Following my private communication with [Ron Graham][2], he kindly shared all what he knew about Erdős' mathematical diaries with me. Here is part of our discussion which I am allowed to share on MathOverflow for the benefit of the public mathematical community. At Ron's request, I removed the name of one of Erdős' co-authors in the below passage. Emphases are mine. 

I would like to sincerely thank Ron for his attention to my question as well as his permission for publishing part of our private communication here on MathOverflow.

> *Besides the literally thousands of letters that Erdos wrote during his lifetime, the best source of his unpublished mathematical thoughts are contained in his **mathematical diaries**, which he meticulously kept for most of his life. In them, he would write what he was thinking about, who he was visiting, etc. **There are 15 or so of them, kept in what looks like laboratory notebooks**. Of course, they are all in Hungarian. When Erdős died, the diaries were given to **his close colleague** [name removed] (who) still has them but **will not let anyone see them**. Many of us have tried to change [name removed]'s mind but to no avail.*  




  [1]: https://mathoverflow.net/questions/307209/how-to-find-erd%C5%91s-treasure-trove#comment764262_307209
  [2]: https://en.wikipedia.org/wiki/Ronald_Graham