Mostly, talk therapy. As you say, struggling with a hard problem for an extended period of time and feeling dumb is part of the process. For me, the shame was excruciating, so I'd turn my attention to anything else to stop feeling shame. The shame was intense enough that the underlying "felt sense/thought" was "I don't deserve to be on this planet". With the help of a therapist, I managed to start looking at myself and _managing_ the shame, so I could then examine my behavior and experience: Oh, I said that mean thing to somebody - I (deservedly) feel bad and want to change how I treat people. Oh, I couldn't get a math problem right away: I don't need to feel negatively about myself because of that. Frustrated, sure, but NOT "I don't deserve to be on the planet". Shame that intense tends to be (and was for me) rooted in childhood: Weak/bad parenting. It's a project to overcome it.