I have reached 2000 rating in rapid at lichess. I am a student, so I have to keep up with my schoolwork. I get around 1/2 to 1 hour on chess on each weekdays and 2hrs on weekends. My question is, if I want to get better, do I have enough time to get a higher rating or it's unlikely for me to improve?
Thank you in advance.
You are young and with your skill, you may reach a master title in some years if you have talent and you study a bit in an efficient way. That can be good for your cv and good for your life and satisfaction.
You must know the difficulty to climb from 1800 to 2000 may be as hard as from 2000 to 2100, or from 2100 to 2150, or from 2275 to Fide Master etc. It is so hard because imagine you play 5 games with 2200 ELO against 5 players rated 2000, you draw 4 and you win 1; you are gonna lose some of your points!
Players that plan to reach FM title use to study with the assistant of a good trainer on a club. That doesn't mean to study more than the 5/10 hours/week you are currently spending on it, but to planify correctly what to study -benefitial opennings, weakness, ...-. And you will need to play federated games, of course, so if you gonna seriously for a performance of your ELO, chess will take most of your afternoons on weekends -game plus some time to prepare it against specific opponents-.
If you plan to do a maths degree, it migth be valuable to have a high level and play for your university and study there. You will also meet people wich is always nice when you are new on a site.
If this is not going to happen soon, you can continue studing a bit, books as "My system" of Nimzhovic, do some tactics, play some correspondance and not only rapid games, analyze your mouvements when the game is finished, watch videos of your favorite opennings, try new ones,....
I haven't seen you playing, but if you were going for GM/professional skill, you should be trained by a master and take some more of your valious time spent studing your lovely mathematics, and I guess that is not what you have on mind.
You can take as an example about how hard is the best chess player of my little spanish region ever. He did 3rd on national spanish championship on 2016, but he has not reached GM -he has been very close, but unfortunately he has still not got it-.
I followed his facebook profile while playing an international open. He was rated 2480 if I remember well -and I think he has yet the normes, he just needed 20 points to get the title-. He complained, after drawing against a 18 years old russian rated 2250, something like:
"Today I played against a 18 years old russian. He played 30 consecutive book moves of a line I knew well, where there is only a chance for black to draw it."
With the time you say you have to spend on chess, of course it's possible to improve. You should remember that chess should never come first though, and it's just a game you enjoy. If you're not aiming to be a professional, don't spend hours on end every day studying it.
Here's a list of chess literature I think would benefit you, at your skill level:
Grandmaster Preparation series by Jacob Aagard. If you can work through all the books in it (I believe there are 5) you'll definitely improve.
My Great Predecessor series by Garry Kasparov. He annotates games of all the world champions (as well as many other strong players), and it's incredibly instructive. I also learned a huge amount of chess history from the series.
Other than that, it's good to continue playing online and doing tactics training. Even if you did only 1/2 hours per day of reading/playing/tactics, you'll start to see improvement. Also, since school should come first, I'd recommend not exceeding 1/2 hours per day, unless you're absolutely set on becoming a GM / professional (which I don't recommend).
You have plenty of time, but, please, concentrate on your study first, chess comes the second.
I have a few friends, well... people I know, like you. They all heavily invest their time in their education and possible employment opportunities. They all still play quite strong, but don't consider chess anything but hobby.
Go find a club and quit making excuses.
Being 2100 on lichess without a FIDE rating is like saying you're division 1 in FIFA 18 without ever having played for a real-life team. Go find a club, because no one cares about lichess.
Once you start playing at a club, your chess will improve at a speed you couldn't imagine, and you will make a lot of friends.
You will grow as a person and learn about yourself.
Good luck.
