i am preparing for Mathematical Olympiads , on the other side i am willing to start advance topics too. But i feel learning advance topics will destroy my originality thinking and i will start thinking complex . please help me .
2026-03-29 23:41:59.1774827719
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Should i start Advance mathematics
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I think a good mix of problem solving and exploring into a subject you are interested in is a good idea. Keep practicing Olympiad problems, but also read about, watch videos etc about whatever advanced mathematics you want. One thing I should warn you about is ‘the calculus trap’. There is an article here for you to read if you want. :)
https://artofproblemsolving.com/news/articles/avoid-the-calculus-trap
If your main focus is to do well in the Mathematical Olympiads, all that really matters is that you keep that in focus. The beautiful thing about mathematics is that it builds on itself and is coherent. If you start learning something new that builds on what you know, it won't lead you to answer a simpler question incorrectly.
Honestly I remember getting a mark taken off in one of the earliest math classes I had because I wrote something like "2-5=-3" and when I asked about it being wrong the teacher said that was not where we were in being taught and the proper answer was there is no answer. But that kind of thing won't be happening in the Mathematical Olympiads. One thing I think you are worried about is over thinking or thinking in the wrong direction. So if you are learning new things and new ways of approaching things, check example problems from the MO as you go and reasure yourself. I guess it depends on how you learn and how you understand things weather it's absorbing it and making it natural from the core to you, or memorizing and learning tricks. If you take on new kinds of problems you make your mind more dynamic and give it more tools and practiced pathways to use or not use when tackling a problem. But if you are worried about distracting yourself and being stuck in a different way of thinking, and that impeding your ability to do your best at the MO you should keep that in mind.
One thing that really stood out to me was that you said you were 'willing to' start advance topics. Not that you were interested in or curious or anything to express desire. I can tell you with certainty that more advance maths don't go against what came before. You use everything that came before in the practice of it. If you want to, dip your toes in, and check back on the MO. You'll see for yourself how you feel. But if you have goals and milestones in mind that matter to you above exploring other things right now, you should think about that.
There have been times where I learned something new and it changed my understanding in a way I could go back through everything I knew before and make really cool realizations and maybe rarely find my own way of making problem solving more intuitive and quicker, but for the most part they give you the most useful tools for solving problems at each level of learning. So calculus gave me a different way of seeing and feeling numbers and situations, but didn't help my algebra beyond a better understanding of the exploration of limits and critical points.
One last thing I just thouht of is how the brain works. If you give it a challenge it struggles and grows. So maybe the act of trying to learn and understand new things will make your brain develop beyond just taking in new understanding and make it work better as a whole, for all problems.
There is no absolute answer to your question. But there are edjucated guesses. Trial and error doesn't work so great when you have one life to live. But at the same time, understanding that can really help. You don't want to regret a bad choice, but you don't want to live consumed with worry about 'bad' choices. They're all unomptimized good choices. And you can't know all the perameters. So accept that and and hapily make an edjucated guess and don't worry about the unkowable unkowns. Focus on your goals and adapt and experiment. And always ask questoins.