u/Pale_Complex7076

I'm his older brother, currently in college majoring in chem engineering. My younger brother is 15 and spends most of his free time doing mathematics. He also keeps a diary where he writes down his mathematical ideas, observations, achievements, and anything interesting he comes across.

This is some of the things he has independently worked on:

Rediscovered the basic trigonometric ratios before learning them in school.

Explored prime-generating polynomials. Explored ideas related to the nth prime.( He was 13 yr old innocent guy then )

Arrived at symmetric variation of the Goldbach conjecture.

-Investigated prime around expressions of the form 2^n + 6 ( if n is even then primes are -3 and + 1 from it and if odd then -1 , +3 from it , works for n as 1,2,3,4,5,6,16,18 etc.

Developed an infinite-triangle method for approximating polygon and segment areas.

Created generators for Pythagorean triples.

Arrived at the positive-index binomial theorem formula by observing patterns in expansions and translating those observations into a general formula.

Etc etc much more a lot of work and ideas he has he is kinda obsessed

I'm not claiming that any of these are new discoveries or that he has solved any famous open problems. I know it's possible that many of these ideas already exist and that he may have rediscovered known mathematics independently.

I'm just curious how unusual this kind of mathematical journey is for someone his age, and what you think would be the best direction for him going forward.

please tell me what to study in what oder from where and do problems for where ( e'ryhting in order plzz , it will be very helpful for me) . i have CTPCM , excusion in mathematics , TOMATO , david 's NT , hall and knight , and problem solving strategies , and doing self-study. i more of an book nerd , who likes to sit with explanations and teach himself stuff slowly.

please tell me what to study in what oder from where and do problems for where ( e'ryhting in order plzz , it will be very helpful for me) . i have CTPCM , excusion in mathematics , TOMATO , david 's NT , hall and knight , and problem solving strategies , and doing self-study. i more of an book nerd , who likes to sit with explanations and teach himself stuff slowly.

i am not 100% convinced that it is real , if real i wana learn it prescribe some book for begginer

if u are an Sanskrit learner outside india then please comment and tell about how u started and how its going ???

I want to study the density and occurrence of prime numbers in Collatz sequences. For each starting number n, I will generate its Collatz sequence and count how many terms are prime. Then I will compare the prime density across different starting values and look for patterns. u can give ur ideas too please... is it good idea should i work ??

I’ve noticed a weird trend in my government school ( kv )recently. There’s an excessive amount of political signage—specifically portraits of the PM Modi —posted in every random corner of our campus.

It’s not just one or two; it’s dozens. And honestly, it’s distracting. There’s nothing educational about them—just the same face, over and over. I feel like our school walls should be used for things that actually contribute to our learning, like maps, scientific diagrams, or a wider variety of historical figures. the chemistry lab has expired chemicals , poster of kalam sir is so outdated that according to it , he still lives.

Is this standard now? what are rules about this , is it normal and Does anyone else feel like this messes with the "neutral" vibe a school is supposed to have? ( NOTE : first post ,used ai for it )