My PI assigned me to a direct supervisor who is academically incompetent. What should I do?
They are supervising you. You will be 100% sure they are wrong and you are right only after external independent confirmation, which you can obtain by attending conferences/workshops, and publishing a paper or two would be the definitive seal.
However, by that time, you may realize why your directly supervising PhD/PostDoc is working that (inefficent) way ...
So, it is better to show some independence and get -intensively- in touch with the PI after a couple of weeks.
With the PI, it should be possible to have an honest discussion, even regarding the point &quot;the supervisor you assigned me cannot help me because of lack of time/needing some time to freshen up his/her knowledge on the Stat-of-Art of Science and Technology on my specific topic&quot;.
If it's not possible to be so open and clear with the PI, well, the issues are way larger than the supervision from said PhD/PD ...