In his book, Hot to Solve it, George Polya, Mentioned: (How To Solve It, PartI, In the classroom Purpose,page6.paragraph 7) "It is foolish to answer a question that you do not understand."
You are more than just smart mathematician to me. Thanks for giving light to us, math teachers. Mr. Polya, you are father of every sincere teacher. Rest in Peace. I’ve read and read his brilliant books but this my first time to see video. I can help but find myself in tears.
Feeling Very Happy !sir ,today I have Observed your Lesson & learned how to get answers by students with joy and happiness in maths teaching .💐 You are Great sir.I'm proud of You 👏
There is nothing more valuable than a great teacher and I put George Polya in that category. This was a wonderful video demonstrating his teaching method.
Having read Polya's book on Problem Solving, could not resist watching this video. What an absolute delight ! Anybody interested in problem solving will love this. You may also learn some geometry & maths. My takeaway is what "teaching" should be !
Today I bought 「How to solve it」in Japanese. I went to book store because I want to know How to solve difficult problem and make an effort. I had wondered How many students solve difficult problem before I met this book! Although I am 19years old now, his books seems brilliant yet!
Yes! thanks for sharing this. I hope MAA will let this remain public. It is in many libraries in video form and so I hope the intent of sharing can be recognized here!Genuine math teachers will enjoy the video and learn from it!
So basically, guess but guess with conviction and a curious mindset that could be proven wrong at any point but possess the courage to derive a new conclusion based off of reasonable induction.
"Teaching is not a science is an art...." says Professor. I believe it is an art, indeed and it is a science notwitshtanding. It compels to it not for the bragging but for the natural will to make science and knowledge worthy to any mind, approachable to any heart, however feeble and fragile that is capable to unleash the will to know in love of knowledge of life, its cause and the result of it...yourself, humanity, world and learn the laws, principles, morality, the ground and unshakeable drive to preserving it. It is a science that prepares the many on the path of science and the many on the path of their lives. However, I do believe that is beyond it, that is an art indeed. No I am going to listen to rest of his lesson.
Great. Sometimes ago I saw a marvelous video showing Moore teaching 8 years old kids which is marvellous and in the same spirit, I cannot find it again on youtube anyone an idea? Note: About the move between guessing/and correcting read also "Proof and refutations" of Imre Lakatos.
Typical of every math class I’ve ever taken. Ridiculously easy, ridiculously easy, interesting, wtf is he taking about…..lost. Still a brilliant lecture never the less.
A teacher's job is to give answers to questions. A pupils job is to remember these Q&A problems. Guess solutions to questions with no answer or incorrect formulation.
A big fan of his classic book How to Solve it. However, I will say that his teaching was ideal, not very realistic. If he was in a high school class of today, maybe he could not conduct an instruction as well as he demontrated in the video. Who were his students? Undergraduate students and/or graduate students at Standford University. They had much stronger motivation of learning than students in many schools of today. And the knowledge base that students had in his class was much more solid than that of most students in today's schools.
An extremely good idea, exercise and practice would be to try and to keep a timed, recorded journal of your own life, of your own each and every minutest to the most major-est of thoughts, both scientific and artistic that you have, your day to day, each and every, savory and unsavory, pleasant and unpleasant experiences and of your own reactions, responses, take aways from them , in a genuine, sincere attempt and effort to make sense of your own life as also of life in general and of this crazy world you happen to inhabit and to indwell. It would make for an engaging and engrossing maybe even an enlightening read. Even the life of the tiniest of virus is not a completely uneventful, and immemorable one.
I must say I'm totally disappointed in this man. I always knew about his discoveries in discrete mathematics, I learned he was a legendary teacher. So be it. But his answers on the blackboard are just wrong. I can easily prepare a set of 3 planes dividing the space into 7 parts, for instance, or 4 planes into 10 parts. He completely disregarded the question of perpendicularity posed by this very clever girl (planes being all perpendicular one to another is only the simplest case of perpendicularity!!). I also don't like how he uses the word "random", which has no application in mathematics. Let's add up 3 and 3 and hope we get 7 this time... I mean, mathematics is not a random trial. And choosing planes which aren't perpendicular is in no way "random". This is a good manual of how not to solve problems.
Yes randomness exists in mathematics, and I think you misunderstood him, of course you can contrive a scenario where 4 planes can divide space into 10 parts but then you’re not answering the question, the point of investigating something that’s random is to take into account the extreme cases as well. In other words, random in this context would mean the maximum number of subspaces that results from 4 planes cutting a space. Randomness forces you to take every case into account and assumes that anything less than the maximum can be achieved. .
@@kaiz8597 Randomness does not exist in mathematics. Mathematics can deal with randomness that supposedly exists in the external world (although that is another story). What he meant was a special case and a general case. I don't remember, now that two years have passed, what the video was about but rather than me misunderstanding Polya, I think you misunderstood my comment. Go read it again.
In his book, Hot to Solve it, George Polya, Mentioned:
(How To Solve It, PartI, In the classroom Purpose,page6.paragraph 7)
"It is foolish to answer a question that you do not understand."
Nothing equals an instructor with this mindset; a passion for both his subject and respect for his students efforts!
You are more than just smart mathematician to me. Thanks for giving light to us, math teachers. Mr. Polya, you are father of every sincere teacher. Rest in Peace. I’ve read and read his brilliant books but this my first time to see video. I can help but find myself in tears.
Feeling Very Happy !sir ,today I have Observed your Lesson & learned how to get answers by students with joy and happiness in maths teaching .💐 You are Great sir.I'm proud of You 👏
Mathematics is Life. It is the most basic and universal of Languages, the Root of all.
There is nothing more valuable than a great teacher and I put George Polya in that category. This was a wonderful video demonstrating his teaching method.
Having read Polya's book on Problem Solving, could not resist watching this video. What an absolute delight ! Anybody interested in problem solving will love this. You may also learn some geometry & maths. My takeaway is what "teaching" should be !
I prefer the word mathematics to the English word maths.
Wish all his lectures were recorded for posterity. If anyone has more of these, I request them to upload all for the benefit of everyone.
SHASHANK TANGWAN GREATEST MATHEMATICIAN IMO
@@davidgarza995 That just proves you haven no clue. There is no "greatest"... this is not a well-ordered set.
yeah really, i would love to see more
i came here after reading his quote,
If you can't solve a problem there is a smaller problem:find it.
Here's another one: change the problem around....solve another problem.
@@reggaefan2700 how can changing the problem help?
@@ChandravijayAgrawal change it to a simper related problem.
@@reggaefan2700 oh okay
I've read some of George Polya books, but nothing compares to watch the magical moment of the classroom.
Today I bought 「How to solve it」in Japanese.
I went to book store because
I want to know How to solve difficult problem and make an effort.
I had wondered How many students solve difficult problem before I met this book!
Although I am 19years old now, his books seems brilliant yet!
You are lucky to have found such a treasure at 19.
It's a brilliant book! You may also like some TRIZ material.
i wish i was younger when i found this book, i just notice this awesome book at the age of 21
@@desmondleeyunghang i found it at 28 .
"Teaching is giving opportunities to students to discover things by themselves"
TEACHERS TEACH "THE ROAD" BUT STUDENTS HAVE TO WALK "THE ROAD"
Plato wrote a play with Socrates on that theme
thinks*
Yes! thanks for sharing this. I hope MAA will let this remain public. It is in many libraries in video form and so I hope the intent of sharing can be recognized here!Genuine math teachers will enjoy the video and learn from it!
i love this professor. I wish some of my lecturers were like him in college.
You missed an important thing. Polya was not an ordinary professor. He was an outstanding mathematician much more than a professor.
What a great share.
I'm surprised something like this wasn't on UA-cam as well.
It works BOTH ways: embedding your problem into a harder one as well. Can give us insight into the problem at hand.
Nothing compares to hearing Mr.Polya
this is such an amazing gem
Thank you so much for having posted this. ❤
GREAT AND LEGENDARY TEACHER.
still amazes me that his age surpasses hardy, littlewood, and neumann(the student he was afraid of). Legend
Hey Scud missile, thanks for the download and a blessing to see our great Uncle George Polly up front and personal.
Only if all kids could have access to teachers like him!
So basically, guess but guess with conviction and a curious mindset that could be proven wrong at any point but possess the courage to derive a new conclusion based off of reasonable induction.
Thank you so much! Yes, this helps; it brings the book to life.
What a legend Polya is.
Great lecture and very interesting problem.
@41:00 15 is correct for 3 dimensional space, if space was 4 dimensional, then 16 would be the correct answer.
Thanks for uploading such a wonderful and rare video. Keep sharing
Now I know what it feels like to be in the presence of a master.
I Love this glamorising the mathematic✨
"Everything serious that we learn is based on inductive evidence"
Timestamp?
Thanks a lot for sharing . Desparately needed today.
What a wonderful man, and such a excellent video. Thank you very much.
Fantastic!!! Thank you very much for this gem.
Where is the "LOVE" button?
Fabulous comment!
Katy Lee
that is only visible to uploader
The only video of legend
"Teaching is not a science is an art...." says Professor. I believe it is an art, indeed and it is a science notwitshtanding. It compels to it not for the bragging but for the natural will to make science and knowledge worthy to any mind, approachable to any heart, however feeble and fragile that is capable to unleash the will to know in love of knowledge of life, its cause and the result of it...yourself, humanity, world and learn the laws, principles, morality, the ground and unshakeable drive to preserving it. It is a science that prepares the many on the path of science and the many on the path of their lives. However, I do believe that is beyond it, that is an art indeed. No I am going to listen to rest of his lesson.
Very good, instructive lecture/demonstration. I found the last anecdote actually moving....
2:34 If you wish to learn it clearly, students have to discover it
2:41 First guess then prove
54:00 Everything serious that we learn is based on inductive evidence.
54:24 What is important in reasonable guessing
this is the guy from Godfather 3, Eli Wallach, Connie's godfather who dies in the opera after eating his beloved candies.
Great Teacher!!!!!
thanks for the upload!!!
Thank you so much for sharing this.
Amazing! Thanks for sharing!
Great. Sometimes ago I saw a marvelous video showing Moore teaching 8 years old kids which is marvellous and in the same spirit, I cannot find it again on youtube anyone an idea?
Note: About the move between guessing/and correcting read also "Proof and refutations" of Imre Lakatos.
Hablo sólo español pero con sólo verlo ya encanta. XD
The old music brings me back to good ol' days. hayss, wish i could bring back good times where there still no covid :( uWu
Its nice reading comments by old people like you grandpa! :)
@@louizcanales7353 your mouth is "pasmado" ah
observation
pattern, law
generalisation
test your guess
analogy
Typical of every math class I’ve ever taken. Ridiculously easy, ridiculously easy, interesting, wtf is he taking about…..lost. Still a brilliant lecture never the less.
you did a great job
Excelent, thanks
Almost all mathematics teacher know who George Polya is
Thanks for group theory
this was great, thanks
This is one that vids we can call "Heritage of Humanity"... OMG, this is surreal.
A teacher's job is to give answers to questions. A pupils job is to remember these Q&A problems. Guess solutions to questions with no answer or incorrect formulation.
A big fan of his classic book How to Solve it. However, I will say that his teaching was ideal, not very realistic. If he was in a high school class of today, maybe he could not conduct an instruction as well as he demontrated in the video. Who were his students? Undergraduate students and/or graduate students at Standford University. They had much stronger motivation of learning than students in many schools of today. And the knowledge base that students had in his class was much more solid than that of most students in today's schools.
Parts or phases what do you mean
Hey, Dr. Scratchansniff!
What was the question i couldnt understand his accent?
am very amaze the solving mathematics.
Honestly feel like I've been cheated by my professors after reading Polya and Rudin. They carried me through undergrad.
Rudin? The paid service?
you mean, not monetized?
thanks
Where did you find that? Do you have it's address?
shoutout pi
3:33 lmao
361 views, wow.
62k
@@谢初玲 68k
An extremely good idea, exercise and practice would be to try and to keep a timed, recorded journal of your own life, of your own each and every minutest to the most major-est of thoughts, both scientific and artistic that you have, your day to day, each and every, savory and unsavory, pleasant and unpleasant experiences and of your own reactions, responses, take aways from them , in a genuine, sincere attempt and effort to make sense of your own life as also of life in general and of this crazy world you happen to inhabit and to indwell.
It would make for an engaging and engrossing maybe even an enlightening read. Even the life of the tiniest of virus is not a completely uneventful, and immemorable one.
52:47
Same
🙏
Shout out ME1B
Accent is so thick i can barely understand, can someone do the subs?
You can turn on Live caption in music control on the top right beside of extension button in the Chrome browser, but it is for English only.
very good
Who else is here for class?
Any body from fps?
The absent minded professor is lecturing on the makings of coming up with a theorem in the classroom.
I must say I'm totally disappointed in this man. I always knew about his discoveries in discrete mathematics, I learned he was a legendary teacher. So be it. But his answers on the blackboard are just wrong. I can easily prepare a set of 3 planes dividing the space into 7 parts, for instance, or 4 planes into 10 parts. He completely disregarded the question of perpendicularity posed by this very clever girl (planes being all perpendicular one to another is only the simplest case of perpendicularity!!).
I also don't like how he uses the word "random", which has no application in mathematics. Let's add up 3 and 3 and hope we get 7 this time... I mean, mathematics is not a random trial. And choosing planes which aren't perpendicular is in no way "random".
This is a good manual of how not to solve problems.
Yes randomness exists in mathematics, and I think you misunderstood him, of course you can contrive a scenario where 4 planes can divide space into 10 parts but then you’re not answering the question, the point of investigating something that’s random is to take into account the extreme cases as well. In other words, random in this context would mean the maximum number of subspaces that results from 4 planes cutting a space. Randomness forces you to take every case into account and assumes that anything less than the maximum can be achieved.
.
Are you man of mathematics? 🙄
"random" is perhaps not the most valuable term (although correct) but "general position" seems better for me
but not possible in small dimensions ...
@@kaiz8597 Randomness does not exist in mathematics. Mathematics can deal with randomness that supposedly exists in the external world (although that is another story). What he meant was a special case and a general case.
I don't remember, now that two years have passed, what the video was about but rather than me misunderstanding Polya, I think you misunderstood my comment. Go read it again.
@scud1234 Pure gold! Thank you for this!