored. I found the analogies wonderful and loved how the example you have crossed into many different domains (linear algebra, CS, etc. ) However, the final conclusion felt a little too obvious, to where I'm wondering if everything that was discussed is just mathematical boilerplate needed to prove something rigorously. I know nothing about this field so I'm not sure if there are any examples that are slightly more complex but still tractable for a video.
In any case, this was an absolute gem. The animations, the characters, and the style was of a very high caliber. Thank you so much for your contribution to the community! 🙏
Thank you for such in-depth feedback! I completely agree with what you're saying, but of course it's an impossible task trying to cater towards those who have almost no formal mathematics experience and those with a lot of it, so when coming up with the examples I did find it incredibly difficult trying to think of something that would be approachable but also interesting. As for more complex examples, it is also rather difficult. Category theory has quite a steep learning curve, the definition is relatively simple, but to do anything profound requires quite a lot of new definitions.
To combat this, I'll probably make another video covering these new topics, with some more obviously useful examples, both in pure maths and in the real world.
Thanks again for your kind words and the feedback, it has been taken on board and I thoroughly agree with what you said, I'll take it into consideration moving forwards :)
This video is soo well made!!! Kudos!
"Eye" love it! Subscribed!