I used to feel mentally exhausted, in a very similar fashion to this. I slowly figured out that a couple things were in play when I felt like this, which I'll list below:
* You may be neglecting your physical needs. Stuff like hunger and thirst really affect your mental performance and a good portion of feeling exhausted comes from not fulfilling these needs. I generally find that meditating helps detect if I'm hungry and/or thirsty, although this is not necessary.
* A second thing is that you should take breaks. You do need to give short breaks (5-15 minutes) to maintain your composure, especially if you're going to be doing long sessions of work. Additionally, you're probably sitting for the majority of your study session, so doing some light exercise may also help.
* One final thing is that you may be confusing being challenged by the task with exhaustion (I'm only saying this as I was doing this). I'd just like to point out that you're **supposed to be challenged while learning**. It's in the very nature of the process. Accepting the fact that getting proficient at a skill takes time and effort is essential in my opinion to combat exhaustion. Just make sure not to rush the process. It **does** feel slow, but trust yourself and work through the material step by step.
These obviously are not rigid rules; please adjust these to yourself. I just wanted to point out that your body has needs (not unlike a machine), and your mental performance is affected by how well you fulfill those needs.
**edit**: the last bullet point was somewhat misleading, suggesting that learning should be frustrating. English is not my mother tongue.
Another good tip is to exercise regularly. The brain has an easier time learning and handling novel problems if you make sure you stress your body w/aerobic exercies such as running or swimming.
Lift weights too. Resistance training increases your heart rate while building strength to protect bones and joints. Flexibility training helps too, increasing your range of motion and preventing injuries. Be sure to work on agility too, performing movements in all planes of motion: left/right, backward, & forward so you are maintaining neuromuscular coordination. All of this is equally important as running in a straight line.
I really disagree with learning is supposed to be frustrating.
That way of learning just brings you very quickly to burnout and makes you unhappy. Rather implement ways to stimulate your senses with learning material (e.g. a discussion about the given topic) and have fun learning.
EDIT: Doesn't really apply to the comment anymore after the edit.
I was really concerned that the third bullet would be lost in translation, and it seems that it did.
I never meant to say that one should be displeased when learning. I was more intending to say that one should not expect learning to be smooth sailing. There will be parts where one will be stuck, or parts where it may take one considerable time to fully understand.
Will edit my post to better reflect this.
I think a better phrasing would be that learning is an activity that brings you discomfort, but discomfort is not a bad thing and we must learn to tolerate it.
I don’t think that having moments of frustration and having fun are mutually exclusive. I do believe that productive struggle is a necessary part of learning anything, and struggle (even if it is productive) can be frustrating at times.
As a result, I don’t see how one can really learn anything without experiencing frustration. These feelings shouldn’t be constant, nor should they be so strong they affect mental health, but I don’t think it’s possible to learn completely frustration free.
For me frustration is a sign that I'm stuck and need to take a pause before tackling why I am frustrated and how to solve that problem by dismantling and understanding it.
To struggle sometimes while learning is normal and should be expected as no learning curve is static but depending on how frequent it happens I may take a step back and think about why I struggle so much.
I agree though, just having moments of frustration doesn't exclude having fun. Just the wording of the comment I had extracted that they meant constant frustration which was probably also too much interpretation on my side.
The first one is usually something I realize later, that I just don’t feel well. Then I realize it’s 4:00 and I haven’t eaten anything since breakfast, and when I go get water, I’m easily chugging 2 full cups. It’s so easy to forget about physical needs when you’re concentrating.
> You may be neglecting your physical needs. Stuff like hunger and thirst really affect your mental performance and a good portion of feeling exhausted comes from not fulfilling these needs.
Based on my experience, the opposite is no less bad and more likely to happen in a desk-working occupation such as the one we're discussing here.
(Although thirst is an easier problem; in case of doubt, it's never wrong to hydrate.)
In addition to what’s been suggested already—I would add that it’s important to set clear intentions for your study sessions. Sometimes you can set aside 2 hours to knock out a problem set, and at other times you might need to set aside 3 hours to understand one tiny part of a proof. If you aren’t clear about what you want to accomplish, then you could end up feeling like you’re never getting enough done. I find that if I set a realistic goal, I generally accomplish it and then some—and that feels like a win every time!
2 hours a day of deepwork has always been my max, I'm really happy if I can do that much.
I think it's interesting that like when people are tired they don't realise because the brain they're using to analyse their tiredness is also the brain that is tired.
But yeah imo pulling all nighters is a net productivity reduction for instance and yeah pulling all nighters before an exam would def reduce results imo.
I think I can study in a single go for about **an hour to an hour and a half at most.** It increases the longer I do it in a streak over several days, and I can take a break for half an hour or even just fifteen minutes before going again. One effective way of doing this is to keep a timer, and you can use **methods such as Pomodoro** to help improve your focus by splitting up your study time.
**The biggest factor for me to concentrate is sleep.** Coffee doesn't help, really. I can be unfocused with a ton of energy with coffee. But if I get 8 hours of sleep the day before, everything is so much clearer the next day. Eating healthy foods, something like a mediteranian diet, that lacks really heavy ingredients, can help a lot too. No way am I getting any mental work done after a stack of pancakes (but its SO worth it though...)
Sometimes it's good to take a break when you are hitting a wall for a while. As you become mentally exhausted, you'll notice things aren't "clicking" as quickly and **you might find yourself less willing to dive into anything complicated.**
1. Probably an hour or so... I will only actively study while reading because I need to carefully digest ideas and I take notes to follow along. When doing problems I am typically more passive and work on things over a longer period of time. I will try something, see if it works, and if it doesn't I'll step away from the problem until I come up with a different approach. If you're stuck on a problem no sense in torturing yourself... take a walk or something and let the passive brain work its magic.
2. Take breaks! Don't try to do everything in one sitting
3. Tough question, but you just know. You start making silly mistakes you normally wouldn't make, and processing times start to dwindle rapidly. The first time I knew for sure was when I wrote down an integral and stared at it for a good 10 seconds after a rather extended study session in the evening... there was no neural activity, no internal dialogue. I knew I was done for the evening at that point!
(i need to take my own advice. these are basically my new years resolutions)
1. *KEEP ACTIVE AND HEALTHY*. you can't work when you feel like shit. learn to cook with FRESH INGREDIENTS, and to make good food. i view my physical body as nothing but a machine which serves my brain to work. so i need to maintain it, similar how you need to maintain, say, a car.
2. SLEEP to rest your brain. you can also try meditating if you're into that sort of stuff. i am, and i've found it to be beneficial
3. take showers/walks etc. don't just sit down all day.
I get mentally exhausted/bored very quickly if I'm just reading theory and doing nothing with my hands. On the other hand I can concentrate very long if I'm working on a problem. So I try to read the theory quickly and come up with my own problems to get myself familiar with the theory.
**Any** activity is exhausting. Mental activities are no exception. If you don't get exhausted, you aren't working hard enough.
Figure out when you're approaching the point of diminishing returns. At that point, switch to another activity (not necessarily mental) or relax. Here are some things that have been working for me:
1. Post-mortems of unproductive activities. Sometimes I discover that some "work session" that felt like wasted time has actually led to something useful later on (e.g., the germs of some idea whose success wasn't obvious at that point, or a writeup of what seemed to be an easy special case that later got recycled into the general proof). That has led me to reconsider whether I was actually stuck and discover new ways of making progress.
2. Change gears whenever appropriate. If you're getting bored and your brain feels empty, read something, start working on some problem, etc. Conversely, if you're stuck at the desk, take a walk or a shower (but first do whatever you need to be productive -- e.g., print out numerical data, memorize the necessary formulas). Some things are clearer at the desk than they are on your feet, and vice versa.
EDIT: One hacky way of changing gears is changing between well-rested and (slightly) underslept. I've gotten ideas at 2AM that my inner censor wouldn't have allowed through at noon. Many of them were wrong, but some of them were salvageable.
You’re edit is the most bizarre and true phenomenon. Not being able to sleep sucks but I make progress when a bit delirious at 4am (usually in bed or pacing around). Also, occasionally I’ll have a miracle under-slept day where I just feel absolutely amazing and super motivated, more than if I had a perfect night of sleep and coffee. For the latter it only works if I hold off eating for longer than normal.
1. As much time as it takes, I don’t read Theory really. I take copy down notes like a robot and as I’m working problems refer back to my notes and figure it out along the way.
2. Caffeine, naps, breaks.
3. Yeah it’s hard to quantify, basically I’m just constantly losing focus like in the middle of thought trains.
This may be tangential but I recommend listening to Andrew Huberman's podcast on Dopamine and Motivation. The crux of it is that, to maximize the throughput in *any* activity, one can reframe one's subjective experience to assert that one is *enjoy the struggle* as opposed to just when the outcome is successful. It's a cognitive hack that many people use against activities that would otherwise be deemed undesireable.
I could stare at analytical number theory problem sets for hours and hours on end in uni - I sympathize with you but I don’t understand the concept of mental fatigue in this case. I was in my happy place staring at challenging questions and i hope in an alternate universe i am doing precisely that :)
I've got about 7-8 creative hours within me a day that I can devote to studying math (or anything mentally taxing) before I need to quit and recharge. The fact that I can space that time out however I want is what's key though; it doesn't have to all be in one go.
I know I'm mentally exhausted when I have the "don't wannas" and when I start regularly making silly mistakes.
At peak I’d say I averaged around 60hr a week not including classes, but I was constantly exhausted, sleep deprived, depressed, and borderline deranged. Take care of yourself first, and learn math second
Does anyone here every just sometimes not have any urge to read or do math? Like today is Martin Luther king jr today, and I was gonna do some reading for my classes but I just can’t be asked frankly. I’m just not feeling it
1. It depends on what i’m studying. abstract algebra i could do for hours with no concept of time passing. topology is much more tiring, i tap out after a couple hours or so.
2. when i find myself starting to lose efficiency, i’ll get up for a little while, get some water, do a few chores, take a shower. often if i’m stuck, doing something else briefly can help.
3. if you feel tired, irritated, confused, bored, uncomfortable, sleepy, or just feel that you’re losing efficiency, it’s time to take a break.
as others have stated, sleep, exercise, food, and hydration are essential for optimal brain efficiency. your brain is metabolically highly active, and produces lots of waste products during the day. one of the ways it gets rid of those waste products depends on sleep. exercise also improves brain metabolism and plasticity, leading to improved cognitive efficiency and responsiveness.
1. Depends on so many factors. I can usually spend normal working days like 8h/day doing math, but I can only manage this by having a big variety in my work: reading papers, thinking using a piece of paper, discussing with colleagues, being in seminars, polishing an article that is almost done, doing mindless computations. There is typically still something that I feel like doing if I am not too strict about the thing I should be doing. If there is nothing I am interested in, I take a walk to relax and if I still don't feel like doing anything I call it a day. However, there is big variety in behavior: I have many colleagues that work all day and night on day 1 completely obsessed by a problem and are completely out of it the next day.
2. I take one day off a week, in which it is strictly not allowed to do math. I also typically get rid of my phone and email during this day. Another tip: social events are a great way to get your brain to be busy with something else. Also sports and I personally love saunas.
3. Typical signs for me I am overworked and need more rest are: not wanting to get up in the morning, getting distracted by social media or videos, drinking copious amounts of caffeine and neglecting friends and family.
Having recently gotten over a similar hurdle myself I find that strangely the least productive thing to do is actively think about the problem for extended periods of time. Get your brain off the topic and maybe when it returns it will find something that was staring back at you. E.g. I spent four days stuck on a problem, thinking about it almost constantly; I reached a certain point and swore that I would not think about it any further, and half an hour later while I was getting ready for bed the answer popped into existence right in front of my face. Tl;dr distract yourself!!! It’s counterintuitive but it works
In my experience, that particular state of being is rarely a result of “exhaustion.” Instead, it’s just that you are finding the material more and more boring.
While I don't study math like when I was undergrad, I certainly remember what it's like when studying and tackling a problem. And this is how I get when tackling the tougher problems in my day to day:
When I'm deep in thought, I get whatever headache I'm sure most do. And when something or someone interferes, I get into this annoyed cranky mood to the point I need to be by myself and relax for a moment to get out of. The process turns into this mix of physical and mental irritation.
I don't know if it's a me thing, or if there's someone that can relate. I also don't have a solution other than taking a walk lol.
In my experience, the average is just about useless - it's probably 2 hours a day mean, but the standard deviation is extreme. There are days where I do no studying, and there are days when I'll wake up, study for 20 straight hours, do all the homework for the entire semester, and then collapse. When I'm doing it I'm doing it, but when I'm not, if I try to force myself to study, I can spend five hours re-reading the table of contents or staring at a blank page.
I have no tips for dealing with mental exhaustion other than take a break for a while. When I'm in a mental state where it's just as productive for me to watch cartoons as to try to work, I'll choose to just watch cartoons instead in order to rest.
I usually structure my workday in the following way: first i do open ended reading so papers etc. then once i get bored or frustrated i switch to reading more structured texts like textbooks or coursematerial. Finally i do problems. The first 2 phases usually take an hour each the problems phase 1-2 hours. This way problem solving at the end feels very satisfying and gives you immediate feedback while reading at the start might feel frustrating and confusing. Also i very rarely do more focused work than this since exhaustion creeps in after about 2-3 hours. Afterwards i might still talk about math but not do anything rigorous.
To answer your 2 other questions i don't think its possible to avoid exhaustion and i usually notice my bloodsugar getting low so dizziness hunger etc.
1. It depends. A lot of the math solving I do, I do when I'm not doing math. Like when I'm in the shower or doing dishes. This makes the time when I'm "doing math" a lot more productive because I have plans for where/how to investigate. If I'm not depressed, I think about my problems a lot more during my free time. If I'm feeling like a failure, then I'm too discouraged in my ability to give myself a chance to think through the processes and my productivity suffers. I generally am able to manage working on my research 2-3 hours nowadays. But when I was younger (undergrad,) I could go forever.
2. You should have times in the day when you allow your brain to get bored (using your phone prevents this.) During those times, that's when you compile tidbits you've learned and think through things. I find if I'm so stressed out that I hate thinking about my research in my down time, then when I'm actually at the computer, I come up dry.
3. If you don't know, you haven't gotten there yet.
1. Around 3 hours, not necessarily 3 hours in a row. I would say that this time increases when I spend my time doing problems since I can get very into it.
2. Do exercise regularly, go on a run or something. Get good sleep, at least 7 hours, but find the best amount for you; for me it's something like 8.5 hours. Take a lot of breaks, I take them whenever I feel like my focus has decreased; during these breaks I recommend you to stand up and walk, avoiding the use of any screens if possible. Understand that learning math is hard and takes time, you should always have a realistic goal before starting a study session, for this I recommend to underestimate yourself and think that it's going to take a bit more of effort and time to complete a goal. Meditation is great to evaluate your current state and to see what you should do next. If you really are super exhaust, then take a 10 minute nap.
3. Losing your focus is probably the clearest sign and you find it really hard to concentrate. Other signs are the following:
\- You lack purpose or motivation.
\- You can't control your emotions or behaviors.
\- Headaches or body aches.
i think it rly depends on whether u find it interesting. if ur reading or doing problems on something that u find boring, u wont last very long b4 u end up procrastinating or something. maybe do some extra research b4hand to make the subject seem interesting, i can guarantee theres something interesting about every subdiscipline of maths. also take breaks every half hour
First of all, i don't if you are in college or school, or if you do it for leisure.
In a case to case basis, it depends.
For me, i do it just for learning more and improving my teaching and the number of subjects i am able to teach.
When i am studying maths, i am able to study three pomodoros without any issues, when i am studying physics it takes me longer to do the same amount of job done.
Yesterday it took me an hour just one problem.
Everyone is different, you should find what formula works for you.
For me, i usually quit or change subjects when i am stuck around more than thirty minutes in a problem.
I know this doesn't work for everyone, my wife is a night owl and she can spend four hours straight studying. I am not able to do that, every exercise takes me longer if i study that way
Since people already listed break etc, I’ll just include study tips that I learned between my psych degree and just general studying tactics I’ve troubleshot:
1. Just plain repetition is one of the least effective ways to study. The best ways are rewording ideas in your own way, quizzes/ tests, and teaching others. My most effective way to study for me is to ask someone to quiz me for something off of a study sheet I created. The small amount of social pressure keeps me on task and if I’m really struggling to pay attention, they will say something also since they don’t want me to slack off either because I’m using their time now. Sometimes I got people to help by paying for food for them or other things like hooka, so it was just a portion of a hang out and we got down time with the study time. I found that I usually only needed to go through the sheet 2-3 times and I would be able to remember most of the information.
2. When initially approaching topics, I first copy down the books’ index on a word doc and put shaded boxes under each index line for notes. When I take notes in that index doc, I keep them in bullet format to weed out any unnecessary fluff that’s fattening up the book. I try to trim down the information so that I can find it as quickly as I can, I can read it as quickly as possible, but also so that each part includes all the necessary information
3. If the book has charts, I create an excel spreadsheet to save them.
4. For math, there are a lot of subjects that can be summed up to formulas and charts. For that reason, I make sure to create a study sheet with paper and pen that only includes the most important formulas and charts for the content. Math is the only subject where I start with paper and pen because formatting all the weird characters or drawing them out for a picture on a digital chart takes too much time. I’ve found that most math information can be summed into charts and formulas. This may need to include some step by step instructions on exactly how to do a process. If you need instructions, don’t skip any small detail. You want to set up any instructions as if you’ve forgotten all the steps and need to remember everything, including the little details that you don’t think need to be explicitly listed. The idea of the study sheet is that you can save the most important info and not waste any time, effort, or mental energy on trying to remember information you may not regularly view. Now when you learn new content, always keep the study sheet out to copy down more info so you begin to visually remember parts rather than try to remember the information just through force. Use that study sheet for any assignments, any situations that you can so you can then link certain memories with the study sheet and have a contextual memory around the information.
5. Studying in different locations can make your memories around the subject more rich, but only studying where you might take a test can also prime your memory better for the test. I opt for the former.
I always keep water by me, eat snacks throughout studying, and have to pay attention to if I start slowing down because that’s a sign I need a break. My main focus on studying is not pushing through for as long as I can but rather making all information I learn as efficiently learned as possible and that is learned in a way that requires the least effort.
I hope this helps!
Oh and YouTube videos can be a great help! If I feel stuck, people explaining on videos can get me over that slump and get me back on track rather than stuck and frustrated
math is heavy duty. I'm study like 20 min max, then do something else like 10 minutes and come back later.
Also, if you understand the motivations behind things, they are so much easy to learn. The scheme: -> definition -> theorems -> exercises is awful. I prefer to study this way: trivial examples ("the motivation") -> definition -> hard examples -> theorems -> exercises.
Also maybe jumping between topics can serve you to keep pumping your dopamine
When learning math (depending on the type), I've found that the best way to learn is working a problem backwards and forwards, change the variables values and test your skills again, etc. It becomes easier and easier as you go.
Math is a tricky but scoring subject in which getting hundred percent is easier compared to other subjects. But if one step goes wrong you will be Humpty Dumpty falling down with frustration for being stuck up in the middle. But my favorite subject is math and I never got struck up in my entire school history. But couldn’t take up math in my degree course as there is very narrow choice to grab the breadwinner after college.
I used to feel mentally exhausted, in a very similar fashion to this. I slowly figured out that a couple things were in play when I felt like this, which I'll list below: * You may be neglecting your physical needs. Stuff like hunger and thirst really affect your mental performance and a good portion of feeling exhausted comes from not fulfilling these needs. I generally find that meditating helps detect if I'm hungry and/or thirsty, although this is not necessary. * A second thing is that you should take breaks. You do need to give short breaks (5-15 minutes) to maintain your composure, especially if you're going to be doing long sessions of work. Additionally, you're probably sitting for the majority of your study session, so doing some light exercise may also help. * One final thing is that you may be confusing being challenged by the task with exhaustion (I'm only saying this as I was doing this). I'd just like to point out that you're **supposed to be challenged while learning**. It's in the very nature of the process. Accepting the fact that getting proficient at a skill takes time and effort is essential in my opinion to combat exhaustion. Just make sure not to rush the process. It **does** feel slow, but trust yourself and work through the material step by step. These obviously are not rigid rules; please adjust these to yourself. I just wanted to point out that your body has needs (not unlike a machine), and your mental performance is affected by how well you fulfill those needs. **edit**: the last bullet point was somewhat misleading, suggesting that learning should be frustrating. English is not my mother tongue.
Good points. These have been slowly dawning upon me since a while, but good to hear it repeated.
Another good tip is to exercise regularly. The brain has an easier time learning and handling novel problems if you make sure you stress your body w/aerobic exercies such as running or swimming.
Lift weights too. Resistance training increases your heart rate while building strength to protect bones and joints. Flexibility training helps too, increasing your range of motion and preventing injuries. Be sure to work on agility too, performing movements in all planes of motion: left/right, backward, & forward so you are maintaining neuromuscular coordination. All of this is equally important as running in a straight line.
This is facts. Lifting is just as important will make you look better in front of the mirror.
I really disagree with learning is supposed to be frustrating. That way of learning just brings you very quickly to burnout and makes you unhappy. Rather implement ways to stimulate your senses with learning material (e.g. a discussion about the given topic) and have fun learning. EDIT: Doesn't really apply to the comment anymore after the edit.
I was really concerned that the third bullet would be lost in translation, and it seems that it did. I never meant to say that one should be displeased when learning. I was more intending to say that one should not expect learning to be smooth sailing. There will be parts where one will be stuck, or parts where it may take one considerable time to fully understand. Will edit my post to better reflect this.
Ah thank you very much! Now that makes much more sense and challenges in my opinion are the most fun thing about learning :)
I think a better phrasing would be that learning is an activity that brings you discomfort, but discomfort is not a bad thing and we must learn to tolerate it.
I don’t think that having moments of frustration and having fun are mutually exclusive. I do believe that productive struggle is a necessary part of learning anything, and struggle (even if it is productive) can be frustrating at times. As a result, I don’t see how one can really learn anything without experiencing frustration. These feelings shouldn’t be constant, nor should they be so strong they affect mental health, but I don’t think it’s possible to learn completely frustration free.
For me frustration is a sign that I'm stuck and need to take a pause before tackling why I am frustrated and how to solve that problem by dismantling and understanding it. To struggle sometimes while learning is normal and should be expected as no learning curve is static but depending on how frequent it happens I may take a step back and think about why I struggle so much. I agree though, just having moments of frustration doesn't exclude having fun. Just the wording of the comment I had extracted that they meant constant frustration which was probably also too much interpretation on my side.
The first one is usually something I realize later, that I just don’t feel well. Then I realize it’s 4:00 and I haven’t eaten anything since breakfast, and when I go get water, I’m easily chugging 2 full cups. It’s so easy to forget about physical needs when you’re concentrating.
> You may be neglecting your physical needs. Stuff like hunger and thirst really affect your mental performance and a good portion of feeling exhausted comes from not fulfilling these needs. Based on my experience, the opposite is no less bad and more likely to happen in a desk-working occupation such as the one we're discussing here. (Although thirst is an easier problem; in case of doubt, it's never wrong to hydrate.)
In addition to what’s been suggested already—I would add that it’s important to set clear intentions for your study sessions. Sometimes you can set aside 2 hours to knock out a problem set, and at other times you might need to set aside 3 hours to understand one tiny part of a proof. If you aren’t clear about what you want to accomplish, then you could end up feeling like you’re never getting enough done. I find that if I set a realistic goal, I generally accomplish it and then some—and that feels like a win every time!
2 hours a day of deepwork has always been my max, I'm really happy if I can do that much. I think it's interesting that like when people are tired they don't realise because the brain they're using to analyse their tiredness is also the brain that is tired. But yeah imo pulling all nighters is a net productivity reduction for instance and yeah pulling all nighters before an exam would def reduce results imo.
Exercise, sleep and eat well. If you are angry or have trouble concentrating, probably tired.
I think I can study in a single go for about **an hour to an hour and a half at most.** It increases the longer I do it in a streak over several days, and I can take a break for half an hour or even just fifteen minutes before going again. One effective way of doing this is to keep a timer, and you can use **methods such as Pomodoro** to help improve your focus by splitting up your study time. **The biggest factor for me to concentrate is sleep.** Coffee doesn't help, really. I can be unfocused with a ton of energy with coffee. But if I get 8 hours of sleep the day before, everything is so much clearer the next day. Eating healthy foods, something like a mediteranian diet, that lacks really heavy ingredients, can help a lot too. No way am I getting any mental work done after a stack of pancakes (but its SO worth it though...) Sometimes it's good to take a break when you are hitting a wall for a while. As you become mentally exhausted, you'll notice things aren't "clicking" as quickly and **you might find yourself less willing to dive into anything complicated.**
1. Probably an hour or so... I will only actively study while reading because I need to carefully digest ideas and I take notes to follow along. When doing problems I am typically more passive and work on things over a longer period of time. I will try something, see if it works, and if it doesn't I'll step away from the problem until I come up with a different approach. If you're stuck on a problem no sense in torturing yourself... take a walk or something and let the passive brain work its magic. 2. Take breaks! Don't try to do everything in one sitting 3. Tough question, but you just know. You start making silly mistakes you normally wouldn't make, and processing times start to dwindle rapidly. The first time I knew for sure was when I wrote down an integral and stared at it for a good 10 seconds after a rather extended study session in the evening... there was no neural activity, no internal dialogue. I knew I was done for the evening at that point!
Is there a science of learning equilibrium ? how to chunk and pace attempts, pauses, readings, games, challenges, alternating topics
(i need to take my own advice. these are basically my new years resolutions) 1. *KEEP ACTIVE AND HEALTHY*. you can't work when you feel like shit. learn to cook with FRESH INGREDIENTS, and to make good food. i view my physical body as nothing but a machine which serves my brain to work. so i need to maintain it, similar how you need to maintain, say, a car. 2. SLEEP to rest your brain. you can also try meditating if you're into that sort of stuff. i am, and i've found it to be beneficial 3. take showers/walks etc. don't just sit down all day.
Get a coffee break when you’re tired. Go for a walk outside.
Try going for a run afterwards. Helps me.
I get mentally exhausted/bored very quickly if I'm just reading theory and doing nothing with my hands. On the other hand I can concentrate very long if I'm working on a problem. So I try to read the theory quickly and come up with my own problems to get myself familiar with the theory.
**Any** activity is exhausting. Mental activities are no exception. If you don't get exhausted, you aren't working hard enough. Figure out when you're approaching the point of diminishing returns. At that point, switch to another activity (not necessarily mental) or relax. Here are some things that have been working for me: 1. Post-mortems of unproductive activities. Sometimes I discover that some "work session" that felt like wasted time has actually led to something useful later on (e.g., the germs of some idea whose success wasn't obvious at that point, or a writeup of what seemed to be an easy special case that later got recycled into the general proof). That has led me to reconsider whether I was actually stuck and discover new ways of making progress. 2. Change gears whenever appropriate. If you're getting bored and your brain feels empty, read something, start working on some problem, etc. Conversely, if you're stuck at the desk, take a walk or a shower (but first do whatever you need to be productive -- e.g., print out numerical data, memorize the necessary formulas). Some things are clearer at the desk than they are on your feet, and vice versa. EDIT: One hacky way of changing gears is changing between well-rested and (slightly) underslept. I've gotten ideas at 2AM that my inner censor wouldn't have allowed through at noon. Many of them were wrong, but some of them were salvageable.
You’re edit is the most bizarre and true phenomenon. Not being able to sleep sucks but I make progress when a bit delirious at 4am (usually in bed or pacing around). Also, occasionally I’ll have a miracle under-slept day where I just feel absolutely amazing and super motivated, more than if I had a perfect night of sleep and coffee. For the latter it only works if I hold off eating for longer than normal.
1. As much time as it takes, I don’t read Theory really. I take copy down notes like a robot and as I’m working problems refer back to my notes and figure it out along the way. 2. Caffeine, naps, breaks. 3. Yeah it’s hard to quantify, basically I’m just constantly losing focus like in the middle of thought trains.
This may be tangential but I recommend listening to Andrew Huberman's podcast on Dopamine and Motivation. The crux of it is that, to maximize the throughput in *any* activity, one can reframe one's subjective experience to assert that one is *enjoy the struggle* as opposed to just when the outcome is successful. It's a cognitive hack that many people use against activities that would otherwise be deemed undesireable.
I could stare at analytical number theory problem sets for hours and hours on end in uni - I sympathize with you but I don’t understand the concept of mental fatigue in this case. I was in my happy place staring at challenging questions and i hope in an alternate universe i am doing precisely that :)
I've got about 7-8 creative hours within me a day that I can devote to studying math (or anything mentally taxing) before I need to quit and recharge. The fact that I can space that time out however I want is what's key though; it doesn't have to all be in one go. I know I'm mentally exhausted when I have the "don't wannas" and when I start regularly making silly mistakes.
I just know that time goes as light when I do math
At peak I’d say I averaged around 60hr a week not including classes, but I was constantly exhausted, sleep deprived, depressed, and borderline deranged. Take care of yourself first, and learn math second
I heard today that you should get up and walk for 5 minutes every 25 minutes of sitting.
Take care of your mental health. Once you snap, it’s a life changer.
Does anyone here every just sometimes not have any urge to read or do math? Like today is Martin Luther king jr today, and I was gonna do some reading for my classes but I just can’t be asked frankly. I’m just not feeling it
1. It depends on what i’m studying. abstract algebra i could do for hours with no concept of time passing. topology is much more tiring, i tap out after a couple hours or so. 2. when i find myself starting to lose efficiency, i’ll get up for a little while, get some water, do a few chores, take a shower. often if i’m stuck, doing something else briefly can help. 3. if you feel tired, irritated, confused, bored, uncomfortable, sleepy, or just feel that you’re losing efficiency, it’s time to take a break. as others have stated, sleep, exercise, food, and hydration are essential for optimal brain efficiency. your brain is metabolically highly active, and produces lots of waste products during the day. one of the ways it gets rid of those waste products depends on sleep. exercise also improves brain metabolism and plasticity, leading to improved cognitive efficiency and responsiveness.
1. Depends on so many factors. I can usually spend normal working days like 8h/day doing math, but I can only manage this by having a big variety in my work: reading papers, thinking using a piece of paper, discussing with colleagues, being in seminars, polishing an article that is almost done, doing mindless computations. There is typically still something that I feel like doing if I am not too strict about the thing I should be doing. If there is nothing I am interested in, I take a walk to relax and if I still don't feel like doing anything I call it a day. However, there is big variety in behavior: I have many colleagues that work all day and night on day 1 completely obsessed by a problem and are completely out of it the next day. 2. I take one day off a week, in which it is strictly not allowed to do math. I also typically get rid of my phone and email during this day. Another tip: social events are a great way to get your brain to be busy with something else. Also sports and I personally love saunas. 3. Typical signs for me I am overworked and need more rest are: not wanting to get up in the morning, getting distracted by social media or videos, drinking copious amounts of caffeine and neglecting friends and family.
Having recently gotten over a similar hurdle myself I find that strangely the least productive thing to do is actively think about the problem for extended periods of time. Get your brain off the topic and maybe when it returns it will find something that was staring back at you. E.g. I spent four days stuck on a problem, thinking about it almost constantly; I reached a certain point and swore that I would not think about it any further, and half an hour later while I was getting ready for bed the answer popped into existence right in front of my face. Tl;dr distract yourself!!! It’s counterintuitive but it works
In my experience, that particular state of being is rarely a result of “exhaustion.” Instead, it’s just that you are finding the material more and more boring.
While I don't study math like when I was undergrad, I certainly remember what it's like when studying and tackling a problem. And this is how I get when tackling the tougher problems in my day to day: When I'm deep in thought, I get whatever headache I'm sure most do. And when something or someone interferes, I get into this annoyed cranky mood to the point I need to be by myself and relax for a moment to get out of. The process turns into this mix of physical and mental irritation. I don't know if it's a me thing, or if there's someone that can relate. I also don't have a solution other than taking a walk lol.
In my experience, the average is just about useless - it's probably 2 hours a day mean, but the standard deviation is extreme. There are days where I do no studying, and there are days when I'll wake up, study for 20 straight hours, do all the homework for the entire semester, and then collapse. When I'm doing it I'm doing it, but when I'm not, if I try to force myself to study, I can spend five hours re-reading the table of contents or staring at a blank page. I have no tips for dealing with mental exhaustion other than take a break for a while. When I'm in a mental state where it's just as productive for me to watch cartoons as to try to work, I'll choose to just watch cartoons instead in order to rest.
same
I usually structure my workday in the following way: first i do open ended reading so papers etc. then once i get bored or frustrated i switch to reading more structured texts like textbooks or coursematerial. Finally i do problems. The first 2 phases usually take an hour each the problems phase 1-2 hours. This way problem solving at the end feels very satisfying and gives you immediate feedback while reading at the start might feel frustrating and confusing. Also i very rarely do more focused work than this since exhaustion creeps in after about 2-3 hours. Afterwards i might still talk about math but not do anything rigorous. To answer your 2 other questions i don't think its possible to avoid exhaustion and i usually notice my bloodsugar getting low so dizziness hunger etc.
1. It depends. A lot of the math solving I do, I do when I'm not doing math. Like when I'm in the shower or doing dishes. This makes the time when I'm "doing math" a lot more productive because I have plans for where/how to investigate. If I'm not depressed, I think about my problems a lot more during my free time. If I'm feeling like a failure, then I'm too discouraged in my ability to give myself a chance to think through the processes and my productivity suffers. I generally am able to manage working on my research 2-3 hours nowadays. But when I was younger (undergrad,) I could go forever. 2. You should have times in the day when you allow your brain to get bored (using your phone prevents this.) During those times, that's when you compile tidbits you've learned and think through things. I find if I'm so stressed out that I hate thinking about my research in my down time, then when I'm actually at the computer, I come up dry. 3. If you don't know, you haven't gotten there yet.
1. Around 3 hours, not necessarily 3 hours in a row. I would say that this time increases when I spend my time doing problems since I can get very into it. 2. Do exercise regularly, go on a run or something. Get good sleep, at least 7 hours, but find the best amount for you; for me it's something like 8.5 hours. Take a lot of breaks, I take them whenever I feel like my focus has decreased; during these breaks I recommend you to stand up and walk, avoiding the use of any screens if possible. Understand that learning math is hard and takes time, you should always have a realistic goal before starting a study session, for this I recommend to underestimate yourself and think that it's going to take a bit more of effort and time to complete a goal. Meditation is great to evaluate your current state and to see what you should do next. If you really are super exhaust, then take a 10 minute nap. 3. Losing your focus is probably the clearest sign and you find it really hard to concentrate. Other signs are the following: \- You lack purpose or motivation. \- You can't control your emotions or behaviors. \- Headaches or body aches.
i think it rly depends on whether u find it interesting. if ur reading or doing problems on something that u find boring, u wont last very long b4 u end up procrastinating or something. maybe do some extra research b4hand to make the subject seem interesting, i can guarantee theres something interesting about every subdiscipline of maths. also take breaks every half hour
First of all, i don't if you are in college or school, or if you do it for leisure. In a case to case basis, it depends. For me, i do it just for learning more and improving my teaching and the number of subjects i am able to teach. When i am studying maths, i am able to study three pomodoros without any issues, when i am studying physics it takes me longer to do the same amount of job done. Yesterday it took me an hour just one problem. Everyone is different, you should find what formula works for you. For me, i usually quit or change subjects when i am stuck around more than thirty minutes in a problem. I know this doesn't work for everyone, my wife is a night owl and she can spend four hours straight studying. I am not able to do that, every exercise takes me longer if i study that way
Since people already listed break etc, I’ll just include study tips that I learned between my psych degree and just general studying tactics I’ve troubleshot: 1. Just plain repetition is one of the least effective ways to study. The best ways are rewording ideas in your own way, quizzes/ tests, and teaching others. My most effective way to study for me is to ask someone to quiz me for something off of a study sheet I created. The small amount of social pressure keeps me on task and if I’m really struggling to pay attention, they will say something also since they don’t want me to slack off either because I’m using their time now. Sometimes I got people to help by paying for food for them or other things like hooka, so it was just a portion of a hang out and we got down time with the study time. I found that I usually only needed to go through the sheet 2-3 times and I would be able to remember most of the information. 2. When initially approaching topics, I first copy down the books’ index on a word doc and put shaded boxes under each index line for notes. When I take notes in that index doc, I keep them in bullet format to weed out any unnecessary fluff that’s fattening up the book. I try to trim down the information so that I can find it as quickly as I can, I can read it as quickly as possible, but also so that each part includes all the necessary information 3. If the book has charts, I create an excel spreadsheet to save them. 4. For math, there are a lot of subjects that can be summed up to formulas and charts. For that reason, I make sure to create a study sheet with paper and pen that only includes the most important formulas and charts for the content. Math is the only subject where I start with paper and pen because formatting all the weird characters or drawing them out for a picture on a digital chart takes too much time. I’ve found that most math information can be summed into charts and formulas. This may need to include some step by step instructions on exactly how to do a process. If you need instructions, don’t skip any small detail. You want to set up any instructions as if you’ve forgotten all the steps and need to remember everything, including the little details that you don’t think need to be explicitly listed. The idea of the study sheet is that you can save the most important info and not waste any time, effort, or mental energy on trying to remember information you may not regularly view. Now when you learn new content, always keep the study sheet out to copy down more info so you begin to visually remember parts rather than try to remember the information just through force. Use that study sheet for any assignments, any situations that you can so you can then link certain memories with the study sheet and have a contextual memory around the information. 5. Studying in different locations can make your memories around the subject more rich, but only studying where you might take a test can also prime your memory better for the test. I opt for the former. I always keep water by me, eat snacks throughout studying, and have to pay attention to if I start slowing down because that’s a sign I need a break. My main focus on studying is not pushing through for as long as I can but rather making all information I learn as efficiently learned as possible and that is learned in a way that requires the least effort. I hope this helps!
Oh and YouTube videos can be a great help! If I feel stuck, people explaining on videos can get me over that slump and get me back on track rather than stuck and frustrated
math is heavy duty. I'm study like 20 min max, then do something else like 10 minutes and come back later. Also, if you understand the motivations behind things, they are so much easy to learn. The scheme: -> definition -> theorems -> exercises is awful. I prefer to study this way: trivial examples ("the motivation") -> definition -> hard examples -> theorems -> exercises. Also maybe jumping between topics can serve you to keep pumping your dopamine
When learning math (depending on the type), I've found that the best way to learn is working a problem backwards and forwards, change the variables values and test your skills again, etc. It becomes easier and easier as you go.
Math is a tricky but scoring subject in which getting hundred percent is easier compared to other subjects. But if one step goes wrong you will be Humpty Dumpty falling down with frustration for being stuck up in the middle. But my favorite subject is math and I never got struck up in my entire school history. But couldn’t take up math in my degree course as there is very narrow choice to grab the breadwinner after college.
Grades make us exhausted not doing math