> How does one keep up when we can produce proofs faster than we can understand them?
Life without understanding may be OK for routine life chores ... we passed that stage when computer chips got into cars and TV sets and when banks turned from calculators to computer iron ... the urge to understand things drives all of science, and innovation.
Arguably, understanding makes us more valuable than machines, adaptable, and happier, especially in our relationships with others. Understanding others lets us give really good advice, rather than milquetoast "reinforcement", which has had devastating (suicidal) effects, when true understanding was needed, and lacking. Ultimately, it's still a world of people. Thoreau warned "But Lo, men have become the tools of their tools" and take that to heart.
> How does one keep up when we can produce proofs faster than we can understand them?
Life without understanding may be OK for routine life chores ... we passed that stage when computer chips got into cars and TV sets and when banks turned from calculators to computer iron ... the urge to understand things drives all of science, and innovation.
Arguably, understanding makes us more valuable than machines, adaptable, and happier, especially in our relationships with others. Understanding others lets us give really good advice, rather than milquetoast "reinforcement", which has had devastating (suicidal) effects, when true understanding was needed, and lacking. Ultimately, it's still a world of people. Thoreau warned "But Lo, men have become the tools of their tools" and take that to heart.