Silence is not the absence of sound, but the presence of something deeper.
At a restaurant do you order what you know is great, or do you try something new? Do you make what you know will sell or try something new? Do you keep dating new folks or try to commit to someone you already met? The optimal balance for exploring new things vs exploiting them once found is: 1/3. Spend 1/3 of your time on exploring and 2/3 time on deepening. It is harder to devote time to exploring as you age because it seems unproductive, but aim for 1/3.
Mathematical intuition often guides the development of algorithms, but it is the rigorous proof that ensures their correctness and efficiency.
The task of philosophy is not to resolve contradictions but to make them visible.