Why should I use Proof Index?
Why can't I just use Khan Academy?
Khan Academy doesn't offer undergrad courses beyond the calculus sequence.
Often, someone on YouTube has a better video on the same topic.
Why can't I just search YouTube?
Many videos are horrendous to watch, or listen to, or both! I have watched the vast majority of videos in the index. I wouldn't show you something I wouldn't be willing to watch myself.
Many speakers have thick accents. I find it takes significant brain power to understand someone with a thick accent. Therefore, I have chosen to tailor the index for American English speakers. If I can afford to hire someone in the future to index videos where the speaker has a thick accent, or speaks a foreign language, I would certainly like to do so.
Some videos contain mistakes. If a mistake is easily recognizable by the student, then it's no big deal. However, a mistake the student fails to recognize will likely confuse them. The student is likely to doubt themselves instead of the teacher. They're likely to think "Why didn't I get the same answer? What did I do wrong?"
Your query may not refer to a unique topic. Let's say you're learning how to find the arc length of a circle. If you didn't know that arc length of a curve was a calculus 2 topic, you might query "arc length." But now you're getting search results for two different topics. More subtly, the "midpoint rule" applies to both integrals and double integrals. If you're learning calculus 2 for the first time, the first video you watch could be on double integrals, leaving you bewildered.
Sometimes, topics have synonyms, which means that unless you've got great Google-fu, you're not getting all the videos related to your topic.
Sometimes videos are titled vaguely. For example, Brian McLogan has a video titled How to Determine All of the Zeros of a Polynomial, but the topic is the rational root theorem.
Sometimes, videos have clickbait titles, which makes their topic difficult to discern when browsing. Also, I think it's likely that when searching for videos on a specific topic, videos with that topic in the title will be ranked higher than those without.
Some videos are titled incorrectly. I remember seeing videos like this, but I can't recall which ones.