First of all, I agree with kty777 that you should not directly confront the woman with facts about what researchers have discovered about serial killers. She has probably come to you for advice, and has already begun to recognize that something is terribly wrong with her son. Take that as a compliment to you, that she feels you are someone she can confide in and perhaps might be knowledgeable. The one thing she probably needs you to tell her is the name of a great child therapist in your area, specifically one that deals with pyromania. If you don't know of such a person, the one way you can be a great neighbor to her, would be to offer to sit down with her one day this coming week and go through the phone book making phone calls from YOUR house asking each and every psychologists/therapist/social worker's office listed in the yellow pages, about whether or not they treat children with pyromania issues. This way, you can help her to find help, and do it privately from your home, so, as to not alert little master pyro into acting out and starting another fire in his anxiety if he should over hear his mom trying to call around for this type of help. I know that this is not much, but seeking a professional's guidance is most important for this young boy. He may or may not become a serial killer, and truthfully, it's a combination of both nature, and nurture. It seems to me that his mother has the right kind of love for her child, so, he will probably be fine, and get the much needed help he needs. Also, there is a possibility of your local social services offering free help for this kind of issue. She can only ask the social services people. PS: If you are really living near such a child, be warned and keep your eyes open for the danger of fire (get smoke detectors, fire extinguishers, etc. for your own home). Such compulsions do not suddenly disappear over night without help.

You know I would probably suggest she take her child to a clinical psychologist, but wow I'd be careful about how I said it. I would probably phrase my response in terms of her own well being and her stress and her family needing some assistance with the son. AND it depends on how old the son was - if he's certainly old enough to know better then I would be more inclined to say something but if he's very young I might not ( wow its a hard one! )

BUT I'd be careful about saying anything. If she is already worried she may just need that neighborly suggestion but if she gets defensive all I've done is cause a neighbor row :( and that's probably the last thing you need with a disturbed pyromaniac living next door.

If she seems like she's 'reaching out to you' then its very hard to ignore.

Would I mention the words 'serial killer' - ah NO! never come out of my mouth - you can't take that back and it might not be that serious...

I would tell her the information. There is a good chance that she knows it anyway as it is well known signs of serious problems. I would advise she get the kid a good doctor to examine his actions.