I don’t agree with this. As you get better and do more problems you DO start to understand it. In the beginning you might not, but like he explained in the video, you look at the problem in a different way and do end up understanding the mechanics
It's a combination of the fact that *they usually are* especially smart, they've probably had a good *education* to really draw out their full potential, and they typically have years of experience. All of that multiplies itself like crazy. And if they're passionate about what they're doing, then WATCH OUT! And if you're at the opposite end of the spectrum on these things, then your perception is going to make it seem even more extreme. Lol 😅
Couldn't agree more. I had great ones; they WERE smart but always prepared even if they had taught the same class for years. After teaching HS math for 20+ years, great questions from students led to different ways of approach. And, learning to be creative on the spot to explain questions and topics.
i totally agree. my basic mathematics fundamentals improved after tutoring at a learning center for so many years. the repeated exposure and experience definitely helps.
I agree with you 100% Wizard. It's the fact through teaching over and over they relearn the subject matter, and often times from a distinct perspective. This also gets enhanced by the interaction with students, as they offer a new angle, or open a line of reasoning that the professor never noticed prior.🤓
I remember sitting in a lecture hall of about 100 with only five of us students in the Cosmology class at a college in Dublin.The subject horrified me and solving the unsolvable seemed to be no chance. My lecturer who was a few years older than me waltzed us dimbos through this material at a breathtaking pace and made the material accessible and presented us with a few questions .By the time I had ridden home on my bike my brain had leaked all that work and those questions seemed impossible and had to be in the in-tray next day. In the presence of our lecturer we felt invincible then reality slapped us in the face we really were and are dimbos. Of course that was a million years ago and our pathetic lecture notes were our pathetic attempt to remember those few seconds in the moment of genius.
Just imagine the sheer joy that person who first saw a Telescoping series must have felt. Uch, my heart when I first saw one of those! The leap of thought that took something intractable and made it simple.
Also, professors and other experts form *communities* with each other, which creates a special *culture,* in which they then have a *lifetime of immersion.*
I am trying to switch to higher-level math but I always get nervous around math teachers, there is this invisible force that just makes your heart rate elevate and cause anxiety
BEWARE THE POINTY VECTOR FIELD!!! Seriously, don't get all stressed-out: if you show up with questions (Write them down.) that demonstrate you've been working on the material, an Instructor should be more than happy to help. Often, misunderstanding a definition of an entity is the biggest roadblock to understanding mathematics. Discussing entities which do and do not conform to a definition forms the basis of enlightening questions.
@3:15 "I don't know how to do that" made me chuckle! I agree! On the last day of last semester I told my university physics teacher (Mr. Hage), that he made it look easy. He was modest and explained that he had been doing it for about 3-4 decades. Definitely one of my fav professors so far! I wanted to add that I took your insights for last semester when I was enrolled for university physics. Though, I thought I was going to have to retake the course after I failed the first exam, I passed the class with a B+! Currently taking calculus II as well! You have helped me (You still are) with your advice, wisdom, and experiences!! I want to say, thank you. ✍ P.S. I bought a "old-looking" timer you suggested when studying (It looks like a barometer!!) P.P.S. I will admit that the timer has made me jump a few moments whenever time runs out🤣
There's an expression in medical education that "even the good tea needs time to steep" and we have to take this to heart. There's lots of talent out there, but it takes practice every day over time to really get good. If a professor has two decades of experience on you then it's going to show. Also, those were two decades where the person knew they wanted to be a mathematician and were focused, whereas for other folks in the 3rd year PDE course it's like maybe I want to be a doctor or an engineer or in finance or whatever and they are also learning biology or materials or economics at the same time, the level focus is different.
Many math instructors said they only understand math better when they start teaching. You become better when you teach something over and over. So, if you did well in Calculus 1, you will understand it better even if you were to teach or tutor only Pre-calculus. In other words, becoming better at 'lower level' math will help you to understand better the next level in that same type of math.
It’s easy to get blinded by the magic. Think of it your a level 20 Paladin and your teacher is a level 50 Mage. I’m just trying to make a Final Fantasy reference. If you did something everyday for decades of course it’s going to look easy. If mathematics is repetition then every year, decade, that person is so efficient at the task, everything that is superfluous is deleted, it’s all about practice and confidence. Don’t let it get you down. If you work hard enough and practice it’ll be instinct.
I can't remember which physicist it was, perhaps Einstein or Feynman, but their message was to really understand something teach it to someone with no knowledge of the subject.
I agree even though I could never hope to even come close to being a math teacher much less a professor. Practice, practice, practice works in many functions of life whether it's academics, athletics or your chosen profession. The more you use something the better you get at it.
I have a different feeling about that. Of course, teaching something is a great way of learning that thing (for me, it's the best way). But I've been a professor for 14 years now, and I saw several of my colleagues who just memorised the solutions. They couldn't go beyond the scope of what they're teaching and couldn't generalise the methods from outside of it. The last example I got was from undergrads Linear Algebra. I was dividing the class with a colleague, and he struggled with the basic exercises. I once asked him why was he struggling, and he explained to me he never got the grip of that beyond the class. At the end of the day, it drills down to who you are and what your interest is in the subject. Anyone who is in love with maths and solving things and questioning can get far by teaching. Not all teachers/professors have that curiosity, though...
Let's be mathematical about this. Assuming a prof has say ten years of experience teaching Calc for instance and that he teaches two sections per semester and one in summer...he has essentially taken that class 10 (2+2+1) times. Or about 50 times, refining and adding to his knowledge each go round. Imagine how good you'd be if you took Calc 50 times.
One of my professors (physics not math) said: the best way to learn a subject is to teach it, as it forces you to not only understand the topic, but also learn to explain it.
the case with math is similar to that of a forbidden foreign language. those who dare seem smart by those who don't. math professors, even the smartest ones, fall into the same pitfall (pun) other people do.
Do they expect graduate students for math to solve math problems without a calculator in graduate school and expect them to remember all the techniques and formulas needed for every class from memory?
Hi Math Sorcerer, I recently discover your channel and I'm loving it. I am currently studying calculus and linear algebra but I have a question related to my daughter's learning. She is at elementary school, fourth grade. She is struggling a little with her learning. I don't want her to get frustrated with math so I try to help her but I feel like I am confusing her more than helping. Have you ever talked about books, or the best ways to teach elementary schools kids? Thank you.
Have you bought her "Everything You Need to Ace Math in One Big Fat Notebook" ? I wish I could go back in time to 1974 and give my 10-year-old 4th-grade self that book. It may be a little ahead of 4th grade, but get it now. I would also recommend Khan Academy. It's free.
Short answer, because they are academically smart, just like every professor. Well, almost every professor. I had one teaching data structures and algorithms, who I caught several times not knowing basics of the topic.
@@TheMathSorcerer I am getting a hectic lot of information by communicating with graduates & students from Eastern Europe. They tell me what they've been taught in their schools & universities. I know one guy who graduated from Moscow State University, which is Russia's equivalent to USA's Harvard University. He tells me stories about professors including some of world's renown nuclear physicists. I am recently learning keywords in languages for searches. I already know some French and German, so I love reading works of French & German mathematicians. Now I'm learning Russian and Ukrainian for math sake.
@@pinklady7184 interesting. for my curiosity, where are you from? I have read about the way mathematics is taught and encouraged through institutions and clubs etc in Eastern Europe.
And I've also found out that with older professor who are also passionate about math, they always find a way to make it simple. And that's one of the biggest pleasures in math, answering a problem that gave you resistance
it's like John von Neumann said, “young man, in mathematics you don't understand things. you just get used to them”
I don’t agree with this. As you get better and do more problems you DO start to understand it. In the beginning you might not, but like he explained in the video, you look at the problem in a different way and do end up understanding the mechanics
I've always seen my teachers and professors as GODS. And the most unforgettable thing of all was seeing them all *debate* each other! 🤯🤩😅❤️
I've seen myself as level 1 goblin and profs as lvl 1000 raid gods 🤣
Experience = doing it.
The human interaction of teaching (and having Problem Set Parties with one's classmates) is a huge part of that experience.
It's a combination of the fact that *they usually are* especially smart, they've probably had a good *education* to really draw out their full potential, and they typically have years of experience. All of that multiplies itself like crazy. And if they're passionate about what they're doing, then WATCH OUT!
And if you're at the opposite end of the spectrum on these things, then your perception is going to make it seem even more extreme. Lol 😅
great comment!!!!!!!!
Couldn't agree more. I had great ones; they WERE smart but always prepared even if they had taught the same class for years. After teaching HS math for 20+ years, great questions from students led to different ways of approach. And, learning to be creative on the spot to explain questions and topics.
i totally agree. my basic mathematics fundamentals improved after tutoring at a learning center for so many years. the repeated exposure and experience definitely helps.
Me entering in the examination hall remembering that you yesterday replied to my comment and feel even more confident !!
I agree with you 100% Wizard. It's the fact through teaching over and over they relearn the subject matter, and often times from a distinct perspective. This also gets enhanced by the interaction with students, as they offer a new angle, or open a line of reasoning that the professor never noticed prior.🤓
I remember sitting in a lecture hall of about 100 with only five of us students in the Cosmology class at a college in Dublin.The subject horrified me and solving the unsolvable seemed to be no chance. My lecturer who was a few years older than me waltzed us dimbos through this material at a breathtaking pace and made the material accessible and presented us with a few questions .By the time I had ridden home on my bike my brain had leaked all that work and those questions seemed impossible and had to be in the in-tray next day.
In the presence of our lecturer we felt invincible then reality slapped us in the face we really were and are dimbos. Of course that was a million years ago and our pathetic lecture notes were our pathetic attempt to remember those few seconds in the moment of genius.
Just imagine the sheer joy that person who first saw a Telescoping series must have felt. Uch, my heart when I first saw one of those! The leap of thought that took something intractable and made it simple.
Also, professors and other experts form *communities* with each other, which creates a special *culture,* in which they then have a *lifetime of immersion.*
I am trying to switch to higher-level math but I always get nervous around math teachers, there is this invisible force that just makes your heart rate elevate and cause anxiety
BEWARE THE POINTY VECTOR FIELD!!!
Seriously, don't get all stressed-out: if you show up with questions (Write them down.) that demonstrate you've been working on the material, an Instructor should be more than happy to help. Often, misunderstanding a definition of an entity is the biggest roadblock to understanding mathematics. Discussing entities which do and do not conform to a definition forms the basis of enlightening questions.
@3:15 "I don't know how to do that" made me chuckle! I agree! On the last day of last semester I told my university physics teacher (Mr. Hage), that he made it look easy. He was modest and explained that he had been doing it for about 3-4 decades. Definitely one of my fav professors so far!
I wanted to add that I took your insights for last semester when I was enrolled for university physics. Though, I thought I was going to have to retake the course after I failed the first exam, I passed the class with a B+! Currently taking calculus II as well! You have helped me (You still are) with your advice, wisdom, and experiences!!
I want to say, thank you. ✍
P.S. I bought a "old-looking" timer you suggested when studying (It looks like a barometer!!)
P.P.S. I will admit that the timer has made me jump a few moments whenever time runs out🤣
There's an expression in medical education that "even the good tea needs time to steep" and we have to take this to heart.
There's lots of talent out there, but it takes practice every day over time to really get good. If a professor has two decades of experience on you then it's going to show.
Also, those were two decades where the person knew they wanted to be a mathematician and were focused, whereas for other folks in the 3rd year PDE course it's like maybe I want to be a doctor or an engineer or in finance or whatever and they are also learning biology or materials or economics at the same time, the level focus is different.
Your last paragraph is spot on. I never thought of it that way, but it seems obvious.
Thank You! I Loved Your Answer, To This Question! Knowing This Is Empowering And Confidence Building For Students! Thank You, For All Of Your Help!
I like that your advanced calculus professor couldn't help you with partial differential equations. Definitely true that no one knows everything.
Yeah he had no idea at all. It's totally normal too, nobody knows everything:)
Many math instructors said they only understand math better when they start teaching. You become better when you teach something over and over. So, if you did well in
Calculus 1, you will understand it better even if you were to teach or tutor only Pre-calculus.
In other words, becoming better at 'lower level' math will help you to understand better
the next level in that same type of math.
That’s what the Feynman method is
It’s easy to get blinded by the magic. Think of it your a level 20 Paladin and your teacher is a level 50 Mage. I’m just trying to make a Final Fantasy reference.
If you did something everyday for decades of course it’s going to look easy. If mathematics is repetition then every year, decade, that person is so efficient at the task, everything that is superfluous is deleted, it’s all about practice and confidence.
Don’t let it get you down. If you work hard enough and practice it’ll be instinct.
I can't remember which physicist it was, perhaps Einstein or Feynman, but their message was to really understand something teach it to someone with no knowledge of the subject.
Me: *thinks I'm smart*
John von Neumann: *appears*
Me: *backs away slowly...*
I agree even though I could never hope to even come close to being a math teacher much less a professor. Practice, practice, practice works in many functions of life whether it's academics, athletics or your chosen profession. The more you use something the better you get at it.
We appreciate the amount of information we receive just by watching your videos. God bless you.
I have a different feeling about that.
Of course, teaching something is a great way of learning that thing (for me, it's the best way). But I've been a professor for 14 years now, and I saw several of my colleagues who just memorised the solutions. They couldn't go beyond the scope of what they're teaching and couldn't generalise the methods from outside of it.
The last example I got was from undergrads Linear Algebra. I was dividing the class with a colleague, and he struggled with the basic exercises. I once asked him why
was he struggling, and he explained to me he never got the grip of that beyond the class.
At the end of the day, it drills down to who you are and what your interest is in the subject. Anyone who is in love with maths and solving things and questioning can get far by teaching. Not all teachers/professors have that curiosity, though...
Excellent comment, thank you so much for posting this!!!
Let's be mathematical about this. Assuming a prof has say ten years of experience teaching Calc for instance and that he teaches two sections per semester and one in summer...he has essentially taken that class 10 (2+2+1) times. Or about 50 times, refining and adding to his knowledge each go round. Imagine how good you'd be if you took Calc 50 times.
So the secret to learn anything is to teach the same thing over and over?
@@kevinyonan9666no, it’s that if you do a lot of repetitions of something, there’s no doubt you will be good at it.
@@kevinyonan9666 It's never the same. Each time you learn more.
One of my professors (physics not math) said: the best way to learn a subject is to teach it, as it forces you to not only understand the topic, but also learn to explain it.
the case with math is similar to that of a forbidden foreign language. those who dare seem smart by those who don't. math professors, even the smartest ones, fall into the same pitfall (pun) other people do.
Young man, in mathematics you don't understand things. You just get used to them. - John von Neumann
Happy to see the family of Math lovers growing soo fast 🥰❤️🤗
Ed Witten and Terence Tao are two mathematicians and Phycisicts I'm aware of that understand multiple subfields of math.
Do they expect graduate students for math to solve math problems without a calculator in graduate school and expect them to remember all the techniques and formulas needed for every class from memory?
Epic hair styles (including beards) contribute to perceived genius.
Thank Einstein for that.
I agree.
Hi Math Sorcerer, I recently discover your channel and I'm loving it. I am currently studying calculus and linear algebra but I have a question related to my daughter's learning. She is at elementary school, fourth grade. She is struggling a little with her learning. I don't want her to get frustrated with math so I try to help her but I feel like I am confusing her more than helping. Have you ever talked about books, or the best ways to teach elementary schools kids? Thank you.
Have you bought her "Everything You Need to Ace Math in One Big Fat Notebook" ? I wish I could go back in time to 1974 and give my 10-year-old 4th-grade self that book. It may be a little ahead of 4th grade, but get it now. I would also recommend Khan Academy. It's free.
@@kevinthompson9953 I will check it out. Thank you.
@@carlaflores4034 You're most welcome. Good luck to you and your daughter.
Because they are smart!
Hello sir, are there any math topics you’d like get better at or relearn? It’s definitely challenging to remember every math topics.
Yes of course! There is so much math!
Short answer, because they are academically smart, just like every professor. Well, almost every professor. I had one teaching data structures and algorithms, who I caught several times not knowing basics of the topic.
Good morning sir
Could you explain the Tracktenberg method of multiplication by 3?
In Eastern Europe like Russia, students in high schools and universities have to give oral presentation of maths.
that's really interesting! That must help a ton!
@@TheMathSorcerer I am getting a hectic lot of information by communicating with graduates & students from Eastern Europe. They tell me what they've been taught in their schools & universities. I know one guy who graduated from Moscow State University, which is Russia's equivalent to USA's Harvard University. He tells me stories about professors including some of world's renown nuclear physicists.
I am recently learning keywords in languages for searches. I already know some French and German, so I love reading works of French & German mathematicians. Now I'm learning Russian and Ukrainian for math sake.
@@pinklady7184 interesting. for my curiosity, where are you from? I have read about the way mathematics is taught and encouraged through institutions and clubs etc in Eastern Europe.
Have you gone through all the books in the background or is it just for show?🎉
Really large book on special functions to have as a reference book?
You should also note that not all phds have the capability to become a professor. Especially the top tier institutions.
Does consuming pizza help with the difficult homework?
Good morning sir ji
And I've also found out that with older professor who are also passionate about math, they always find a way to make it simple. And that's one of the biggest pleasures in math, answering a problem that gave you resistance
If you walk smart, talk smart, MATH smart ... it's because you're smart ! 😀
They seem smart because they ARE smart.
hy ٫ What books should I use to find out about application of matrices ?
Are u mathematics teacher?
He's a professor
Why do trousers look wearable?
The real question is, when are you going to get a haircut? :)
His hair is the secret to his math smarts. It shall not be cut.
ROFL
when delilah gives it back to samson, when newton loses his wig, when the crows leave the tower of london
Not even long. He can get longer ;)
I would say the same argument applies to physics professors as well.