If we never study anything that we can't immediately think of a direct use in our life for we would still be sitting around a fire hunting with sticks.
@@marcgrec5117 When we lived in the woods a lot of people died all the time from easily preventable methods and we had an extremely short expected lifespan. Odds are if we did go back in time, you and I would be one of the people who died of something simple like salmonella, a cold or a food shortage instead of the people we selectively imagine to live out long and free lives in the woods. Though I agree it would be nice if our lives could be simpler yet still retain a modern level of health.
I remember one simple application of math that I did for my friend. It wasn't taught at school. He is a painter and there were different methods of painting from a picture, he told me about painting by hand/eye or grid method. He says he has difficulty with painting by hand/eye and doesn't like the robotic nature of grid method. So I told him if there was a 'point' method where he picks the points of interest from an image and just scale it up or down the paper. He was confused he thought it was still the grid method and I always have difficulty explaining my thoughts. So I made him a simple demo using desmos just scaling the points to whatever paper size he is using. He tried it and he's been using it for 4 years now using the same link. I do agree that the main problem here is the education system. I got really lucky because I realized early on that grades meant nothing (especially as a I got older). I didn't drop out but I wasn't too hard on myself. To the education system's credit, it wants a tangible way to measure intelligence and this is currently the best one that they thought of. It is improving especially since schools are adapting more to the individual's skills and inclinations.
As a history person “useless” mathematics is what drives human innovation, without the accumulation and study of “useless” knowledge human advancement would be slow, inefficient, and utilitarian. Or in other words I completely agree.
Probably for the same reason we actually should learn geology or geography or basics about plants. Because if we DID, things like the fires of California could have been avoided or mitigated because people would understand that the geography of that area was one big matchbox waiting to go off. Replace that second sentence with : Expand our intellect in our spare time and make better mental choices.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
As a math teacher, I don’t bother trying to argue for its usefulness. Yes, you learn skills like how to follow instructions, be detail oriented, or recognize patterns, but they’ll never learn those lessons if they are expecting it. We learn best when we are not expecting to learn.
That's terrible. No wonder most avoid - if not dislike - math. Only few would bother to explain the why and its goal. It's hard to feel motivation when you don't even known where you're going.
@@ultimaxkom8728well there is no reason or goal for learning math other than knowledge accumulation. Applied fields are where you learn math for a goal and are given a reason. The math used in those fields is calculus, linear algebra, differential equations. Mostly.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
I don't know if math helps with critical thinking, tbh, but it does train our brain to think the stuff we need but would not be able otherwise. For example, we make models all the time when dealing with finances. Or, for another example, calculus may sound impractical but once you get the gist of the idea, you'll be shocked by how often you'll catch yourself seeing derivatives and integrals in stuff that is basically counting.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
I am currently in college, and math is my favorite subject. some times it doesn't make sense, I get it, maths can be hard some times, but that doesn't mean it is completely useless. Personally, doing a lot of maths has made my thinking power better. It teaches you the ability to think critically. You definitely earned a sub 👍
Great video. As a high schooler, I’ve been thinking of this same exact questions everytime I’d have compelling questions on my math tests, however, this explanation was able to make me enjoy what I’m learning more!
I was the slowest kid in 5th grade math, er, arithmetic. Hated memorizing. Then, in 7th grade, I discovered how math related to other things like interpolation. Would switch from math to chemistry to physics and back to the related and needed math every few months. By ninth grade I was checking out calculus books from the library. I then found math incredibly easy but only once I connected it to something. Once I understood a relationship and use remembering stuff became automatic.
*A.* Memorization. Knowledge interpolation. Mystery-like extrapolation. *B.* Calculation. Understanding extrapolation. Puzzle-like interpolation. The critical thinking math teaches is quite different than the others.
Math is about sorting that information inside the Brain. So yes learning math is key to build a foundation to build architecture many different subject inside our brain.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
I like the argument in this video. It is a great argument however it is flawed. The uselessness of math is not much of an issue. Take something that you enjoy (playing sports, watching some time of movies or shows, listening to some type of music). Most likely that activity is "useless" to you beyond its enjoyment. However, since you do it, and you enjoy it, you will find a justification for it (you can justify sports because they keep your body healthy, or spending time into pop culture because it keeps you up to date with your culture. Even people who enjoy recreational drugs or even more harmful activities can find a justification for doing it). But the justification is an afterthought (we trick ourselves into thinking that the justification is the reason to do the activity, but it is more likely that doing the activity is the reason why we find a justification)... The fact is that it is not important whether something is useful or not, what matter is whether you enjoy it or not (and unfortunately, the education system does a good job killing the enjoyment of math) True, math can help you with your critical thinking... but so can many things (even taking bets at vegas can help you think critically if you do it seriously)... It is true that if you "cheat" you don't develop your own skills... but perhaps it is time to wonder, why do people "cheat" if it is not in their best interest? Well, this is a problem of alignment. You cannot cheat when your goal is selfimprovement. But you can cheat when your goal is to get a degree. From that, we begin understand why people cheat.
As a mathematician I can say that math is certainly not useless. The framing is intended to level with those who see math as something inapplicable to their lives. I completely agree, very well said!
Very long story, I graduated a year early from High School, but my education really doesn't go past 3rd maybe 4th grade (I can barely do basic division) and decided not to do college. But I spent my child and teen year building carpentry skills and doing armature mechanical engineering, and through none of that did I need anything more than multiplication and division. I've accepted that I'm not smart academically, it's still kinda embarrassing when I talk to people 5 years younger than me and they're shocked I don't know any algebra, but I also have a job I enjoy and make good money doing before I was even an adult (and I don't have any debt). Meanwhile the younger people I talk to are stressed and not enjoying life, which is sad and mainly an issue with our education system and not math its self. Anyway, my point is to just provide another view from someone who isn't educated. I agree that math can help develop critical thinking, but I also use myself as an example of why you can still live a meaningful life without it. Hope more people see your video!
Yep You can go pretty far without education in life But education is a Safe way No risk Study 10-20 years Job Very safe Whereas no education Very risky Unless you got backing from family or sum
Wrote a long ass commen about how the four-card problem illustrates the limitations of applying our intuition in unfamiliar settings, giving various examples of how math has help me reveal the fundemental motifs connecting new ideas to seemingly unrelated, known concepts - halfing my study time and allowing me to spend nearly all of it on multimodal, higher order learning. I then accidentally refreshed the page, closed the laptop in frustration, but came back to let you know how well your message resonnated with me. In general, critical thinking might be vital today more than ever. Knowing how and why people get the four-card problem wrong (denying the anticedent and affirming the consequent) could be useful. It might be a crucial skill in a time when the majority of the polulace often fail to identifying the logical fallacies used in the rhetoric of the people in influential positions of a society where the vastness, variability, and availability of information grows rapidly by the hour. This one got a bit long as well.. Anyways, I'm excited to see what you'll make in the future!
I really appreciate you! I'm so glad my message resonated with you! I will definitely look more into the four card problem when I have some time as I am unfamiliar. Thanks!
I seriously hate that portrayal. I can’t even tell some people I’m a math major without them saying something like “Your a math major huh? Then what’s 3452 times 576?”
2:34 I don't understand how using a calculator is cheating. A calculator can multiply two numbers for me, but I still need to know which two numbers to multiply
If you’re learning about multiplication in school and your teachers hands you this homework: 2x3 = __ 5x3 = __ 4x4 = __ If you use a calculator that would certainly be cheating and you wouldn’t learn how multiplication works. Later on you might be solving an integral, and if you’re using an integral calculator to do your whole problem then that would also be cheating. No one would probably care if you used a calculator to do multiplication in that scenario, but that’s only because it is assumed you already know how that works so it’s not worth your time. See how it depends a bit on the circumstances?
Great content , Keep Going . I’d appreciate your thoughts on a question that’s been on my mind , do you think everyone can learn math with enough effort or are there people who simply can’t, no matter how hard they try? Is there such a thing as "math talent" or "genius," or is it all just a matter of hard working and practice ?
@@RSSALMath anyways i been thinking math isnt intently useless math finds it application in wildest of topics in sciences, computer science and economics and other more like in physics lets take example of topology and some people see it as useless but its application in quantum mechanics and other fields of studies
Do you think practicing certain types of math even after the class concludes is a useful way to retain your mathematical skills? For instance, I want to continue practicing discrete math and combinatorics through the provided textbooks even after the classes conclude.
Absolutely, the best way to retain math knowledge is to use it regularly. Because I teach calculus 2 I am very proficient in the integral and series calculus even though I took the course over two years ago.
The people who learn "useless math" the best also make the best lawyers, surgeons, actors, musicians, traders, coders, etc. They have such high "base stats" in the game of life that they can do almost anything. It's ridiculously OP!
Sometimes, math feels like an elaborate prank on my brain, but I love it anyway. One minute, I’m confidently following axioms, and the next, I’m questioning reality over infinity and the nature of numbers. It’s humbling (and mildly offensive) when concepts like 0.99... = 1 or the placement of irrational numbers on the number line leave me staring into the void. Yet, somehow, I keep coming back for more. I really appreciate your mix of math and philosophy, because, let’s be real, after enough math, you either start philosophizing or completely lose it. We need more of that; exploring not just how math works, but why it makes sense (or stubbornly refuses to) in the bigger picture. Cheers!
Love the "you either start philosophising or you lose it." cx Wasn't Einstein that said something in the lines of "Mathematics is the only certified way of becoming insane"?
I agree, but I would add that math also has to be taught right in order to be useful, especially in schools. If you can cheat your way through math classes by memorizing formulas and using an electronic calculator, your teacher (or the curriculum they have to stick to) is doing it wrong. At my school I never really liked math lessons even though I was very good at it and participated in all the math competitions (Math Olympiad etc.) that were offered. Those were actually interesting and much closer to "real" mathematics, as you'd have to find proofs and write them down in a logical, understandable way. Something you almost never do in the normal math lessons (in Germany). Now chatGPT is a different beast, that can actually --to an extent-- do the logical reasoning and proof-finding for you, especially for the kind of easy problems you would give to students in schools. I wonder what society might be like in the future if people develop the same mentality to things that AI's will be able to do, that they have towards things "ordinary" calculators can do now: "Oh I won't need to be able to do simple arithmetic, I always have my calculator app!" becomes "Oh I don't need to be able to think critically or problem-solve, I'll just ask chatGPT!"
I completely agree. I used to be a Computer Engineering student, but have now switched to Psychology. Despite this, I'm minoring in Mathematics. When people ask me why, or if I'm a genius, I tell them no, and that I, in part, do it for the reasons mentioned.
Unrelated to the video, but how manageable is studying both a math related field and philosophy? I'm currently a freshman in highschool and have been considering doing something similar, like physics and philosophy or something, but i haven't seen many people going down the same route. Just curious about the work load, how busy you are, opportunities after college, things like that. (Great video btw, you earned a sub)
Thank you! For me getting the two degrees has been very manageable. There is a surprising amount of overlap in the kind of thinking required by my degrees. Though, I went into my undergraduate with about 50 credit hours, so my workload has not been anything crazy at any point. I would say go for it, there is a kind of free creativity that happens in philosophy that balances the strictness of physics and math. Pursuing two degrees in very different areas like math and philosophy makes you appear as a very well rounded student which is something that can give you an edge when applying for anything.
Im a second year stats/data science major but want to know more pure math. Personally, i just do math cuz i want to. Its a selfish thing really, but u could also morph that into me loving math. Tho i know this attitude can clearly change, and honestly me struggling with high school level math in probability stuff embarassed the shit out of me to the point of wanting to quit the course, i still just want to know some more math for my own sake.
No, math past a certain point is useless generally to the public. There are few careers in which you will utilize such advanced math, and I believe that math middle school should be optional because of that. No one I know that isn't in an advanced technological or mathematical career recalls any math they learned and has never used anything more than multiplication or fractions. Clearly, unless you plan on going into an occupation that requires abstract or advanced math, it is pointless. Your argument that it is the only subject that promotes critical thinking is absurd as well. Aside from the fact that those who have a disdain for math will not be open to learning skills besides those of face value, ALL subjects are designed to further critical thinking skills, especially the far more core and connecting subject of English. You find much more human connection, which is what matters chiefly in life, within the other basic subjects, something like History or English. Yes, math is exceptional in aiding in critical thinking skills, but other subjects are just as if not more efficient in such tactics.
Это все круто конечно, но разве этот видос не посмотрят по большей части американцы, которые в десять лет не могут умножать хотя бы двухзначные числа даже на бумаге?
One might argue that the universe is not inherently mathematical, however our representations of it are. I agree with you, though, it is disappointing how math has become stigmatized in America.
I strongly disagree that math is the closest to a critical thinking class. Only applications of math require critical thinking. English or science classes promote critical thinking way more.
English requires literacy and comprehension, science requires memorization and experimental design, but math requires creative problem solving skills and an understanding and intuition of concepts beyond their definitions . Which of those would you say is critical thinking.
@@RSSALMath Math also requires literacy and comprehension and memorization. When you do the lab portion of a science class it's not just memorization. Your description of what math requires sounds more like a description of what science requires. Math is defined and ruled by definitions and what comes from them, which is powerful generalizations. Rarely do math problems require creativity, most times you either know the math to do the problem (and you just have to realize that) or you can't even begin the problem.
I disagree. I am not a math major but i am pretty enthusiastic about math. And i would say really nothing after basic algebra matters and will really "train your brain to think" that much. Except discrete maths and especially proof writing and formal logic. This does indeed teach critical thinking but learning calculus won't teach or train anything outside of math.
The only way i could see this being false is if a student develops a system for metacognition. Which happens extremely rarely. Math is intuitive. Most people don't have this george polya style thinking where they use a specific methodology to solve problems consciously. Even when people try to get creative and look at a problem differently, it will usually be without any order and may not even work
I have to disagree, your argument is analogous to saying that although bench pressing is great, a football player will never need to bench press another player on the field. That's simply not what it's about. Using your brain to navigate math is like training a muscle, when you use it in a highly specific way, you find that in other places it performs much better. A football player will never bench press another player but he does use his chest when defending.
I would recommend studying higher level maths if you truly believe that math is intuitive. A lot of mathematics is highly counterintuitive. The time spent critically thinking about a problem that is difficult to even understand in the first place is invaluable to your brains information processing and problem solving capabilities in general.
@@RSSALMath true and i understand why you think math is counterintuitive. You have this sort of maturity in mathematics that enables you to think about mathematics and its problems like how a mathematician should, which allows for solving problems that are extremely hard and take a very long time. But that's not calculus or any highschool mathematics i encountered. The problems most people face are usually intuitive and very rarely do people need to truly think critically and creatively. I still do think mathematics and every other subject should be studied the way they are since they still help maintain an educated society.
If we never study anything that we can't immediately think of a direct use in our life for we would still be sitting around a fire hunting with sticks.
Amen
Fr dude...
hot take: we opened pandora's box by inventing tech; we should've never left the woods
@@marcgrec5117 When we lived in the woods a lot of people died all the time from easily preventable methods and we had an extremely short expected lifespan.
Odds are if we did go back in time, you and I would be one of the people who died of something simple like salmonella, a cold or a food shortage instead of the people we selectively imagine to live out long and free lives in the woods.
Though I agree it would be nice if our lives could be simpler yet still retain a modern level of health.
nobody's gonna talk about the backround thing?
What background thing?
@@RSSALMath the bouncing ball inside a circle on the left
@@RSSALMath the ball bouncing around
No clue what you guys are talking about ι:
@@RSSALMath what's that thing name? It is really amusing
I remember one simple application of math that I did for my friend. It wasn't taught at school. He is a painter and there were different methods of painting from a picture, he told me about painting by hand/eye or grid method. He says he has difficulty with painting by hand/eye and doesn't like the robotic nature of grid method. So I told him if there was a 'point' method where he picks the points of interest from an image and just scale it up or down the paper. He was confused he thought it was still the grid method and I always have difficulty explaining my thoughts. So I made him a simple demo using desmos just scaling the points to whatever paper size he is using. He tried it and he's been using it for 4 years now using the same link.
I do agree that the main problem here is the education system. I got really lucky because I realized early on that grades meant nothing (especially as a I got older). I didn't drop out but I wasn't too hard on myself. To the education system's credit, it wants a tangible way to measure intelligence and this is currently the best one that they thought of. It is improving especially since schools are adapting more to the individual's skills and inclinations.
As a history person “useless” mathematics is what drives human innovation, without the accumulation and study of “useless” knowledge human advancement would be slow, inefficient, and utilitarian. Or in other words I completely agree.
Is Utilitarian a bad thing?
Probably for the same reason we actually should learn geology or geography or basics about plants.
Because if we DID, things like the fires of California could have been avoided or mitigated because people would understand that the geography of that area was one big matchbox waiting to go off.
Replace that second sentence with : Expand our intellect in our spare time and make better mental choices.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
As a math teacher, I don’t bother trying to argue for its usefulness. Yes, you learn skills like how to follow instructions, be detail oriented, or recognize patterns, but they’ll never learn those lessons if they are expecting it. We learn best when we are not expecting to learn.
That's terrible. No wonder most avoid - if not dislike - math. Only few would bother to explain the why and its goal. It's hard to feel motivation when you don't even known where you're going.
@@ultimaxkom8728well there is no reason or goal for learning math other than knowledge accumulation. Applied fields are where you learn math for a goal and are given a reason. The math used in those fields is calculus, linear algebra, differential equations. Mostly.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
I don't know if math helps with critical thinking, tbh, but it does train our brain to think the stuff we need but would not be able otherwise. For example, we make models all the time when dealing with finances. Or, for another example, calculus may sound impractical but once you get the gist of the idea, you'll be shocked by how often you'll catch yourself seeing derivatives and integrals in stuff that is basically counting.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
I am currently in college, and math is my favorite subject. some times it doesn't make sense, I get it, maths can be hard some times, but that doesn't mean it is completely useless. Personally, doing a lot of maths has made my thinking power better. It teaches you the ability to think critically. You definitely earned a sub 👍
Thank you! Love to hear about a fellow math enjoyer
Great video. As a high schooler, I’ve been thinking of this same exact questions everytime I’d have compelling questions on my math tests, however, this explanation was able to make me enjoy what I’m learning more!
Glad it was helpful!
I was the slowest kid in 5th grade math, er, arithmetic. Hated memorizing. Then, in 7th grade, I discovered how math related to other things like interpolation. Would switch from math to chemistry to physics and back to the related and needed math every few months. By ninth grade I was checking out calculus books from the library. I then found math incredibly easy but only once I connected it to something. Once I understood a relationship and use remembering stuff became automatic.
It's hard to benefit from something you hate, I could learn critical thinking from many other subjects too
*A.* Memorization. Knowledge interpolation. Mystery-like extrapolation.
*B.* Calculation. Understanding extrapolation. Puzzle-like interpolation.
The critical thinking math teaches is quite different than the others.
Math is about sorting that information inside the Brain. So yes learning math is key to build a foundation to build architecture many different subject inside our brain.
Maths personally really helped me handle multitasking (albeit small-sacel multitasking), it really is mental exercise.
One of the main reasons people fail to solve problems is because of their inability to be brief, tranquil and factual in verbal communication. Contempt for simplicity and accuracy is probably the number 1 reason for unsolved problems in the real world, outside of the classroom.
I like the argument in this video. It is a great argument however it is flawed. The uselessness of math is not much of an issue. Take something that you enjoy (playing sports, watching some time of movies or shows, listening to some type of music). Most likely that activity is "useless" to you beyond its enjoyment. However, since you do it, and you enjoy it, you will find a justification for it (you can justify sports because they keep your body healthy, or spending time into pop culture because it keeps you up to date with your culture. Even people who enjoy recreational drugs or even more harmful activities can find a justification for doing it). But the justification is an afterthought (we trick ourselves into thinking that the justification is the reason to do the activity, but it is more likely that doing the activity is the reason why we find a justification)... The fact is that it is not important whether something is useful or not, what matter is whether you enjoy it or not (and unfortunately, the education system does a good job killing the enjoyment of math)
True, math can help you with your critical thinking... but so can many things (even taking bets at vegas can help you think critically if you do it seriously)... It is true that if you "cheat" you don't develop your own skills... but perhaps it is time to wonder, why do people "cheat" if it is not in their best interest? Well, this is a problem of alignment. You cannot cheat when your goal is selfimprovement. But you can cheat when your goal is to get a degree. From that, we begin understand why people cheat.
As a mathematician I can say that math is certainly not useless. The framing is intended to level with those who see math as something inapplicable to their lives. I completely agree, very well said!
Very long story, I graduated a year early from High School, but my education really doesn't go past 3rd maybe 4th grade (I can barely do basic division) and decided not to do college. But I spent my child and teen year building carpentry skills and doing armature mechanical engineering, and through none of that did I need anything more than multiplication and division. I've accepted that I'm not smart academically, it's still kinda embarrassing when I talk to people 5 years younger than me and they're shocked I don't know any algebra, but I also have a job I enjoy and make good money doing before I was even an adult (and I don't have any debt). Meanwhile the younger people I talk to are stressed and not enjoying life, which is sad and mainly an issue with our education system and not math its self.
Anyway, my point is to just provide another view from someone who isn't educated. I agree that math can help develop critical thinking, but I also use myself as an example of why you can still live a meaningful life without it. Hope more people see your video!
Absolutely! Thank you for sharing your perspective!
Yep
You can go pretty far without education in life
But education is a
Safe way
No risk
Study 10-20 years
Job
Very safe
Whereas no education
Very risky
Unless you got backing from family or sum
Thank you so much! Just subscribed!
"This video is sponsored by Duolingo's new Math course!"
Finally a real human being. Really great channel! Keep going! 👍
Thank you! Will do!
Wrote a long ass commen about how the four-card problem illustrates the limitations of applying our intuition in unfamiliar settings, giving various examples of how math has help me reveal the fundemental motifs connecting new ideas to seemingly unrelated, known concepts - halfing my study time and allowing me to spend nearly all of it on multimodal, higher order learning. I then accidentally refreshed the page, closed the laptop in frustration, but came back to let you know how well your message resonnated with me.
In general, critical thinking might be vital today more than ever. Knowing how and why people get the four-card problem wrong (denying the anticedent and affirming the consequent) could be useful. It might be a crucial skill in a time when the majority of the polulace often fail to identifying the logical fallacies used in the rhetoric of the people in influential positions of a society where the vastness, variability, and availability of information grows rapidly by the hour.
This one got a bit long as well.. Anyways, I'm excited to see what you'll make in the future!
I really appreciate you! I'm so glad my message resonated with you! I will definitely look more into the four card problem when I have some time as I am unfamiliar. Thanks!
I've actually had to use "useless" math in game development :P
The mathematics behind game development is fascinating, I watch a lot of videos explaining that kind of thing.
Oh my god women are real
TV shows portray math genius as human calculators no wonder they look down on us.
I seriously hate that portrayal. I can’t even tell some people I’m a math major without them saying something like “Your a math major huh? Then what’s 3452 times 576?”
this is so painfully real lmfao
This is a great video Ryan! Keep up the good work!
Thanks!
2:34 I don't understand how using a calculator is cheating. A calculator can multiply two numbers for me, but I still need to know which two numbers to multiply
If you’re learning about multiplication in school and your teachers hands you this homework:
2x3 = __
5x3 = __
4x4 = __
If you use a calculator that would certainly be cheating and you wouldn’t learn how multiplication works.
Later on you might be solving an integral, and if you’re using an integral calculator to do your whole problem then that would also be cheating. No one would probably care if you used a calculator to do multiplication in that scenario, but that’s only because it is assumed you already know how that works so it’s not worth your time.
See how it depends a bit on the circumstances?
@@Alex-02 That makes sense. I have no clue how I didn't think of that.
IF YOU´VE READ THIS COMENTARY YOU MUST SOLVE THIS EQUATION (you have no choice
x=log5(3)-log5(2)+1
Math isnt fun when i cant understand it and me not doing well means i fail
Great content , Keep Going . I’d appreciate your thoughts on a question that’s been on my mind , do you think everyone can learn math with enough effort or are there people who simply can’t, no matter how hard they try? Is there such a thing as "math talent" or "genius," or is it all just a matter of hard working and practice ?
Your really right , loved your video
Thanks for watching!
@@RSSALMath anyways i been thinking math isnt intently useless math finds it application in wildest of topics in sciences, computer science and economics and other more like in physics lets take example of topology and some people see it as useless but its application in quantum mechanics and other fields of studies
Do you think practicing certain types of math even after the class concludes is a useful way to retain your mathematical skills? For instance, I want to continue practicing discrete math and combinatorics through the provided textbooks even after the classes conclude.
Absolutely, the best way to retain math knowledge is to use it regularly. Because I teach calculus 2 I am very proficient in the integral and series calculus even though I took the course over two years ago.
The people who learn "useless math" the best also make the best lawyers, surgeons, actors, musicians, traders, coders, etc. They have such high "base stats" in the game of life that they can do almost anything. It's ridiculously OP!
Sometimes, math feels like an elaborate prank on my brain, but I love it anyway. One minute, I’m confidently following axioms, and the next, I’m questioning reality over infinity and the nature of numbers. It’s humbling (and mildly offensive) when concepts like 0.99... = 1 or the placement of irrational numbers on the number line leave me staring into the void. Yet, somehow, I keep coming back for more.
I really appreciate your mix of math and philosophy, because, let’s be real, after enough math, you either start philosophizing or completely lose it. We need more of that; exploring not just how math works, but why it makes sense (or stubbornly refuses to) in the bigger picture.
Cheers!
Thank you! Check out my video on time if you haven't already :)
Love the "you either start philosophising or you lose it." cx
Wasn't Einstein that said something in the lines of "Mathematics is the only certified way of becoming insane"?
I agree, but I would add that math also has to be taught right in order to be useful, especially in schools. If you can cheat your way through math classes by memorizing formulas and using an electronic calculator, your teacher (or the curriculum they have to stick to) is doing it wrong.
At my school I never really liked math lessons even though I was very good at it and participated in all the math competitions (Math Olympiad etc.) that were offered. Those were actually interesting and much closer to "real" mathematics, as you'd have to find proofs and write them down in a logical, understandable way. Something you almost never do in the normal math lessons (in Germany).
Now chatGPT is a different beast, that can actually --to an extent-- do the logical reasoning and proof-finding for you, especially for the kind of easy problems you would give to students in schools. I wonder what society might be like in the future if people develop the same mentality to things that AI's will be able to do, that they have towards things "ordinary" calculators can do now:
"Oh I won't need to be able to do simple arithmetic, I always have my calculator app!"
becomes
"Oh I don't need to be able to think critically or problem-solve, I'll just ask chatGPT!"
I completely agree. I used to be a Computer Engineering student, but have now switched to Psychology. Despite this, I'm minoring in Mathematics. When people ask me why, or if I'm a genius, I tell them no, and that I, in part, do it for the reasons mentioned.
Unrelated to the video, but how manageable is studying both a math related field and philosophy? I'm currently a freshman in highschool and have been considering doing something similar, like physics and philosophy or something, but i haven't seen many people going down the same route. Just curious about the work load, how busy you are, opportunities after college, things like that. (Great video btw, you earned a sub)
Thank you! For me getting the two degrees has been very manageable. There is a surprising amount of overlap in the kind of thinking required by my degrees. Though, I went into my undergraduate with about 50 credit hours, so my workload has not been anything crazy at any point. I would say go for it, there is a kind of free creativity that happens in philosophy that balances the strictness of physics and math. Pursuing two degrees in very different areas like math and philosophy makes you appear as a very well rounded student which is something that can give you an edge when applying for anything.
New sub. Great video🙏
Thanks!
Great video, great channel!
Thanks for the visit
Good way of thinking.
This why I’m business
whats the background song?
Great video.. could you please make a video on the real world applications of calculus please.
Im a second year stats/data science major but want to know more pure math. Personally, i just do math cuz i want to. Its a selfish thing really, but u could also morph that into me loving math. Tho i know this attitude can clearly change, and honestly me struggling with high school level math in probability stuff embarassed the shit out of me to the point of wanting to quit the course, i still just want to know some more math for my own sake.
No, math past a certain point is useless generally to the public. There are few careers in which you will utilize such advanced math, and I believe that math middle school should be optional because of that. No one I know that isn't in an advanced technological or mathematical career recalls any math they learned and has never used anything more than multiplication or fractions. Clearly, unless you plan on going into an occupation that requires abstract or advanced math, it is pointless. Your argument that it is the only subject that promotes critical thinking is absurd as well. Aside from the fact that those who have a disdain for math will not be open to learning skills besides those of face value, ALL subjects are designed to further critical thinking skills, especially the far more core and connecting subject of English. You find much more human connection, which is what matters chiefly in life, within the other basic subjects, something like History or English. Yes, math is exceptional in aiding in critical thinking skills, but other subjects are just as if not more efficient in such tactics.
I fear you misunderstood
Это все круто конечно, но разве этот видос не посмотрят по большей части американцы, которые в десять лет не могут умножать хотя бы двухзначные числа даже на бумаге?
In America, a large portion of students of all ages see math as frustrating and pointless beyond school.
@RSSALMath это тупо. Вселенная - математический объект и, раз уж мы в нем живём, стоит понимать хотя бы базис его законов
One might argue that the universe is not inherently mathematical, however our representations of it are. I agree with you, though, it is disappointing how math has become stigmatized in America.
@@odryblueburn3899 That's very obvious, but it's incredible how most people don''t see it like that
@@RSSALMath кто будет спорить с этим, познает мир платоновых идей, оставшись лишь идеей в нем, но не физическим воплощением🐘
I strongly disagree that math is the closest to a critical thinking class. Only applications of math require critical thinking. English or science classes promote critical thinking way more.
English requires literacy and comprehension, science requires memorization and experimental design, but math requires creative problem solving skills and an understanding and intuition of concepts beyond their definitions . Which of those would you say is critical thinking.
Though certainly math is not the only place where critical thinking is necessary. I don't make that claim.
@@RSSALMath Math also requires literacy and comprehension and memorization. When you do the lab portion of a science class it's not just memorization. Your description of what math requires sounds more like a description of what science requires. Math is defined and ruled by definitions and what comes from them, which is powerful generalizations. Rarely do math problems require creativity, most times you either know the math to do the problem (and you just have to realize that) or you can't even begin the problem.
@@whatever6874Have you ever studied university-level maths?
@ILoveMaths07 lmao. Have you ever brought math to reality? Also be more specific about classes.
Yo lil bro
Cool hair
I disagree. I am not a math major but i am pretty enthusiastic about math. And i would say really nothing after basic algebra matters and will really "train your brain to think" that much. Except discrete maths and especially proof writing and formal logic. This does indeed teach critical thinking but learning calculus won't teach or train anything outside of math.
The only way i could see this being false is if a student develops a system for metacognition. Which happens extremely rarely. Math is intuitive. Most people don't have this george polya style thinking where they use a specific methodology to solve problems consciously. Even when people try to get creative and look at a problem differently, it will usually be without any order and may not even work
I have to disagree, your argument is analogous to saying that although bench pressing is great, a football player will never need to bench press another player on the field. That's simply not what it's about. Using your brain to navigate math is like training a muscle, when you use it in a highly specific way, you find that in other places it performs much better. A football player will never bench press another player but he does use his chest when defending.
I would recommend studying higher level maths if you truly believe that math is intuitive. A lot of mathematics is highly counterintuitive. The time spent critically thinking about a problem that is difficult to even understand in the first place is invaluable to your brains information processing and problem solving capabilities in general.
@@RSSALMath true and i understand why you think math is counterintuitive. You have this sort of maturity in mathematics that enables you to think about mathematics and its problems like how a mathematician should, which allows for solving problems that are extremely hard and take a very long time. But that's not calculus or any highschool mathematics i encountered. The problems most people face are usually intuitive and very rarely do people need to truly think critically and creatively. I still do think mathematics and every other subject should be studied the way they are since they still help maintain an educated society.
Oh my god the unwise fool
I find higher level math more theoretical but it kind of trickles down to everyone else eventually.