> Professional mathematicians peak in their 20s, just after they stop solving "shallow" questions, and start poring over "deep" ones.
This is a ridiculous myth. As a truism, person's creative intellectual output is greatest when they are working hardest and have the greatest number of tools of creation available to them. I could go down a long list of mathematicians (famous and not famous) whose most influential work was done later in their careers.
Criticizing Khan's videos on history is shooting fish in a barrel; the videos are short and concise and history is long and complicated. I could write many paragraphs of what is neglected or biased in just about any introductory books on mathematics, but I wouldn't really be making a statement about their quality. Quality would be determined by evaluating these resources by their effectiveness at fulfilling their purpose.
This is actually the root of the controversy in my opinion: the real purpose of all this online educational material (Khan academy, various youtube channels, MIT OCW, etc) is still pretty multifaceted and ill-defined.
I'm making my videos because I think that well-crafted videos make material more appealing and accessible to a lot of people on the internet. My hope is that people who are already learning the material will supplement with my videos and people who are introduced through my videos will get interested and seek out other sources. In this sense I would hope that they provide a window OUT of the "Skinner box", as would any other reasonable piece of educational material that stokes the desire to learn.
This is a ridiculous myth. As a truism, person's creative intellectual output is greatest when they are working hardest and have the greatest number of tools of creation available to them. I could go down a long list of mathematicians (famous and not famous) whose most influential work was done later in their careers.