Conversation between freshman from senior high school and retired professor who suffers from Alzheimer's disease I live at a university town where I am freshman at a
senior high school.
Some years ago a car steered by an inebriated driver
smashed me off my bicycle and run over me. 
Nowadays I am a paraplegic sitting in a wheelchair. 
I can keep my head upright and move my left arm and 
hand. Any other limb of mine currently is still -eh- 
out of order. 

Due to my physical deficiencies I don't do much 
sporting activities. I get along with little sleep
(about 4 hours/day).

I have permission to go to the library of the faculty 
of mathematics and natural sciences of the university.
I am interested in number theory and therefore I use
to spend large parts of the evenings and nights at the
library.

Two weeks ago at the cafeteria of the library building
I got into conversation with an elderly gentleman who 
started small talk. After about half an hour I realized
that the small talk had turned into a private lecture 
that I was recieving about the topic which I learn about
in the library (quadratic diophantine equations with
2 unknowns). The gentleman didn't seem to perceive
the surroundings any more and he was engrossed in
monologues at dissertation level.
I was deeply impressed. 
At some point of our conversation I learned that he 
is 86 years of age and a professor emeritus.

The next evening I met him in the cafeteria again
where he seemed to have been awaiting whether I
would drop in too. He had brought along some books and 
papers which he thought I might be interested in.
Again the conversation turned into a lecture after 
a while and again he seemed to enjoy teaching maths and
being in his element.

We met every evening since in this constellation
and I enjoyed these meetings.

But today a woman who introduced herself as his daughter
cut our conversation short. She told me that her father 
in fact is a retired professor of the faculty of 
mathematics and that he suffers from Alzheimer's disease 
and that she wished to apologize for any inconvenience 
her father might have caused.

To me the point is: Subject of our conversation was
number theory. I did not realize myself that he suffers 
from that disease. Thus to me it seems that the disease
did not affect our conversation in a negative way. 
I enjoyed our meetings and to me it seems that he also 
enjoyed talking to me about maths.

At the moment I have the feeling that currently he still 
is capable of talking about number theory and 
that currently he still enjoys talking about that subject.
I fear that discouraging him in doing so by now would mean 
anticipating some aspects of the disease having reached 
levels that probably aren't reached yet.

How would you deal with the situation?
One of the things that helps Alzheimer's patients the most is routines - especially routines from earlier parts of their lives (such as when he was a full-time faculty member). Keeping the brain active by thinking through number theory is also very helpful in staving off further progression of his dementia.

So if it was part of his routine when he was active faculty to go to lunch everyday in the dining hall and then to lecture, then you have now become a living part of his past and current world and helping him (and his family) stay functional.  As long as you are both enjoying it, there is no reason not to continue.

As gnometorule says, I think his daughter would be heartened to hear that 1) you enjoy this and 2) you would not have known he had Alzheimers had she not told you.  As gnome says, though, I would keep her apprised if you notice any changes.