The term 'egghead' is often used to describe someone who is highly intelligent. The crossword solutions for this term include 'GENIUS' (6 letters), 'INTELLECTUAL' (12 letters), 'SAVANT' (6 letters), 'BRAIN' (5 letters), 'GEEK' (4 letters), 'INTELLECT' (9 letters), 'NERD' (4 letters), 'SAGE' (4 letters), 'smartbell' (9 letters), and 'humptydumpty' (12 letters). All of these words refer to someone who is very knowledgeable and has a high level of intelligence.