Can I hide the fact that I dropped a PhD program when I apply for another PhD? I am an international grad student in the US. I would like to quit the PhD program(mathematics) in where I spent 2 years without "any degree" for some reasons. I am in the status prior to the research. If I want to apply for another PhD in other universities, will leaving the fact that I dropped a PhD program without a degree off make serious problems?  Does it make some legal, ethical, moral trouble in the academia?

Lastly I just wonder whether, if I am admitted to another grad-school, the department will track or check my previous academic record by inquiry VISA status, SSN, or the other ways.

According to the FERPA(Federal Education Rights and Privacy Act) act, can I control my educational records myself? I asked about this to some schools, they said, even if it's true, the school can also have the right to require the student's educational record in the case of application to the school.

If I got a degree in a school, I also think I should put the fact in the application.
But should I write my all post undergraduate record in my PhD application even if I didn't get any degree and just quit?
Most (all?) universities in the US require that you mention all the schools you attended on your application, regardless of whether you obtained a degree from them. Omitting any school is a violation of the rules and, if discovered, could be grounds for rescinding a potential admission offer, even long after it has been granted.

In other countries, it varies.