The Dark Truth About Learning Advanced Mathematics
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- Опубліковано 4 лип 2023
- Learning advanced mathematics is extremely difficult. It takes time, patience, and an incredible amount of effort. In this video I talk about this and how it relates to balance. Do you have any advice for people watching this video? If so, please leave a comment below.
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Thank you:)
I used to tell my Elemnetary Statistics students, "You know that feeling you get when you look at a math problem, and you don't know what to do, or where to begin, and it doesn't even look familiar? The difference between you and me is I like that feeling." Somehow, you have to find a way to "break on through to the other side."
Fair enough to me. One can relate to a math problem as to a hard job or as to an interesting challenge, a source of that magic rewarding feeling of solving a problem. Second one is a much more comfortable mind set to deal with. 😌
Failing and retrying is a part of the game (or even is the name of it 😁).
Kudos for citing the Doors
Thats exactly how I see it. Mathematics is básically a logical puzzle, so those ideas you cant wrap are like pieces of a part of the puzzle you have not figured out. So you have to fino the sorrounding pieces and so
We use to say in stats you can tell who is going to pass. Those who can figured there odds of success passed, those who couldn't failed.
❤
I'm not a professional mathematician, but an old lady, who loves to learn advanced mathematics. And I am a very happy person. 😊
Wow, That's a cute comment, and I'm glad you're happy 😊
I love your username
Wow, such a lovely granny I wish to have 😊
@whizgranny6203 Keep that up and your mind will remain "sharp as a tack" forever. If you have grandkids challenge them to "Stump-The-Granny" contests so that everyone wins.
A year ago, I didn't know anything about math. I started learning math from algebra 1, and now I'm reading Axelrod's linear algebra book and another book on multivariable calculus. All of that, beside my university and work, is why I think the key to doing anything is consistency. Start with a small amount, and after some time, you will become addicted to achieving new goals, studying more, and getting out of your comfort zone.
Thank you for your efforts.
Thanks for your comment. I'm 22 and studying philosophy in university; sadly I didn't give mathematics any attention in school, so my knowledge is lacking - but I am interested in studying it. So I started with the big fat notebook on geometry two weeks ago, finished it and today started with college algebra. And I hope to go to advanced mathematics at some point in life. The hardest thing is that there are many thoughts interrupting me everyday of how I'm learning middle/high school mathematics when the goal of doing advanced mathematics is so far away. Your comment affirmed to me that it is possible and will help me on my day-to-day work. Thank you!
@@snowmanofpoopp At first, it took me months to take the decision to start learning mathematics seriously, and I had the same emotions as you. But after some time, you will feel happy and proud of yourself, and you will say, Well, while others rest on their couches watching Netflix, I'm here exploring the most beautiful ideas ever. Sometimes you will feel it's really hard, sometimes super hard, but after understanding it, you will feel really happy and confident, and actually, it takes a shorter time than you think. Just learn it well, read proofs, do some exercises, and repeat it.
Small advice: I think you should read Axler's precalculus book; its content is really enough to study all calculus after finishing it. You will also like to read Larson's book on calculus; it's the best calculus book in my opinion, and you can study a lot of math areas, and with your philosophy background, you can dive really deep in mathematics.
best of luck.
Great Great great
@@ShibaPlay15please do!😊❤
For me, the crucial moment in my grad studies was when my PhD supervisor sternly warned me to finish with the category theory crap that I had gotten fascinated with and go to work on the serious research problem he had given me. It was an ultimatum. He was going away for a month, and I had better show some progress when he got back, or else. I spent almost every minute until his return alone in my apartment, living like an animal, eating random crap and sleeping only when I dropped, working like hell on a very deep and very speculative idea that had come to me. I only figured out how to finish the proof the night before he returned. Summoned to his office, I showed him the “junk” that I had done instead of doing as he had ordered. After some silence, he said “Holy shit! Go to the library and bring me a good book on category theory.” That was the beginning of the balance-breaking that resulted in my PhD thesis.
Uh huh. And then everybody clapped.
not a good approach to research
no one likes hearing this type of story, i hope you dont tell it often
If I hadn't worked everyday on mathematics I wouldn't be where I am now at 17yo. Through hard work I learned quantificationnal logic, proof strategies (how to prove it, velleman), Calculus 1, 2 and 3 (The math sorcerer's course on udemy+stewarts calculus) and so on. I managed to do this in 2 years from absolute scratch. I am not an intelligent person, I am just dedicated. Yes I went through burn-outs, but one must remember that successful people aren't motivated 24 hours a day. Even when they're not motivated they work, and they always learn from their mistakes.
Dang, where you from bro? What kept ya going? I honestly am a very slow solver of math qs, so it takes lotsa time
Hey bro do you have discord?
I have respect for you but I guarantee if you’re not a math matician that won’t mean shit.
I struggled with math anxiety for years, gave up on two degrees because of it.
This week I passed my calculus and Algebra Exam with a B after ridiculous amounts of studying.
Now it just feels normal to study math like any other subject, as opposed to this unscalable mountain.
Thank you for your inspirational content.
I don't think this is talked about enough with pure mathematics undergrads. It's slightly demoralizing at first to be working upwards of 40 hours a week just to barely keep up with a 3-hr course. I remember the first time I jumped from an applied Calculus track to a rigorous course in Groups, Rings, and Fields. I hadn't even taken an introductory proof course or even set theory at that point, so the learning curve was astronomically steep. You definitely can get a lot of concerned looks and make a lot of sacrifices to get the most out of those courses. I've talked to a lot of different students, and no matter who you talk to, everyone has got that ONE course that was just a warzone. However, the mathematical maturity that gradually develops in the process of the grind is faithful to follow...I think there should be a disclaimer on various courses that says: "If you think you have time for life balance, think again."
My summer vacation with ny family in Italy is going on now. My wife doesn't understand why I prioritize studying in the mornings while here.
I understand this video very much. I'm obsessed!!!!!
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I started going to school for engineering last year and have been taking the calculus classes since the winter quarter. This channel has been a huge help and I’ve recommended watching to my classmates and friends since I’ve gotten so much benefit.
Anyway, I’m 22 years old, and married with a little boy and a baby on the way. Ive been working full time to support my family as well as going to school.
It’s been a challenge but embracing the challenge has been fun and inspiring. Since I have limited time to focus on school, family and work, it forces me to be more productive with my time if I want to be a good dad, husband, employee and student; if not, then im falling behind in one or more of these areas.
As a result so far, my marriage has been great, I’ve been producing at a similar level at work to what I was prior to school (if not more) and I’ve been getting good grades in my classes (all A’s except for a B in Calc II).
Calc II was easily the hardest class I’ve had so far and I studied more for that class than I have ever in my whole life.
i’m going into calc 3 next semester and i couldn’t agree more with your statements. I find you super inspirational to keep on going! Thank you so much!
I adore your wisdom and life experiences, the way you use it to share with us most useful and honest advice is truly amazing and brings so much comfort. Thank you!!
You making these videos makes me feel like I'm not alone on this journey. My area of interest isn't math, but your words still apply.
Great video, thank you! 100% agree. There are seasons when you have to go “all in”. Trick is making sure to stay self-aware and come up for air occasionally from the deep dive. Your thoughts articulate my experience from engineering degrees and a career in engineering.
I’m a retiree learning Spanish and find your insights/opinions/experiences very valuable. After I listen to you, I feel empowered and motivated! 😊 Thank you!
Wow, thank you!
I am in the situation that I am returning to college to earn a degree in mathematics to become a teacher. I am spending so much time studying math in order to get ahead of my classes so that I don't encounter any nasty surprises during a semester.
It's hard, people around me find it annoying that I spend so much of time doing this rather than hanging out with them.
I can't help that. I have a goal I want to accomplish, and anything that is not a part of accomplishing that goal is going to have to wait.
I hope you achieve your goals.
Thank you, I needed this, I spend most of my time learning web development. I'm Nigerian so I have to go the extra mile to get courses, books and practice. I have also experienced the joy and reward of foregoing present social interactions for ones passion/project.
I always tell myself while practicing: "If working hard hurts, I am doing something right". This pushed me past Calc II as somebody who will just enter college in just a couple of weeks.
This is an amazing talk! Thank you for sharing! You've mentioned the idea of one problem a day and that has really helped me. I think about if often.
Thank you for one more inspiring video. I am starting university in August (math major), and I am currently going through calculus and linear algebra to be as prepared as possible to achieve high results. I dedicate several hours of the day to studying, motivated by the amount of course material I am able to get done in a certain timeframe.
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Thanks, useful discussion and video here
This is a lecture about life & excellence. Thank you!
Thank you for this video ❤! I was quite good at math and physics when I was younger, but later in life I simply didn’t need it anymore. I have been thinking about doing some studying at home, and I even bought some books, but I have been too scared to start again for fear of failing hard at it as an adult. Getting this video in my recommended might actually push me over the edge, to get started again 🙏!
Did you finally start again with math?
@@naakatube Yes, I did actually 😁! I worked through about half of the first book, then I decided I wanted to learn Biblical Hebrew and then I quit math again 😂. This is a problem that I have, jumping from one thing to the other, but I will definitely get back into it and finish this math book 😉. Thank you for reminding me!
Great video! Also, i loved my advance calculus. One of my favorite classes so far. I wish I could take the second version of it.
Thanks TMS for showing us the other side of the coin. I’d heard you say we should limit study to one hour, etc. and while I could see how that could help, it seemed inadequate to come even close to my personal goals. What you said today puts things in great perspective and helps me understand that they’re both vital approaches in the proper circumstances.
I completed my undergraduation in 2020 Maths major ...but i found few subjects difficult like real analysis.. so i discontinued studies ... Its been a year watching your videos and i feel to do my masters in Mathematics after 3 years ... I will do my best ...as my love for Mathematics is still same as before .. So thanks for motivating all the students by your channel .. keep making such videos .. 🙂
Hii
I did my undergraduation in 2019 in math major. I was doing my masters during covid. I used to love math since childhood but during covid I lost interest in studying anything. I used to miss my classmates, class. After my masters I tried to study and do other stuff but soon I felt that I am missing studying math badly and that's the one thing I used to enjoy most. So I have started studying math again. It's really interesting. I have learned and improved a lot since 2022. I still haven't achieved my goal though.
@@shookysfamily Yup... Just keep doing what makes you happy 🙂
I'm just in this moment of my mathematical life. This period is the second semester of my PhD in applied math, I have faced tough moments with math before, but I have always managed to overcome them. Now, after watching this video, I feel even more convinced that it's time to take my understanding to the next level. This video confirms what I must do.
I enjoyed listening to the way you explained this. It was deep. We all have to make a living as well.
Really needed to hear this! you got this guys/girls !!!
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Amazing video. Very inspiring. Thank you. This applies to EVERYTHING.
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Thank you for your amazing videos!
I think you are right in the sense that, to really master something, we need to be willing to sacrifice some intense bursts of imbalance, atleast in the short run. In the long run, we need to be cautious and compassionate towards ourselves to restore balance.
What a great, genuine video. Thank you sorcerer.
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This was a really honest video, thank you.
Inspiring Sorcerer, thank you, man!
I go through low and high productive periods. During the slow progress periods, I dabble with the challenging subject material. During these low periods, progress slows or even stalls. Anxiety and frustration might grow during these slow periods. Then, I get into a high productivity period when my understanding improves and the progress flows smoothly. During Advanced Calculus, I struggled for the first few weeks. Then, something clicked. And I was able to get through a lot of hard topics very quickly. I did 7 weeks of work in a few hours. My persistence during the slow period set me up and gave me a deeper understanding that translated into fast progress. Those few hours of intensity were not sustainable.
Well, as an undergraduate student in mathematics, I feeel demotivated with constant doubt for that price to pay in order to make it to the next level.
I feel kind if relived to find out that it is actually normal to break that balance and to have all of these doubts, even questioning how you life your life in irder to get to that place where very little people go.
I needed to hear that. Thanks Math Sorcerer.
I needed this, thanks
I couldn't agree with you more! Trying to learn Topology, Real & Complex Analysis you need to break the balance. Whenever I feel I know some hard topic no matter how small, higher maths always sets me straight - I'm still a babe in the woods and I've got so much more to learn. It's basically a never ending struggle
man, you looks happy almost always))
Hehe thanks I had just woken up when I made this video 🔥
That balance Vs breaking balance is literally what life is all about. I think this is why I'm subscribed to this channel. It's not just a maths channel. It's the story and psychology around doing anything.
I felt so related. This helped me so much!
Excellent video.
Thanks, i was struggling and this just reminded me to stay focused
Thank you soooo much!❤️🔥. This goes beyond even studying advanced math, to knowing that we are indeed meant for advanced things. Beyond the realm of ordinary. And that itself is pure satisfaction. Break That Balance. Not even as a reward title but the reward within is priceless❤️
It has really resonated with me when you said that we've got to break the balance in order to excel at something and that it doesn't only apply to maths. I, for example, have spent so far nearly 3k hours on the Finnish language and when I look back, I marvel at the deep linguistic knowledge I've acquired so far
I have been watching your clips since i was a high schooler, now i am majoring in pure mathematics..... your clips are so inspiring! Thank you
Wow this so good!!! Good work 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥
This video is awesome. My buddy and I listen to David Goggins for motivation. Everything you have said aligns with his messaging.
This really hits home. The fun in living is knowing you are strong enough to break the balance. But wise enough to learn the lessons along the way.
Great video, you made several videos on Topology but didn't make any on Differential Topology yet. Please make a video on DT
Yeah, thankyou for your advice, l think your a teacher with the right stuff !
That was me when I was taking a course in abstract algebra. I lived it. I loved it! It was my whole day every day. Luckily my husband was also taking the same course. Not that we shared ideas. The teacher used to laugh at how different our approaches were to each problem.
I broke the balance several times if not most of times, but at some point I realized that I had to stop and take a hiatus from unbalanced lifestyle because it's detrimental in the long run health-wise, which is something that I believe is too important to mention in the video! And remember, different people have different 'unbalance degree' to which they need to go in order to achieve what they want. That said, one should keep in mind that there is a saturation effect to challenging oneself for the sake of doing so.
Thanks for the upload!
I gave up love, drinking and regular job to learn math at the library, while it was lonely i have zero regrets i learned how derivatives, parabolic equations simplify statistics my true❤❤
I took up drinking when I really got into math...oops. 😖
Thanks man, I really do need to break the balance, at least for the goals I've set for myself.
I'm 20 (about to turn 21 by December), I will start college maths this year and you inspire me a lot.
I will perform to show it's never too late.
My PhD is in physics ... and I can say that advanced study requires a huge amount of focus and dedication. One of the biggest hurdles (wasn't really for me .... I have other difficulties) was dealing with the constant failure .... always feeling stupid. Then one day, I realized that this is hard for everybody, and feeling inadequate is a totally normal part of the process. But many people can't deal with that which is sad because in most cases they are plenty smart.
This is something I need to constantly remind myself of. I did my Ph.D. in theoretical chemistry (a mish-mosh of chemistry, physics, and mathematics) 30+ years ago and felt inadequate the entire time I was in grad school.
I definitely had to break the balance to do really well in my physics classes. I worked 12-15 hours a day seven days a week. The most crushing classes were advanced physics lab and electricity and magnetism (E&M), which required solving tons of complex triple integrals (in the days before the advent of computer algebra systems).
The one thing I have to say is simply ..totally agree ... you have to give 100% effort for a long long time if you wish to achieve Top Advanced Math wizard like knowledge. There is simply no other way it is a Difficult complex subject.
Your words inspire me a lot..
Thanks. You are definitely right if that is what it is about. Without going back and watching all you clips I don't know if you talked about structure or something alike. For me, I am in a war zone always getting knocked off my feet, there is no way around it, balance, is not a problem well at least I can't take balance any further without structure. Structure is my demise.
I should apologize in advance, but for some reason, your message about "balance" made me think of this hilarious video "Life After Poincaré: A Grigori Perelman Story" (a must watch!) 😊
This is absolutely true and it applies to any occupation in life
I had been tripping on your usage of the word "balance". While they might essentially have the same meaning, I might swap the word "equilibrium" for balance. The metaphor I might use is that of a bodybuilder who has to risk injury and recovery time to advance and surpass plateaus. One might have to risk feeling broken, incompetent and clueless before experiencing a breakthrough. I had always liked and excelled in math but wound up with a degree in English. You're clearly talking about graduate level pursuits of math. Thanks for your insights.
the process is dynamic any way, go ahead but always stay in your "elastic region " so that your nervous system doesn't experience any fatigue ( or more seriously nervous break down) advance normally if you are gifted in a "quasi equilibrium fashion" so that your body undergoes a reversible process and can go back to rest in peace after achieving any progress in your desired field , other wise you arent gifted in that field and try another more relaxing field which makes your physical and mental health well. as a matter of fact if you are lucky enough to know the field you are gifted in ( and you go in that field) , your mental and physical health will be perfect "theoretically".
I think it's great to break the balance abd have wonderful goals in learning advanced Mathematics but this shouldn't be confused with unnecessary struggle: let's consider learning real Analysis and starting with a most rigorous book not suitable for beginners and then hating yourself five weeks down the road for even trying your luck on that tough subject..... That's why receiving expert opinion before starting a Math journey is simply priceless 🤔
The problem is: once you understand something or you solve a hard problem, it is the modt rewarding thing ever and I feel great. Thats the reason why I am addicted to doing maths! Currently I am working on minimal surfaces in S^3 and some more topics in differential geometry and it is amazing how far one can get studying Mathematics for 4 years! Keep going... It gets better and better
I really like this guy!
I've bn trying to break the balance for my communication skills. Ive bn reading about the Social Sciences for the past decade off and on. I found a group recently where I can talk to ppl. But outside of that group is very different. Ive read about a number of social science textbooks. But now Im on Positive Psychology & Interpersonal Communication. Interpersonal Communication seems so far to help me understand people more. But to me reading about interpersonal communication is like how people feel when they have to read about math. It's difficult & comparatively I'm taking a lot of notes.
Generating complex computer code is a similar situation. However, once you have achieved your goals, you are changed. You can never go back. Sort of like Plato's cave. Right now most of my programming constructs are foreign to most in my community. However, a similar thing happened many times. For example the lisp community in the 2000's and their use of macros. Similar thing with the TCL community. Sort of like the Kansas song "Carry on oh wayward son". When you get to close to the sun you are changed.
I'm currently in my first year as a master's in mathematics student and I've suffered a lot during the last year. I've managed to graduate in November with the maximum score (110/110 cum laude here in Italy), but the last semester was incredibly frustrating for me.
I spent almost the entirety of the last three years without any kind of "balance" and I paid a heavy price for that. I just focused on my studies and on getting the best possible results in every single exame. This consumed me and was a huge mistake I think.
Now I've spent quite some time trying to balance my life and be happier. This has cost me in terms pf academic achievements, since it's a while that I can't get the great results I usually got in the past. However, I reckon it's vital to take your time, enjoy life and try to be happy. Don't destroy yourself in the attempt of reaching perfection, ok the long run it's just been counterproductive for me.
At te moment, I'm trying to get back to work and to improve my result again. It would be quite sad if I couldn't go on with my math studies just because I harmed myself too much in the past aiming for unachievable goals.
Thank you for harsh Honest representation
Great subject. Over the years I've wondered if there's a personality element which comes with the inclination to not be balanced and to go overboard in activities that require a lot of time to master or just consume a lot of time in general. From a young age I had that approach to hobbies, and it has stuck around until now where I'm 51.
I returned to high school math at 45 and, just to prepare for entry to college math, I literally lost two years worth of entire weekends where I would be consumed with the subject, and it only got worse once I started college, my social life was almost non-existent. I didn't feel bad about it though. I viewed it as a necessary (and often fulfilling) evil; It's made me wonder if people who take on math, or any other time consuming or difficult subject, are more likely to skew towards less balance in general.
I have similar tendencies so I can relate!
I think you're accidentally on to something that I've come to believe is a larger issue than most people realize. I fit a similar description as you.. I've had the difficult, time consuming, all encompassing hobbies that I can lose myself in. I went back to college about 10 years outside of high school, did a bachelors in physics and mathematics and am trying to finish my PhD right now, and I found myself unable to make it through school without going throwing balance completely out the window. Much to the detriment of my relationships, too. I found out this year that I'm both autistic and have severe ADHD and have since realized that many of my classmates meet a lot of the criteria and had a destructive lack of balance too. Not all of them, of course, but it seems surprisingly common. I'd be incredibly surprised if that wasn't the case with other, similar programs everywhere.
I'm not sure what is cause and what's effect, though. I don't know if neurodivergent people tend to be drawn to subjects and hobbies like that, or if they simply are just more well suited because of the tendency to hyperfocus and how necessary that can be to work through them. Whatever the case may be, you're right: there DOES seem to be some element that drives certain people to do things in an unbalanced fashion. I just wish more was known and understood about it for the sake of their mental health.
Well, I don’t think it’s always necessary to break the balance (unless one wants to be truly innovative and create important new theorems every month)
The 🔑 to keep the balance which I discovered for myself and my students is to apply what we can spontaneously call the „phenomena of transfer of ideas“.
For example: adding a 0 occurs quite often in Epsilon proofs. If we are passionate about our subject, we will quickly develop a feel WHEN to apply a 0 and when to do go on straight.
In order to keep the balance when learning about differential forms, I recommend us to develop a true spatial intuition for what it is. (thinking about slats). We will see that this helps IMMENSELY to intuitively come up with ideas how to tackle proofs. If we cannot imagine hyperspaces, we can just go down to IR^3 and study the patterns there and then generalize back to IR^n.
For saving time, the engineer‘s approach to advanced calculus is king, even when it comes to developing proof ideas. Of course a sketch isn’t precise or reliable enough but it helps a lot to avoid studying too many past similar cases and makes us more intrinsically innovative.
Meditation also helps a lot over time because a lot of mystics of the past (including Nikola Tesla) were CONVINCED that we aren’t really developing the ideas in our brain but are rather DOWNLOADING it from source once proven worthy of it. This means a quiet mind with true love for math is automatically BADASS at maths because it leads to having a secret (divine) muse on its side.
Another advise which I have for us is: instead of trying to remember every detail of a proof we study, we should try to focus on the MAIN IDEA and FILTER IT OUT. In other words: we should remember only the CORE IDEA of a proof and SUBCONSCIOUSLY TRANSFER it to other theorems which we need to proof. When we do this, we will quickly notice the net structure (not a chain like many think) of maths. This approach saves A LOT of time. There are more analogous proofs than many realize. Of course many details will be very different but the core of the proof, it’s main idea will be often quite similar.
Thank you! Very inspiring. I had a community College teacher who belittled the class if they didn't understand college algebra yet. It was discouraging and he's an idiot. All it takes is practice.
Thanks so much sir
time under data set can be slow and quiet , thank you for your persistence/stubborn as you are
Great videos! Thanks a lot!! I have a question that maybe is answered in other video. I've 46 years old and I'm married with a 2 year old child and have a regular job and I've just failed an Algebra course for a Physics Major that I'll try next semester again. What happened to me for example is that for this Algebra course I have classes 3 times a week with 3 hours each class. In total this class have like 300 available exercises to do and it happened to me that I was like 30 minutes with just one exercise, give up, see the solution and say "Ohh I need to apply that formula combined with that one", and sometimes this happens like a lot so I don't know if it is good to see the solution for the exercise or keep trying or move to the next exercise but in that case I feel that I'm missing some important concept that I need to apply. Also I'm using the Pomodoro Technique but after one Pomodoro with one excercise I feel frustrated, ignore the break and start another Pomodoro of 25 minutes with that same exercise. Maybe is it too much to try this major at this stage in my life, or maybe I'm not fast enough and I'll struggle. So I'm looking for some advice if there a way to learn faster and keep pace with the speed of the course without breaking life balance. Thanks and Sorry for the big comment!!
Don't be afraid of the math. Its only numbers. I tell myself. I had no understanding of calculus only a few months ago. Still don't understand much of it. But now I can recognize things I see in calculus videos as things I've learnt in algebra textbooks. Then I see things in algebra textbooks that I recognize as things that I've seen used in calculus videos but didn't understand when I saw them in the calculus videos Think I'm going to like doing limits and derivatives Don't now if any of that makes any sense. I can do most of the algebra and that isn't a issue. I suggest watching videos of math you don''t understand to familiarize yourself with it even if you don't understand the math as you are watching the videos.
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I too feel that one has to be unbalanced in the start to reach a certain height then one can decide to balance things out. But one important point is that the unbalance should not go out of scale, however crazy it sounds we have to have a balanced unbalanced life
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Thanks ❤
I think, if you don't have some strict deadlines - for example, you're learning math by yourself, it's possible to stay balanced. I feel honestly sad and sympathetic for your past relationships.
Keep your health and relationships in good state, don't break the balance if you don't have to.
I'm starting to learn math in my 30's just because I can. I'm a software engineer and I just want to be better at it. And I'm going to study quite intensively but never to break the balance. The good part is my gf supports me fully - she's great at math and she learns programming now, so, we are quite complimentary to each other
I strive to set the minima of my analytical abilities above the average of the mouth breathers of Walmart, but I've many times been accused of being unbalanced... lol. Seriously though, every great comprehension and analytical value I've added to my life was garnered during a time of obsession and hyperfocus to the exclusion of all else, but that's me. Complex analysis, Tensor Calculus, and Differential Forms don't lead to light conversation at the dinner table. To have friends or family drop by for a visit and they ask you what you've been doing... this huge divide opens up between you... because there is just no possible way you're going to be able to explain it to them, so you just say "Stuff, I've been doing some stuff." I wouldn't change a thing though.
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I do have an opinion. My thought is, “what is balance?”. I believe that you determine what balance is to you. It’s all perceived. So I like to think what my balance is. Is it possible to shift my balance where I direct it? Why or why not? If not can I create an illusion therefore making me productive which leads to the winner effect?
My personal balance is one which I can dedicate a specific time/s of the day to fully focus on an activity, then relax to recharge from the expended energy and be with family and have some fun. I personally would be happy focusing really hard for 8-10hrs daily and then getting the rest of the day to do whatever I want, whether that’s being with family if possible or researching interesting things, or other creative endeavors.
Good comment thank you 🔥
Great
I need to watch this every day for the next forceable bit of time because I am trying to push boundaries
Its a moment that asks now or never, do or die. Its about sacrifice, discipline, motivation and maintaining that momentum until the job is done. And repeating this a few times or sometimes a life long process. And its not even sexy, but the results are real and are there if you want it.
Love from India.. You made my remaining day❤
👍🏽👍🏽👍🏽👍🏽👍🏽👍🏽 BE FEROCIOUS FOR YOUR GOALS PERIOD …..COMPLETE THEM BY ANY MEANS NECESSARY
Mental discipline... the real discipline. Math combines the ability to focus, remember, persevere and repeat the cycle over and over again, climbing an unseen helix up into the unknown ❤
Breaking the balance, aligns with balance. If we want to achieve balance in all things, doesn't that imply that we need to balance balance as well. Balance it with imbalance in the way you suggest.
I think you have to achieve a certain golden mean balance between the hard work of maths and life outside of maths. If maths is a sufficiently big part of your identity then you have to make the sacrifice to be what you are. On the other hand if there isn't that element of balance things could go awry. Its a case of finding where the fulcrum point is. You need to stay healthy in mind and body. When you do something practical and physical its very good for your mind. Internships are not necessarily a good thing for prospective mathematicians. Going picking grapes in France for a few weeks in the summer might do you a lot of good though, and help recharge the mathematical batteries. A refreshed mind works well.
Dual numbers were introduced in 1873 by William Clifford. In 1876, Clifford suffered a breakdown, probably brought on by overwork. He taught and administered by day, and wrote by night. A half-year holiday in Algeria and Spain allowed him to resume his duties for 18 months, after which he collapsed again. He went to the island of Madeira to recover, but died there of tuberculosis after a few months, leaving a widow with two children.
Damn! That's a really horror story.
People have to spend a good amount of time in anything even with family so they can get a good result of out of everything 👏👏👏👏❤️❤️❤️❤️ thank you're my motivator Mann thank you ❤❤❤❤👏👏👏👏
I don't know sometimes; as a jee aspirant I have a huge syllabus to cover I mean sometimes I feel lost.
Math, i,m mech engineer and now I transfer lines in real world. When you see steel structure , math is behind, when you drink water math is behind, when you see flying plane, math is behind.... Sometimes in my work some results is sometimes weird but one must belive in math beyond this numbers. That is life.
you are right
Thank you for this video. Always inspiring. But I have one question: when you say advanced mathematics, what do you mean exactly? Because some people refer to trigonometry as advanced mathematics, while others refer to differential geometry or general topology as advanced courses...I just want to know at what level of learning mathematics can we call our courses advanced.
In medical school I would study 8 hours every day. Now as a fellow, I still study several hours every day (when I’m not at work). Sacrifice is necessary to accomplish anything great.
Mathematics is a Universe where have to face a challenge in every interval of time.
Being a masters student in mathematics sometimes I love the challenges and spend hours focusing on a theorm or a problem but sometimes it becomes so irritating . Whenever I complete a challenge in mathematics the satisfaction and the joy which I feel at that time is next level. But gradually i can see my behavior changing towards my friends and family . I feel irritated when they surround me and I think it is biggest limitation of Mathematics that It leaves you unsocial. I don't know why i am becoming so rude.
I have a question to all people who study, studied, will study, got back to studying math again! And the question is also directed to me; where does all this studying (even advanced math) lead you to? When I learned to play a musical instrument I knew that one day I wanted to perform on stage. And I did for many years where it was an extra income for myself and fun at the same time. I like math even though I did not excell in it. And even now I go over calculus books and read upon the subject while doing some math exercises. But where does it lead? I can only see one purpose for it; to keep the mind active. Otherwise I don't need to take a derivative in order to see how much gas I need, count my change, to know what this or that costs and apply some simple arithemtic not to get cheated in a store. Yes, one can ponder over some mathematical questions but anyone studying very hard math must have a set goal in front; to become a true mathematician. And that is just all.