Going back to your first dilemma, think about the broader scope of an intellectual discovery - restricting your own perceptions of intellectual discoveries to just an "intelligent" or eureka moment hinders the growth of personal growth and ideas. So, take a moment and step outside the "physical" realm of intellectual discoveries, and consider ways a character could perhaps demonstrate growth of thought, growth of spiritualism, or even just growth of character.
Intellectual discoveries, at its core, discusses breakthroughs and new insights about humanity. It allows the audience to connect with the character in an entirely new dimension - it causes them to think more closely about certain ideas, values, and attitudes. One of the most well-known intellectual discoveries was the wheel. Perhaps, you could use this to aid your own critical thinking about discovery.
You could very well link it closely with other core discovery values, such as spiritualism - critical thinking (intellectual discoveries) elevates spiritualistic ideas for the audience -, adventure - innovation sparks adventure - pragmatism, and many more. The possibilities are only as wide as your own understanding - so take a step back, and reconsider what it means to have intellectual discoveries.