After learning a new concept, it is important to “play with it” for a while. Because the new concept is initially not associated with anything, so you probably will not see what it is good for.
For example, if someone tells you “a prime number is an integer number greater than one that can only be divided by itself and by one”, that is easy to understand (even easier if they also give you a few examples of primes and non-primes), but it is not obvious why is this concept important and how could it be used.
But when the person also tells you “the number of primes is infinite… each integer can be uniquely factored into primes… some numbers are obviously not primes, but we don’t know a simple method to find out whether a large number is a prime… in arithmetic modulo n you can define addition, subtraction, and multiplication for any n, but you can unambiguously define division only when n is prime...” and perhaps introduces a concept of “relative primes” and the Chinese remainder theorem… then you may start getting ideas of how it could be useful, such as “so, if we take two primes so big that we can barely verify their primeness, and multiply them, it will be almost impossible to factor the result, but it would be trivial to verify when the original two numbers are provided—I wonder whether we could use this as a form of signature.”
After learning a new concept, it is important to “play with it” for a while. Because the new concept is initially not associated with anything, so you probably will not see what it is good for.
For example, if someone tells you “a prime number is an integer number greater than one that can only be divided by itself and by one”, that is easy to understand (even easier if they also give you a few examples of primes and non-primes), but it is not obvious why is this concept important and how could it be used.
But when the person also tells you “the number of primes is infinite… each integer can be uniquely factored into primes… some numbers are obviously not primes, but we don’t know a simple method to find out whether a large number is a prime… in arithmetic modulo n you can define addition, subtraction, and multiplication for any n, but you can unambiguously define division only when n is prime...” and perhaps introduces a concept of “relative primes” and the Chinese remainder theorem… then you may start getting ideas of how it could be useful, such as “so, if we take two primes so big that we can barely verify their primeness, and multiply them, it will be almost impossible to factor the result, but it would be trivial to verify when the original two numbers are provided—I wonder whether we could use this as a form of signature.”