Do I need to ask a permission to acknowledge a respected mathematician in my paper? After writing the first draft of my paper, I sent the proof to an expert in my area. He responded my email in a neutral way, something like: I think if your argument is true then it would be nice,... I suggest you may read the paper ... to ... 

Now, I would like to acknowledge him in my paper, sth. like: "I would like to thank Professor A for his comments". In my opinion, I should do this to show my gratitude. Besides, this also makes my paper somehow more concrete and professional, I think so.

My question: Do I need to ask Professor A the permission to acknowledge him? Or I just acknowlegde him without asking?

Thanks.
I don't think it's necessary to ask permission for something like this - there's really nothing he could do to stop you from acknowledging him if he did take issue with it, so the permission isn't even his to give to begin with.

That said, you're acknowledging him because you respect and appreciate his comments, and want to formally recognize the working relationship you have with him. It couldn't hurt to send him an email thanking him for his contribution, and mention that you will be acknowledging him in the paper. If he really has a problem with it, he'll have the opportunity to ask you to do otherwise at that time.