Does Failure Help You Learn Math?

In this video I try to answer a question I received from a viewer. Their name is Eda and they are asking about failure and mathematics. I will also show you one of my topology books. It is called Introduction to Topology and it was written by Bert Mendelson. Do you have any advice or opinions? If so, please leave a comment below.
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Thank you:)

[@Weareonenation303]

Mathematics naturally has a ton of trial and error. You can definitely learn from your failures, the problem is failing during a test. If you're studying math for fun, failing isn't nearly as punishing given that nothing is on the line.

[@evanurena8868]

Doing math in school teaches you how to fear failure where doing math for fun teaches you how to learn from failure.

[@peaelle42]

a well-crafted test offers questions at various levels of difficulty. because honestly, whoever sets the test really doesn't wanna take more time out of his/her research to set yet another bloody test (and then make you sit through it, mark it, go through all that admin shebang, etc) just because you failed it and require a re-exam..

[@xylh5085]

The only reason I got halfway decent math was pushing through failure. The sheer satisfaction of getting it right is like the satisfaction of clearing a difficult board in Castlevania III or Fire Emblem! Slowly math started eating up all of my videogame time because the elementary algebra clicked for the first time and unlocked a beautiful world, and I'm currently studying proofs for a similar reason. Math is so open-ended and the only limits are your creativity imo.

[@pinedelgado4743]

Without at least ONE failure in our lives, we would NOT be human. Failures happen so that we may learn from them to be better than before.

[@me.es.1023]

First you have to love it, and be aware that sometimes it will no love you back. Second the perseverance & stubbornness of a mule, the subject is not for the faint of hard. It can be the hell of challenging and time consuming. Third it is your life so you be the judge of what that failure or failures will do to add or to subtract whatever objective you have in mind.

[@mohamedmounir6770]

Failure are the building blocks of success. You have to accept it and make it a reference point for moving forward and toward, until you reach the pinnacle of success.

[@daniellindner826]

Thank you for this video. This video spoke to me. After failing my test i was devastated. I looked for books to learn math from on KZbin and found your "learn math from start to finish " video in 2020, bought some books and since then i learned an incredible amount of math, now math excites me.

[@BuddyNovinski]

Failure is part of life. -- It's what one does with it that counts, preferably as a learning experience. I gave up on linear algebra around this time in 1977, and I've spent decades putting the missing pieces together. As I've written in LinkedIn in 2015, there are three major reasons for the frustration: lack of background, lack of visualization, and lack of practice. Yesterday I just found out that I missed a concept in analytic geometry because I never had analytic geometry! It's a caclulus book with visuals!

[@clonebin0]

love the mtg themed coasters!

[@ProtoMaxoid]

The MtG coasters are awesome

[@patrickgambill9326]

That signed part is so cool! I love the quote with the signature

[@HYPERLOG]

Congrats on 500K!

[@ripperduck]

Problem with STEM is students are at the mercy professor teaching quality. So many profs hasted teaching undergrad courses because it took them away from research, or chasing after research money. You have to realize many of your teachers are awful teachers, aren't prepared, or don't care if students learn, and that indicates a failure of the department, not students...

[@BlueGiant69202]

Dr. Roger Schank, PhD is a major advocate for Mentored Experiential Learning and admits that as a professor he did not regard teaching as part of his job and didn't care about undergraduates. Dr. Schank was a math major that got into artificial intelligence research. A professor that really did care was the late Edwin T. Jaynes who tried very hard to find ways to impart to his students in one year what it took him two years to learn. Professor Jaynes regarded the quality of education to be important to the quality of research.He tells some good stories about researchers vs. educators in a retirement party speech.

[@HellonWheels777]

When I'm working on my math exercises, I wait until I come up with a satisfactory answer to the problem, then I check my work in the back of the book. I leave the wrong answer where it is. Then I write the right answer with a note stating what I did wrong the first time and what I can learn from my mistake. I just started with discrete mathematics self studying after watching a video of yours about how to learn math in the ground up. I really didn't get much education growing up and I've always wanted to be good at math. That is what I have started working toward in 2023. I refuse to accept that I'm always going to be bad at math.

[@argonwheatbelly637]

Spectacular failures are a most excellent learning tool!

[@83jbbentley]

Never to suffer would have never to been blessed. - Edgar Allan Poe -

[@spousal-ant6086]

Happy 500k subs!

[@colinmaharaj]

Yes but after a failure, you need to make corrections. You need to know you've failed. If others know your fall, but not you that's dangerous.

[@God-ld6ll]

feedback i instead call it. Failure could be more useful for if you are getting feedback by flying a jet vs a pure math test.

[@tamaszsombortolvaj7517]

Answering the question: yes, it does. Ive failed many math tests during my first semester (or more like, I didnt get too many points). This fueled me with anger, which made me prepare in advance, so that I wouldnt fail again next time. In my 2nd semester, I failed one of the math subjects. Fortunately, I got the signature, so I had to only do the exam again. During the break, I managed to reach out for a maths teacher, who helped me understand many things, which I didnt previously. Thanks to him and my own efforts, I got a 4 (grade B), which now raises my current semester grade mean.

[@yuvrajsingh099]

Great video.

[@bandhanmondal4685]

Try, fail , take feedback, learn....

[@Manuel-pd9kf]

Great book

[@ahmedabbas3998]

Most of math's failures come from distraction. A distracted mind forgets alot, and forgetfulness leads to errors.

[@vrchacho]

You mention near the end of the video that the absolute function is a metric on the real number metric space. A bit pedantic, but perhaps it's more correct to say the absolute of the difference of two real numbers is a metric, since we need a two parameter function to define a metric. Other than that, thanks for the insight you share in the video :) Everyone struggles with failure in math, it's important to know how to deal with it.

[@AmbushEveryone]

Failure always helps me learn a way not to do something. Pretty helpful sometimes lol

[@ronaldjorgensen6839]

questions with no answer can make you rethink it answers are perceptual shift

[@BlueGiant69202]

This is a subject that I would love to discuss over donuts full of coffee . I would add that one should emphasize that in order to fail, it's necessary to DO math and to reflect on the failure, preferably with a mentor/coach/teacher to guide one. That's one reason why I like Brilliant and the Khan Academy mastery exercise software and videos. Failure should be the beginning of learning and an assessment tool not a filter. In talking about education reform in 1921, H.G. Wells in his book, "The Salvaging of Civilization", used his own student problems with mathematics to point out deficiencies in the educational system. Hermann Weyl was a mathematician that contributed to physics and although his efforts in physics seemed to be failures and Dr. Einstein claimed his math led to physical effects that were clearly incorrect, they created a tsunami in physics leading to things like use of Group Theory and Gauge Theory. "Weyl's gauge theory was an unsuccessful attempt to model the electromagnetic field and the gravitational field as geometrical properties of spacetime." " Einstein admired Weyl’s theory as “a coup of genius of the first rate”, but immediately realized that it was physically untenable. After a long discussion Weyl finally admitted that his attempt was a failure as a physical theory." - Gauge Principle and QED by Norbert Straumann "Here I must admit your ability in Physics. Your earlier theory with g(prime)ik = λgik was pure mathematics and unphysical. Einstein was justified in criticizing and scolding. Now the hour of your revenge has arrived." - letter of Wolfgang Pauli to Hermann Weyl Note on the absence of the second clock effect in Weyl gauge theories of gravity by Hobson, M. P. and Lasenby, A. N. It seems to be turning out that Weyl's mathematics contained something that Einstein missed because of confusion over the physical interpretation of the mathematics and use of physical principles used in General Relativity. "Once again I am impressed by Einstein’s profound physical insight, which served him so well in assessing the significance of mathematical equations in physics. Of course, his conclusions depended critically on the mathematics at his disposal, and displacement gauge theory was not an option available to him." - Gauge Theory Gravity with Geometric Calculus by David Hestenes Dr. Albert Einstein, PhD stated that he wasted two years working on General Relativity because he misinterpreted the meaning of a mathematical result and in response to a child's letter regarding problems with math, he encouraged the child to persist by confiding that he also had trouble with math. It was true but he was very proficient with mathematical tools and he was working with advanced mathematics where the meaning of equations and the physical interpretation of the math wasn't clear. He didn't have Mathematica and 3-d graphing software to help him. Dr. Einstein was even corrected more than once by mathematicians and he once said that since the mathematicians [like his professor Minkowski] got into Relativity he didn't understand it himself. That was a quasi-truth but without help from his wife and his friends like Marcel Grossman, and fellow physicists and mathematicians, Dr. Einstein would not have been working with tensors and nobody would ever have heard of Gauge Theory. www.askamathematician.com/2009/12/q-do-you-exactly-know-what-einstein-meant-by-do-not-worry-about-your-difficulties-in-mathematics-i-can-assure-you-mine-are-still-greater/

[@whatrtheodds]

Hi, I have a freeze response, that causes me to blank out and miss important content in class. I know I'm capable but sometimes I shutdown and it all goes. I study a subject for hours do mock tests get good scores at home, then I'll get asked in class and I will go completely blank. :(

[@pdraper919191]

If you never fail, then you are not taking risks... so that means you are not challenging yourself enough.

[@Trekki]

If you make a mistake try to make another one as fast as you can so the last one will be forgotten quickly.

[@Maths_3.1415]

Failure is very important to succeed in life :)

[@a0z9]

Todo fracaso va precedido de 1/100 éxitos. Todo éxito va seguido de 100 fracasos. Entre dos éxitos siempre hay 100 fracasos. Cada fracaso es la centésima parte de un éxito

[@emale03]

This book is in Dover paperback, 3rd edition, thanks MS.

[@metildajoseph5265]

Greetings Mr.Professor, Thoughts : - Good Topology Textbook and also a rare amazing Classic copy.. Response : ' Learning is a Progressive Process accompanied by Success and Failure in all aspects ' Thanks... Take Care, Professor. With regards, RanjithJoseph (R.J)

[@karar5387]

One day i will master Algebraic topology and differential geometry, algebraic geometry and conquer the world..

[@dimitrioskalfakis]

it's complicated and it depends. if the failure is overwhelming or repeated you must have a solid objective and tenacity to prevail over the turmoil. if you do manage to stay afloat, so to speak, you definitely learn a few bits and not just math. do not rely on failure ;-)

[@gmcenroe]

Nice book, I found the same hardcover on ebay for $20, bought it.

[@TheMathSorcerer]

Oh that is an awesome deal! Very nice!!!!!!

[@boogerie]

I don't know if it "helps" but I know it's unavoidable

[@sicko_the_ew]

"And if you meet with Triumph and Disaster/ And treat these Imposters both the same / Yours is the world, and all that's in it ... " Whatever you did for success (which is often just a feeling of vanity you can flatter yourself with) you didn't do for math. So you did it, to some extent, distracted. So it carries with it a certain element of failure. Try harder next time. If you never fail, you're obviously not trying very hard. Chances are you're holding back from your true potential, just to protect sensitive feelings - just for vanity's sake. Holding back like that is worse than just "being vain, and so bad" (I mean bad, schmadd, who cares?); it's allowing your own sense of your own value to be determined by something extrinsic like some arbitrary concoction of circumstances you decide to deem to be a "success" (something you allow yourself to be all vain and conceited about - your permission to yourself to be an unpleasant person, if you're not careful with that). So you're handing over a piece of your own sense of self worth to "them" (since we construct our vanities the way sheep would construct theirs, if they had them - i.e. by looking at "what everyone else is doing"). You're outsourcing your inner sense of your own worth to people who will probably not cherish you as much as you should cherish your own dear self. To the extent that you need to be weighed according to success or failure, you don't need to bother to figure out what you weigh, yourself. Don't worry, other people will always be there, ready and willing to either judge you, or size you up, cut you down to size, or be nice to you and value the parts of you that are of real value, instead. There's always someone else willing to put in the effort it takes to run you down. No need to do it yourself. The extreme side of an immunization against the harmful, and infectious aspects of a pursuit of success (which can be a fairly good thing, if properly tamed and moderated) would be to have a high toleration of failure. Don't beat yourself up. Everyone fails unless they're playing it so safe that they can't. And you're not worth what your "success measure function" has as its output; you're worth what your worth measure function outputs. Don't muddle them up; it's bad math to muddle things like that. Maybe the idea is something like: Pursue success; don't let it pursue you. Is failure worth anything on its own? I'd say yes. It's something you can use to make yourself strong, for instance. It's your sharpening stone, too. Approach something with a "blunt" understanding - lacking in rigor, for instance - and it's a little failure that might show you there's something wrong with it. Without the failure there's nothing to motivate the change. (That's excepting things like timely help that saves you the trouble. There's so much more to life than success or failure.) Especially if your reason for learning math is extrinsic (probably the case for most people), failure is one of those things the world outside will pay you well to overcome. "Problems" (since you could think of a mathematical "failure" as just a "problem waiting for a solution" a lot of the time). If you encounter a lot of "failure" (or the many things we incorrectly call "failure") on your mathematical path, you'll have had to attack a lot of problems with determination and intelligent strategies to overcome these. You'll be a good problem solver - or better than someone protected better from the danger of being confronted with problems than you've chosen to be. So in this sense the more intractable the problem you're facing, the better it's equipping you to deal with problems "in the real world". But what is failure, really, anyway? If you tackle one of the toughest open questions in math, today, and you don't solve it, is that a "failure"? Is that the right word for it? If you tackle the toughest open question you're facing with the math you've managed to learn, to date (whatever that is) and you don't succeed right away, is that a "failure"? If you try and fail repeatedly, and then give up in despair, what's the right word for that for this particular problem? I don't think it's always "failure". Change context. If you try to write a beautiful poem, and it ends up ugly, is that a failure? I suppose so, but that's only because you maybe set yourself a goal that's too far beyond your reach. If you try to build a space elevator in the back yard, you're probably going to fail the same way. It seems harsh to condemn the failure, though. So are there any "condemnable" failures? Are there "excusable" failures? What do you need excuses for? Who do you have to report to and account to? (Yourself, probably? - So why not just rig your inner jury to be kinder to you?) I don't know. Those are not rhetorical questions. Maybe it's a good strategy to reframe the difficult things as just "problems" (which have neither Triumph nor Disaster imposturing upon them'; just solutions or an unsolved status). Problems, challenges, puzzles - where solution is not "success", and non-solution is not "failure". You could still have a sometimes useful concept of "failure" to go with that. A failure would be something like "giving up too easily"? (But also hanging on too long.)

[@arturopadilla4619]

Hello math sorcerer! Im taking calculos 2 in 2 weeks. Any advice?

[@radiatedracer3830]

I had to take Calc II 3 times. It was definitely a stepping stone for me. Most would blame the teacher or the subject for their failure. I knew for a fact I was a dumbass and had to make the effort to change it. Haven't failed a class since.

[@mostafaashraf5619]

Hello How can i study abroad in a foreign university? How can i have a student's loan to pay the expensive university fees ? How can have the material and study it with myself without getting a certificate?

[@---00764]

Can you recommend anything help me in mathematica, to apply the fixed-point method?! I urgently need it🙏🏻

[@Wandering_Horse]

So what gives with the coasters I have seen in the last several videos? You kinda move them around and figgit with them throughout the videos.

[@firstname4337]

if failing helped you learn then I'd be a freaking genius by now

[@giuliorondelli2141]

well you must love math to learn from failing, otherwise you won't be looking at failure as a "success"

[@kx4532]

Failure gets you kicked out of school.

[@olafusiolamide27]

You are meant to do practice questions, learn from the mistakes. Do more practice questions with the additional experience. Repeat. By the time the exam comes you have so much experience that you get a top grade!

[@kx4532]

@@olafusiolamide27 School is a sorting system to test for those with the means to have learned the math before taking the class.

[@peterers3]

@@kx4532 if your wealthy to afford peace and silence to study you already have a good foundation...to put in all the effort you want to put in to succeed.

[@kx4532]

@@peterers3 It's fine and dandy but failing is not ok in math. You get kicked out.

[@BlueGiant69202]

Yes, academic suspension is done but really is contrary to the aims of education. The blame is usually placed on the student rather than on the professor or institution. A lot of assumptions are made about why the student failed rather than actually find out the real reason. My calculus professor always emphasized the importance of doing the textbook exercises and we had a weekly calculus lab with a graduate student teaching assistant. I actually did worse my second time around in an introductory statistics course. I was amazed when I read "Probability Theory: The Logic of Science" by Edwin T. Jaynes because Professor Brewster fit Jayne's depiction of frequentists and Ronald Fisher perfectly. I wish I could have had Professor Jaynes as my professor and I love his posthumously published book edited by Larry Bretthorst.

[@Iamrightyouarewrong]

no.