It's a common theory and is fairly plausible but there's no official confirmation. All we know is that.
>Ash's Mom has known Prof Oak since she was a young teenager at least.
>She was one of his students as well
>She had Ash when she was 18 since her official age is 28
>She's hung out with him ever since and goes on vacation with him on a fairly regular basis.
So the idea that Prof. Oak knocked up one of his students and his been taking care of her and her son since then seems kind of likely. We also haven't seen the rest of Oak's family except Gary so it could be he's a widower or something.
