The Restricted Burnside Problem asked whether there is a bound on the size of a finite group with $d$ generators and exponent $n$. Kostrikin proved there is a bound for $n$ a prime in the fifties. Hall-Higman theorem reduced it to prime power $n$'s. Zelmanov gave a positive answer for prime powers (the odd case appeared 1990 and the even case in 1991, so we are borderline 25 years). The proof is very difficult and as far as I know it was never simplified (or at least not substantially).

The Restricted Burnside Problem asked whether there is a bound on the size of a finite group with $d$ generators and exponent $n$. In the 1950s, Kostrikin proved there is a bound for $n$ a prime. Hall-Higman theorem reduced it to prime power $n$'s. Zelmanov gave a positive answer for prime powers (the odd case appeared 1990 and the even case in 1991, so we are borderline 25 years). The proof is very difficult and as far as I know it was never simplified (or at least not substantially).

The Restricted Burnside Problem asked whether there is a bound on the size of a finite group with $d$ generators and exponent $n$. Kostrilin proved there is a bound for $n$ a prime in the fifties. Hall-Higman theorem reduced it to prime power $n$'s. Zelmanov gave a positive answer for prime powers (the odd case appeared 1990 and the even case in 1991, so we are borderline 25 years). The proof is very difficult and as far as I know it was never simplified (or at least not substantially).

The Restricted Burnside Problem asked whether there is a bound on the size of a finite group with $d$ generators and exponent $n$. Kostrikin proved there is a bound for $n$ a prime in the fifties. Hall-Higman theorem reduced it to prime power $n$'s. Zelmanov gave a positive answer for prime powers (the odd case appeared 1990 and the even case in 1991, so we are borderline 25 years). The proof is very difficult and as far as I know it was never simplified (or at least not substantially).