How Hard Do Smart People Work

Рет қаралды 25,259

Жыл бұрын

In this video I answer a question I received from a viewer. His name is Mohammed and he is asking about people who seem smarter and how hard they work. I will also briefly show you one of my Real Analysis books. This is the one by Royden.
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Пікірлер: 143

@MichaelWMann-kl5ty Жыл бұрын

When I was studying for my PhD qualifying exam in Real Analysis I would work in the morning and then spend the afternoon giving my brain a rest by working in the yard. The mathematician who finally proved Fermat's Last Theorem worked at home to keep his efforts a secret. He had 3 children under the age of five, who insisted on playing with Daddy in the afternoon after spending the morning working on the problem. That break made his effort more productive. The takeaway: Give your brain a rest, doing math isn't the same as digging ditches. Mixing challenging work with breaks to think about something else is the best strategy. Your brain can only do so much before it needs a break.

@douglasstrother6584 Жыл бұрын

... and those little squirts go from 15 in the blink of an eye.

@petrmasek4506 Жыл бұрын

I'm majoring in bioengineering, and I've realised this quite recently. Every time I tried to work for long periods, I tended to get tired and unmotivated. Breaks always seemed to me like a waste of time. Once I tried to go to the gym even though my schedule was packed, I realise, I was more productive then. Ever since I try to incorporate some physical work into my schedule. It really does help. Agree with you! (English is not my first language, sorry for that).

@Ensource Жыл бұрын

helpful comment! your brain will work on what you do not, consciously. same idea with sleep. "sleep on it" helps reframe an idea

@callmedeno Жыл бұрын

Not that I've done anything amazing, but my sense is that our brain works on math problems best when there are other inputs other than math. Same thing happens with art, when I go all in and just think about and do art I notice things go down an ever narrowing tunnel. With taking mental breaks and doing other things, when I return to art or a math after a few days / weeks everything is 'settled' and the water is clearer. Whereas after long periods of myopia it feels like the constant single-frequency vibration causes all the mud and sediment to make it hard to see anything

@douglasstrother6584 Жыл бұрын

@@callmedeno Our subconscious mind is under-appreciated.

@asbjrnandersen4765 Жыл бұрын

Faster =/= smarter.... Smart people are those who think deeply and originally, not those who solve some problem fast.

@crown_420 Жыл бұрын

Agreed

@JarodM Жыл бұрын

Also agreed~

@MrDerp72 Жыл бұрын

Yes, but in general smart people are able to grasp more complex concepts easier, which translates into having less difficulties solving problems, which usually means being faster. So what I mean to say is that in general smart ARE faster at solving problems, but that doesn't mean that someone that solves a problem fast is smart.

@tricky778 Жыл бұрын

Speaking of which who has thought deeply about the definition of f(A) being the image of A under f where f is any relation from X into Y and A is any subset of X... f(A) =equiv= { y in Y : y = f(x) for some x in A } being definitional equality I expect I can substitute f(x) recursively but that only works when X is a set of it's own subsets. Maybe when used in an equality relation proposition, the proposition is a set for every (x in A,y) in f but that looks like it won't extend naturally to every equation though I haven't ruled it out as unworkable. Does anyone know how to interpret this notation with consistent rules? Clearly f(x) is function notation and the relation is a generalisation st. the equality is mapped over the image of x rather than y being the image of x and we have a set of equality propositions of the same cardinality as the image of x but the fact we don't have denotational semantics is going to give a lot of sharp edges. Is this just a careless unification of two branches of maths or is it formally good?

@bargainbincatgirl6698 Жыл бұрын

But the TV shows I watched contradict you... checkmate! Now seriously, House was one of the shows where the doctors NEVER consulted a book or medical article and all the solutions were from a bolt of inspiration.

@TDG361 Жыл бұрын

I cannot consider myself a smart person, but I learned at an early age that dedication and hard work can take you a long way. In the beginning, I struggled with Mathematics and computer science, but I decided not to give up easily and try my best to understand the subjects at hand. After some time, I was able to do better than some of the best students in my class, and today it seems to me that I have a natural talent for computer science, programming, and problem-solving, although that might have come after several years of dedication and hard work. I think that most important than hard work is your motivation. I work hard not to be the best student or whatever, I worked hard because it was something I really enjoyed. I love to learn as much as I can, so I would grab my favorite book on whatever topic I want (mathematics, physics, computer science, etc) and would read it and solve the problems within it.

@lazyh0rse Жыл бұрын

Motivation should never be trusted, and you should always ignore how you feel at the moment and just grind, the time you have will forever be gone. I wasted so many years on the cycle of motivation and losing interest.

@rashedulkabir6227 Жыл бұрын

@@lazyh0rse Do you have research paper on this?

@lazyh0rse Жыл бұрын

@@rashedulkabir6227 yes, it's called "trust me bro" science

@marujob6619 Жыл бұрын

@@lazyh0rse 😂😂

@nihilisticnirvana 9 ай бұрын

that's really motivating :)

@GetOnTheSession Жыл бұрын

One of the beautiful things about mathematics is that it is so accessible. You can be of average intelligence and enjoy starting with arithmetic and then gradually learn as much mathematics as you want to or have time to.

@TheMathSorcerer Жыл бұрын

That’s such a good point👍

@douglasstrother6584 Жыл бұрын

To get the "WOW!" of Mathematics, I encourage people to start with a little bit of Georg Cantor's work on infinite sets, since we use Natural Numbers, Integers and Rationals in our daily lives. It's still striking to me that all three sets are the same infinte size ("cardinality", I know!), and that the set of reals has a greater cardinality than the former. Geometry is another great place to start due to its visual and tactile nature. All of the things that can be constructed with a compass & straightedge are astounding.

@gertwallen Жыл бұрын

Smart people are those who can deeply understand how it all works, and have the ability to explain complex things in a simple manner. A genius is someone who additionally can discover something that is not written in any book on Earth. Someone who is knowledgeable of the math tools and able to crank problems fast is not necessarily smart, he may just be an efficient engineer.

@douglasstrother6584 Жыл бұрын

Success = Effort * (Talent + Motivation) + "an arbitrary constant". I always lost points forgetting that last term.

@God-ld6ll Жыл бұрын

"Wu Wei, Not forcing. It is not that you don't cut wood, but it is that if provided that you want to. Do it along lines where it is easiest to cut.", paraphrase of Alan Watts.

@curtheisler1200 Жыл бұрын

I love this!! Thanks for sharing.

@God-ld6ll Жыл бұрын

@@sentientartificialintelligence Rowing 🚣‍♀️ vs ⛵️ sailing. A hypothetical different way of saying it, if it clarifies.

@ApolloTerra Жыл бұрын

okay here's maybe a piece of cool advice that ive been developing recently: do the work that you don't think you can. i've been thinking this for a while and a prof in grad school just told me this exactly. smart people have a higher barrier of entry on what problem they might attempt. spending time with the hard questions and doing them anyways is one of the quickest ways to level up from my experience. may not be helpful to your specific case, but making sure there isnt anything you're really shakey on is a good start i find

@ILoveMaths07 Жыл бұрын

I had a friend who was doing his master's in maths, but had a computer science background. He also had a job, so he would work for 10+ hours every day. He had to take undergraduate analysis and algebra before he could join the programme. He was unable to attend these classes as they were in the mornings and he would be at work, but he managed to ace them both. In his master courses, I believe he got all As. He didn't know maths well, he still doesn't like pure maths and he wouldn't get time to study thoroughly, but he would still get As. He told me that he wouldn't get time to solve too many problems, but he would keep thinking about the theorems and their proofs and applications. He would ensure that he understood every concept deeply. He didn't work hard solving tens of problems from every chapter, but he still made it. Now how do you explain that?

@meartin Жыл бұрын

Interesting

@vedant9637 Жыл бұрын

He is lying 🗿

@fishslab Жыл бұрын

Some people are different. Not all learning methods are applicable to everyone

@zzzzzzzjsjyue2175 Жыл бұрын

A lot of people who work very hard are used to it and under estimate how hard they work

@CrisOnTheInternet Жыл бұрын

What matters is not the amount of problems you solve but the types, if you know how to solve a type you only need to do a few exercises.

@godsofwar1186 Жыл бұрын

In order to answer the question first we must define several terms: 1. What is being smart and how do we quantify it? 2. What is talent and does talent work in every math situation? 3. What does working hard mean? Only after we give definition to the terms above we can begin to answer the question of Mohammed...

@faithlesshound5621 Жыл бұрын

That's putting the cart before the horse. If the question is, "How can I get ahead?" a good place to start would be, "How did others get ahead?" It's an engineering problem, not a physics question. If I remember rightly, Mohammed had noticed that smart people didn't seem to do a lot of work, so he thought he shouldn't either. In my time at university, kids aimed to be cool: being "brilliant" meant seeming to do no work at all. But those kids also disappeared from sight often, and I presume they were working their socks off. They must have found they worked better alone. Others find it better to work collaboratively. That may apply especially to "gaming" the exam: predicting questions from past papers and the like, and working out winning strategies. Others have gone before you, and you don't have to discover everything alone and for the first time. If you can, use your best times of day for the hard intellectual stuff: try not to do that before you go to bed. Wind down before you sleep instead. But don't forget that there's more to university study than classes and scheduled labs. To go further, you need to get involved in research, give presentations, and if possible publish ... so you need to volunteer for that, get involved in relevant clubs, and look out for internships.

@tricky778 Жыл бұрын

@@faithlesshound5621 I would suggest that asking how others get ahead will require that you not get ahead of them

@faithlesshound5621 Жыл бұрын

@@tricky778 Education is not a zero-sum game if we go for a spirit of proletarian emulation rather than capitalist competition.

@tricky778 Жыл бұрын

@@faithlesshound5621 EDIT, wrong comment wrong conversation, made no sense in my mental context but I thought I was posting elsewhere

@Ensource Жыл бұрын

it is all relative. you measure up to the majority.

@markharder3676 Жыл бұрын

Who's the little guy with a pearl bigger than his head? Is that the pearl of wisdom he's holding?

@TheMathSorcerer Жыл бұрын

It is:)

@MetapherTasse Жыл бұрын

Finally, but i honestly don't really prefer to work much because I just want get better at sleeping.

@ameanaf737 Жыл бұрын

Your videos push me and inspire me more and more ty very much, From tunisia

@sicko_the_ew Жыл бұрын

An alternative to competing with other people is to just "pick a good mountain". Find a sufficiently "impossible" task, and set out to accomplish it. Tell yourself you're a Hobbit, and the target is deep in Mordor, then make a brave quest there. The easiest such is to try and get 100%. (And give yourself at least some time to be disappointed instead of pleased if you "only" hit 99. It's wiser to be kind to yourself, and accept that in the end you can only do what you can do, and so forgive yourself for falling off Mount 100% instead of saving the world quite quickly; but a bit of disappointment can work just as well as "success". Often setting "realistic" targets just protects your ego, and doesn't expose you to enough pain and hardship, and other such character-building experiences - the stuff a real quest is made of. Smart people getting good grades without trying are failing (failing themselves) when they do so.) Careful, though. It's easy to be stupid about this (just like people get stupid about their various competitions in life - the kind of thing that makes so many little kids scream at people on soccer pitches, instead of just enjoying themselves - although the real danger is of turning oneself into septic person nobody in their right mind could like, even if they tried really hard - so you end up with only idiots as friends.)

@xaviergonzalez5828 Жыл бұрын

Thank you for all your suggestions. And it comes just when I need.......

@markmclaughlin3277 Жыл бұрын

one thing that changed my study habits was reading the book "deep work" by Cal Newport.

@ILoveMaths07 Жыл бұрын

Thank you so much... just downloaded the book! Will definitely read it asap.

@dimitrioskalfakis Жыл бұрын

the smarter you are the harder you work and in fact you should work! i have known much smarter people than me (both professors and fellow students) and they were never exempted from this - not to confuse effort in achieving good results with time invested in learning. at the very least you should work hard to make sure you are right and not missing nuances let alone the obvious!!!

@applefish745 Жыл бұрын

“You ask me if an ordinary person-by studying hard-would get to be able to imagine these things like I imagine. Of course. I was an ordinary person who studied hard. There's no miracle people. It just happens they got interested in this thing, and they learned all this stuff. They're just people. There's no talent or special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields that comes without practice and reading and learning and study. So if you take an ordinary person who's willing to devote a great deal of time and study and work and thinking and mathematics, then he's become a scientist.” - Richard P. Feynman

@TheMathSorcerer Жыл бұрын

This comment caught my attention. I thought, "wow amazing comment" as I read it. Then I realize it's a Feynman quote, wow. Thank you for this!

@applefish745 Жыл бұрын

No problem. In my opinion, I think there are two kinds of hardworking people: those who show their hard work, and those who are master at hiding their hard work(“smart people”)

@applefish745 Жыл бұрын

@@sentientartificialintelligence no problem

@dylutant Жыл бұрын

I was firmly in the middle of the pack until around the middle of undergrad (maths + physics), during ODE assignments if memory serves, I started asking questions and demanding myself to answer. You know, stuff like "I wonder if a 2nd order ODE could have two solutions, each of a different type of orthogonal polynomial" or "I wonder what an oscillator excited with external force expressed as a step (AKA Heaviside) or triangle impulse function or Dirac delta would look like." It wasn't about smarts, you'd know if you knew me, but more a combination of curiosity and having my 'toolkit' mature enough to intuit those problems intelligently.

@hussainfawzer Жыл бұрын

I too would love to have a math book from you.. (I don’t mind even if it’s really really cheap) Not because I couldn’t afford one but I love to have a math book from my idol… You inspire me a lot. If it’s not a burden, send me a book❤

@finrod55 Жыл бұрын

That Royden book is the exact text we used in my UNDERgraduate senior class in real analysis back at Cal in 1979. Except for the true geniuses in class we thought it was a bit too hard. One thing was, it was my first math text with NO pictures! (Well, it had a couple of diagrams). Don’t laugh-pictures are important for visual learners like me. Also, the author (and the instructor) didn’t allow proof by contradiction. That screwed me uo (and still does-I’m just not clever enough). Anyway, I still have the book and look at it now and then. It has good problems.

@joshual5597 Жыл бұрын

Hello. I love your videos! and as a math major, I find your videos really motivating especially when I get stuck with a math problem, or if there are proofs that I cannot seemed to wrap my head around. but I think that's what makes math fun and beautiful; you learn it by doing it. by the way, I'm also a fellow math major (pure math) here in the Philippines. pls continue making more math videos.

@TheMathSorcerer Жыл бұрын

I'm so glad!

@mellow-dandtherhythmoflife3239 Жыл бұрын

I would always do all the problems and typically found that the more complicated problems were at the end of the list. If you don’t intend on doing all the problems, try doing them in reverse order.

@moonlightcocktail Жыл бұрын

When I see a long series of boring simple problems, I usually try to write a lemma instead that generalizes them all so I don't have to go through the slog. Then by solving the general case I feel I get a deeper understanding of the problems than if I had solved them one by one. Then I end the general proof with "using this lemma, we can solve problems 3-20".

@kummer45 Жыл бұрын

There are far better smart people than any of us. The field medals for example. But should we get frustrated by it? No. Mathematics is a way of life. There are always gifted people that teaches us the right path. Let us thanks OUR lord for such individuals that makes our carpentry of mathematics a really beautiful discipline.

@Living_for_Him_Alone Жыл бұрын

Thank you

@markharder3676 Жыл бұрын

Mohammad, how do you know if someone, another math student for example, is smart? Because they perform well, do their homework faster, get better grades? If so, then the belief that they are smart or smarter is a tautology. I know they're smart because they perform well, and they perform well so they must be smart. Ergo, people who perform well are people who perform well. It means nothing, i.e. you can never know if people do better than you because they're smart or because they work hard. And you know that if you work hard(er), you will do well (better). Of course, working harder has its limits. On more than one occasion I've been surprised by how well I can complete a challenging task if I take a break for some social activity or other. Another point: I think that if you come from a background engaged in a particular line of work, or with similar experiences as those in which you are engaged, you grew up in a culture formed by an adaptation to those activities and requirements. That's why sons and daughters of say, politicians, often enter politics and succeed as well as their parents. George Bush and his son George W. Bush, or early 20th C. POTUS William Howard Taft and his son Robert Taft, an important mid-century American senator. I imagine the same must be true of mathematical families, and that's one reason Sorcerer's friend was able to do so well in math classes.

@83jbbentley Жыл бұрын

His logarithms are sweaty, knees weak, TI-84 are heavy There’s vomit on his Unit Circle already, his trig functions he’s forgetting, He’s nervous, but on the surface integral he looks calm and ready To drop anti derivatives .

@TheMathSorcerer Жыл бұрын

ROFL!!!!!!!!!!

@petrmasek4506 Жыл бұрын

great one

@nerd26373 Жыл бұрын

We appreciate the amount of information you've given us. God bless you always.

@greghansen38 Жыл бұрын

When I was taking physics, there was one guy I'm thinking of in particular who was clearly smarter than me. He finished his homework, got most of it right, and still had time to go golfing or go to the local bar for the Flabby Man Olympics (where the winner is the one with the score closest to AVERAGE). Meanwhile, I felt like I needed every available moment, and I relied on partial credit. Maybe he was just better at studying than I was. But I think some people are just plain smarter, they pick it up faster, they get their homework done faster, and they get better grades. It's true in athletics, I don't know why it shouldn't be true in academia.

@Maybe_the_Truth Жыл бұрын

The answer of do smart people work, is first smart people don't need to work hard on any given day compared to the average, essentially by definition, that's what makes them smart. So, you will definitely see smart people do very little work and get good or even excellent results on a wide variety of tasks. Of course, that smart people don't need to work hard on any given day and "do good" is not how they became smart or stay smart, but just a capacity that goes along with being smarter at whatever it is. So, that smart people can do A (not work hard today) and get away with it, doesn't mean that doing A (not work hard today) will result in smartness. Rather, it is just manifesting previous work, study and reflection on the subject matter. In terms of school, a smart person that's interested in the subject matter may also go and study much harder concepts in their spare time which renders the class material a lot easier and perhaps even trivial to them, that they don't bother to practice, but they are doing hard work already reading the next year or even years of course work in their spare time. This may not result in top results, but a smart person may reason that it's more interesting to explore the vastness of the intellectual universe and rely on their smartness to do well, rather than chase marginal gains on specific tasks they may not need in the future. Some smart people want to be top of the class for insert reasons and some smart people think it's smarter to economise energy to do other things; of course, depends on what they are trying to accomplish in life. But generally, the best way to conceptualise a smart person is that what they are completely dedicated to whatever they are focused on so there is no time set aside for work but their entire life and nearly all their mental energy is dedicated to understanding their areas of interest, so in this context the idea of working habits may not be so meaningful; someone who is truly thirsting for knowledge is always at the limits of what they are able to drink.

@SequinBrain Жыл бұрын

So many variables here: good/bad days, the intersection of preferences with what the test requires (you may enjoy factoring, I don't, etc.), the human brain being so complex and diverse it's impossible for science to adequately comprehend its several functions which gives rise to the fact of varying retention rates. A quote from Dune gets to my point: "For the others, we can say that Muad'Dib learned rapidly, because his first training was in how to learn." Figuring out what causes both memory and retention on a personal level is way more important than I have ever heard anyone in school explaining to any degree. Schools seem to do well on helping us with memorization, but not at all with retention, say 5-10 years after school. Brushing this off as "the student's responsibility" is both obvious and insufficient given today's major educational decline in nearly every field. So, find out what makes you both remember and retain (not always the same thing given longer time periods) and you still may not be smart, I know I'm not, but you should see some type of improvement. Since everyone's rates of both learning, hearing, remembering, and retaining are very different, making comparisons will yield less fruit than targeting your own weaknesses and acknowledging & shoring up your strengths.

@mannydossantos9603 Жыл бұрын

Intelligence, hard-work and discipline... not easy for young people affected by social distractions, but well-worth it.

@weselefigara Жыл бұрын

My advice would be that ability to concentrate/focus is incredibly important and it can be thrown away by doing things that dissipate your mind. I think it really helps to be on a sort of "information diet". I wholeheartedly recommend a book titled "The Intellectual Life" by A.G. Sertillanges, it calls it "a zone of silence". Also: great channel : )

@enigmatico6209 Жыл бұрын

I personally feel like some people is just very good at some things, or maybe they happen to like something a lot, and it takes them much less effort for them to learn or do that stuff than others. Personally I think that, in theory, we are all humans and we all should have, under normal circumstances, the same capabilities. But maybe we just show those capabilities only when we have enough motivation for it. Like I know people who is very good at math but maybe they might not be as good at CS as me, and the opposite. I might be better than them at CS but they are better than me at math. And I think that's a wonderful thing as well. "You do what I can't do, and I do what you can't do", as they say. Ultimately, I think it's not about being better than anyone else, but rather being better than you were before. I guess that won't help you ace your exams if you have to do exams. Perhaps not today. But in the future, who knows...

@TheReallyRealKim Жыл бұрын

I think really smart people find more challenging problems (like literally find harder problems or study harder/deeper subject) while the "normal" people like me struggle to finish the assigned problems.

@Ensource Жыл бұрын

"you go where you can"

@rauldempaire5330 Жыл бұрын

In my HO....for an average person it helps if you organize ans start planning study time, organize the study material, good note keeping,....(for math in particular)......adopt a problem solving strategy like the Polya method and work on improving your memory....

@jianhuang3434 Жыл бұрын

It is always pointless to consider your "talent." Extrapolating from the quote you mentioned, in fact, the most optimal course of action is to work as hard as you can possibly work as that is the only variable you have control over. This is of course in the case of taking a course where you are confined to competing in that specific course. I think a more general approach entails that you look for where you might have the most talent and have the most intrinsic attraction for a specific subject and then work very hard in it. In a controlled setting of a classroom all you can do is do your best and hope you come out on top. The hard part is doing your best. And even if less than your best is enough to be on top you should still do your best as practice. In the real world, you have another variable you have to account for which is: am I putting in effort in the field of work in which I am most naturally talented? If no, then you must find something that you both enjoy and are naturally talented in. In fact, enjoyment is not very important because if you are good at something you will feel good about it just by being good at it and out-competing others. Perhaps at that stage in your life, it won't just be about talent and the subsequent enjoyment but also whether you can derive purpose from it. That has been my journey. It is rarely useful to judge your performance in accordance to what others are doing. The only thing that you should focus on is your personal relationship to the work at hand; are you doing your best? Do you enjoy it? Do you drive purpose from it?

@mitchellm4197 Жыл бұрын

My advice, which is also my own advice to myself is.. focus less on others and more on concentrating all your energies on how you can become better and what is holding you back. This does not mean ignore others altogether, STEM fields are collaborative so it's important to work together sometimes and utilize your resources, such as 'The Math Sorcerer'. However, by focusing more on yourself and digging deeper into your own mind, your own internal battles you will get to know yourself much better and thus you will be better equipped when studying and facing difficult problems, because now you are attacking an actual target, rather than see what targets others are attacking... just my two cents I hope it's helpful!

@ctfholtz3257 Жыл бұрын

learn most things 3x speed, 10 days in math and learn real analysis, calculus did become easy,.. :-) executive function develops til age 30, is 30% behind in adhd. ""sit down and learn",..

@CrisOnTheInternet Жыл бұрын

I'm in the middle too, it's funny how when something is "easy" I'm left behind quickly if I don't even do the bare minimum.

@aikidograndmaster1781 Жыл бұрын

Royden is the worst book to learn graduate level Analysis, try The schaum’s outline of Lebesgue measure and integration by Murray Speigel

@lebambale Жыл бұрын

What distinguishes smart people from the rest (socially (!)) is "relevance". It relates to a natural ability of 'making sense' - of elements or environments - and reproducing relevance is an extremely contextual, complex and adaptive skill. Relevance favors pragmatic rational solutions, e.g. engineering. Highly perceptive people are capable to think of decisions that are a good fit (judging by evolutionary fitness) and devise plans that match circumstances at hand. So maintaining relevance is simultaneously also about an ability to determine, project and affect consequences. However, autistic and social 'smartness' are different aspects of this (but they do add up) - through autistic mode, constant values are attached to things (that in itself enables technology; i.e. describable physical properties we can measure); through a symbolic mode, (social) arbitrable shared meanings are constructed via discourses and it's the basis for most of the philosophy. Math have features of both, since it's an instrument to assess, evaluate as well as an instrument to do transformations of meanings and symbols, and to build models (!). In the end, relevance, fitness is all about the models. "All models are wrong, but some are useful." The really smart people are good modelers!

@Bran4901 Жыл бұрын

Lesson from my racing days: Swim with bigger fish, to get better. Embrace the challenge!

@TheMathSorcerer Жыл бұрын

Love it!

@fishslab Жыл бұрын

I think the opposite also applies: hard work can improve average talent

@a0z9 Жыл бұрын

Cuanto más brillante más se debe trabajar. El único lugar donde la brillantez está delante del esfuerzo es en el diccionario. Only place where success is before work is dictionary. When not in dictionary , both goes hand in hand

@FlaminTubbyToast Жыл бұрын

At least in America, the smart person doing x is a misnomer. In math specifically, observations of intelligence are usually just observations about mathematical maturity. This is especially important because a lot of math is intertwined. And problem solving in one sub-subject can generalize to multiple. I would say that talent comes from hard work.

@Ana8star Жыл бұрын

For anyone wanting advice. Read, practice, watch videos, listen to math problems with your eyes closed and let your resting brain allow math terminology to just swamp your unconscious. Then when actively practicing, consider how much relativity chemistry, astronomy and etc is involved in math. Your confidence will naturally increase and reading a textbook will become a manual that is desired. ✍🏻

@SimicChameleon Жыл бұрын

I believe it all about collaboration and team work for the maths. That other student from parent expert in math has help him become smart. Spend time with five other people and you become the average of them.

@LorenzoWTartari Жыл бұрын

In my experience the smartest students are the ones who study the most, a friend of mine is absolutely brilliant, way out of my league, but she also studies a lot more than me, a lot more than i could physically could .

@rich_in_paradise Жыл бұрын

I think clearly some people are smarter than others, but I also think that two things dominate raw ability: work and experience. You talked in the video about hard work, but could it be possible that your friend was better at math than you, at least for a while, because he'd done more math than you at school? Or maybe he'd been home tutored and had already covered some of the areas you were doing then? I see this all the time in programming - it's always much easier to write a particular type of program a second time compared to the first. There's this myth of the "10x programmer" - someone who's 10x more productive than other programmers. I feel happy calling it a myth because 10x just isn't a reasonable factor to apply to a human activity. But it is true that some programmers are much faster, but when that occurs it's usually because the person has a lot of experience in the area they are currently working in. Throw them some novel problem and they wouldn't be much faster. Anyway, my advice to the person with the question is: do all the problems you have time for. Familiarty is the key, not some notion of talent or smartness.

@brandonmanuel2842 Жыл бұрын

I watch your videos sometimes. You do have alot of math books. I wonder how many math problems are out there in the world? I am thinking there are infinite math problems to solve from pre algebra to calculus.

@Fekuchand_ Жыл бұрын

Great advice

@accolade.99 Жыл бұрын

man, someone must've really loved that book 😆

@capgains Жыл бұрын

I’ve been the one who gets it last. Yet from not getting it to getting it there’s a getting it and losing in that process. Very odd where in one moment I got it and one number can change or the problem can be written from whiteboard to paper and im like wtf is happening

@maxdominate2481 Жыл бұрын

I don't compare myself to anyone but myself. Having said that, the book GRIT reveals that a person's ability to learn can better so with passion, patience, and hard work you will get there. So, Mohammed should focus on that.

@ChechoColombia1 Жыл бұрын

Is there a way to apply math to muscle hypertrophy.

@JarodM Жыл бұрын

You can apply it to anything.

@gopalparam6401 Жыл бұрын

Dear Math Sorcerer, Thank you for the wonderful advice to Mr. Mohamed's question. It is useful to all of us. I was intrigued by comment that Real Analysis by Royden is expensive. In India the current version revised by Fitzpatrick is currently available for Rupees 575 or $7. Is this not a book about "Measure Theory"? Also, I have a request; will you please review a pair of old Russian books by Piskunov titled "Differential and Integral Calculus - I & II." Thank you!

@rochehoniball Жыл бұрын

I relate to you Mohammed! I completed my first year of University last year and I was baffled by my classmates, particularly in Math. They all seem so calm and collected and sometimes even bored in class while I was struggling to keep up. I felt like the dumbest person in the class. I pushed myself and worked incredibly hard and I managed to pass the class, but so did those people who never seemed to put in any effort. Sometimes my friends wouldn't even show up to class or they would walk out in the middle of a class because they were bored or tired, while I sat through every single class and did my homework as well as extra problems and I went to see my lecturer for more help which they barely did. At the end of the day those classmates did slightly better than me or got the same mark I got even though they really didn't even put in half the work I did. It's unfair and broke my spirit, I just don't understand how they do it. Don't misunderstand, they are my friends so I'm happy for their success, but the saying "what you put in is what you get out" does NOT apply in academics, I've seen it time and time again and it just doesn't work. It's sad but true, hard work will often go unnoticed and unrewarded and you must just find a way to carry on regardless...

@fencerlacroix2512 Жыл бұрын

I LOVE MATH AND I AM FIRST

@Vizorfam Жыл бұрын

Why do you love math?

@Vizorfam Жыл бұрын

@@Leo-qu2xo i was asking him why the op loves math

@InfiniteQuest86 Жыл бұрын

It's unfortunate that both Royden and Rudin wrote analysis books. So confusing. I actually got a copy of Royden from an NSA mathematician. Pretty cool.

@dont-want-no-wrench Жыл бұрын

i'm pretty smart (validated by SAT, etc), and i don't work nearly as hard as i should.

@Singularitarian Жыл бұрын

“The smarter the student the less work they do” This is so backwards. The most distinguishing trait of a genius is obsession.

@xybersurfer Жыл бұрын

@@sentientartificialintelligence interesting theory, but i suspect that the exposure doesn't have to be very directly related to the subject

@hansbaeker9769 Жыл бұрын

We used Royden's Real Analysis in grad school. I bought a copy in anticipation of taking the grad course in Real Analysis, but ended up never taking it. A friend of mine who dropped out of grad school over an argument with a math department administrator (that was in the 1970s and I no longer remember what their argument was about) went to work as a cook and spent his free time studying math. One of the books he worked his way through on his own was Royden's Real Analysis. He later teamed up with a grad student in another department to form a software company which they later sold. I lost track of him and have often wondered what he did next.

@AmmoBops Жыл бұрын

I’m as slow as a rock, but given enough time I can find a solution, like usually when I’m learning something, I miss a lot connecting the dots, but when I try to solve a problem, I go into deep thought and usually start to realize the stuff that I didn’t 😂. But I have friends who can just put the peices together on the spot It annoys me, I’m probably just average smart 😢

@salihalbayrak-es8ky Жыл бұрын

im a simple man so dont judge but: this statue looks super cool how can i get one xd

@fatehakhrib9653 Жыл бұрын

what if all the clase are bad , becouse i 'm the best in my clase but also if you are avrege i'm the worst

@Adventurin_hobbit Жыл бұрын

Sir Why don't you reply on my emails.

@enisten Жыл бұрын

You're Ramanaujan. He should be contacting you!

@Adventurin_hobbit Жыл бұрын

@@enisten 😂😂👌 exactly

@charlesward8196 Жыл бұрын

There is a difference between how well you work, how much you work, and how hard you work to achieve “success.” We are all genetically gifted with inherent abilities at birth, breeding matters, if not, you could teach a horse to do calculus, and write symphonies. If you are gifted, or “smart” you won’t have to work as hard at some things. If you are not gifted, then no matter how hard you work, you will never reach the highest level of accomplishment. You cannot make a silk purse out of sow’s ear. This is very “politically incorrect” in our social climate dictating “equal outcomes.” Sometimes abilities will be latent, and develop in people at a later age, as their brains reach full development. This is why men’s car insurance rates and credit scores improve after age 26, on an actuarial basis. That temporal lobe has to be at 100%. This is known as “the power of yet.” When I tutor frustrated students who complain, “I just don’t get it!” I tell them to instead say, “I don’t get it YET!” I encourage them to work a little longer, a little harder, or most importantly, come back to the task later, and then they will probably master the skill. By working harder, exerting MORE effort for a LONGER period, you may make up for SOME lack of genetics and achieve a certain level of success, though you will never play a Paganini violin solo, bat .375 in baseball, or solve Fermat’s last theorem. As actor Clint Eastwood used to say, “A man has got to know his own limitations.” We have all heard of people who were spectacularly gifted, wasted those gifts, failed to achieve success and were, like the Hare, surpassed by the Tortoise in the old fable. I was always “bad at math” but I mastered enough skills to use algebra and geometry to accomplish practical tasks like building construction and renovation, traffic accident investigation, and personal finance planning. As a retired law enforcement officer I volunteer as an elementary school classroom aide tutoring struggling students and helping them reach grade level proficiency, just as my Mother did for me. In some classrooms the teachers have me working with gifted students, teaching above grade level materials. I get “paid” when student say, “Thanks, it get it now.” My advice: Work hard to apply your unique gifts to reach the highest level of ability you can, and then find some task in life that matches your abilities, skills and your industriousness to benefit yourself and society, and never stop striving to improve.

@charlesward8196 Жыл бұрын

@@techtutorvideos You are right, nobody else can tell you what your limitations are. That is why you have to figure that out, FOR YOURSELF! As I quoted Clint Eastwood, “A man has got to know his own limitations.” No matter how hard I tried, I was never able to run a sub-5-minute mile because I am GENETICALLY prone to asthma; nobody TOLD me that, but after 3 years of pounding the track in high school, I finally admitted it to myself. I will never play in the NBA because I am GENETICALLY less than 6-feet tall; I just had to look in the mirror on that one. None of my parents or grandparents had superior math skills, or musical skills (there is a connection there). There is a STATISTICAL likelihood that if your parents have certain innate abilities, that you will, too. Not surprisingly, neither my son, nor my daughter have superior math skills, BUT, they both pursued as much post-secondary education as they wanted, and both enjoy the work that they do every day. Eugenics is an evil perpetrated on individuals by Progressive government who want to “perfect” humanity. It is for cows and corn, not for people.

@3438jff4 Жыл бұрын

why are you trying to get books in Spanish? :D

@TheMathSorcerer Жыл бұрын

I have a youtube channel in spanish:)

@3438jff4 Жыл бұрын

your Spanish sounds like you also know Russian or another Slavic language

@MihailParshin Жыл бұрын

I disagree with one thing. I know this both for myself and for a lot of people that I know. Normally you work hard for something you don´t know or understand, but not so hard for something you know. For example, when I was young math was very easy(till around 6-7 grade I was very good, but then it became worse and i just turned out to be little above average). I didn´t spend almost any time to learn about math, even when we had our yearly tests. And I always got the best or second best grade in all those years(depending if I did a major mistake somewhere or not). Sometimes I had a whole school year in which I only got the best grades in mats. Almost without any studying. It just was too easy to me and I didn´t need to spend time learning something that I already know or understand. But in the same time, I was very poor on essays(that we do in literature, or subjects like history, psychology etc) and sometimes I had to spend whole weekend just to barely write 2-3 pages in essay, searching information from school books, or normal books(back then there was no internet) or encyclopedias. It was so exausting and I was never able to get the best grade in any essay whole my life(and we have done a lot of them). But later in life, when I was like 10th grade and above, even math became harder. I started spending a lot of time to study, but in the same time things became harder and harder. And as harder as I studied, the things became harder and harder and I just lost ´my talent´ from math. All those geometry or trigonometry bullshits that we were learning, were hard for me to understand or memories. But the algebra part was always easy or max semi-difficult to learn. So overall it happens that when you ´work hard´ most of the times is because you don´t have ´the talent´ for that thing and have to compensate for it by losing a lot of time and efforts. But if you have the talent, you spend less time and still do very good.