How do you prefer meeting people: organically through friends, spontaneously, or third parties arranging serendipitous encounters?

I prefer to meet them on my terms, for a reason (other than I am an ass).

I have the fortune/misfortune to have my farm on a major biking and walking route for tourists coming to Northern Michigan. When it was originally built the outbuildings were put right at the setbacks for the road. I am in favor of tourists 19 hours a day. I am more than happy to show them around the farm and let them see the goats, horses, chickens, etc. During the summer I probably average 2-3 tours a week. I also run my woodworking and carving shop and on premise

But when it is milking time, (two times a day, for 2-1/2 hours 0430-0700 and 1630-1900) I have no time for tourists. I have my hours posted. But many tourist do not care. I cannot even afford to walk slow. The screaming goat commercials are not far off. 48 screaming goats who want their grain and to be milked (a full udder is painful) is a crappy situation, and timely milk sanitation is literally a consumer safety issue.

I try to be polite, but if they don't get it the first time, I give them a choice; "start working, get ignored, or come back in ___hours". Unfortunately I've developed a reputation for being a grouch with the tourists, except the ones that accept my invitation to come back in an hour or two.

I'd welcome a set up...although I've never had one...

Either through friends or social activities.

Questions........
#1 have you known this professor for a while?
#2 Is he arranging the meeting as a dinner/drinks atmosphere or strictly business?

I'm an introvert. Most of my meetings are through work or organically through friends. It's not that I'm anti-social, only I am more comfortable going over my own thoughts than listening to someone blather on about theirs and quite frankly, I'm not one for chit chat and small talk.

I don't much like any of the responses. I would be courteous and probably welcome the interaction. It's still not my preferred method of meeting people.

For me I much prefer meeting people through work or school. By encountering those people every day you learn a lot about each other and many of my greatest friendships have spawned through work and school.

Church groups are another good one. One of my best friends (although we've sort of had a falling out recently) and I got to know each other through youth group. She wasn't the only person I befriended there either.

It's all about being in situations where you and someone else have something in common. Even if it's only one thing it can be enough to spark a conversation that me lead to a lasting friendship.

Depends on how lonesome you are.

I think a full conversation and understanding of the events as they're unfolding is what is needed here. There's only a little context for us to go on. If the prof is indeed trying to have you make friends while working out, I could understand your lack of enthusiasm. My gym time is pretty sacred to me as I only get a little of it each day. I'd rather not be bothered with being social to strangers. I don't even like talking to friends when I work out. If, on the other hand, he is trying to maybe help his friend out by having you meet them outside the gym for pointers or something, I'd take it as a compliment. It takes a lot for a stranger to ask for help sometimes. Either way, I would NOT just stop going to the gym unless he won't leave you alone. I WOULD approach the situation and individual with some tact. (My younger self would hit me for even suggesting tact...)

What is the point?

Personally, I don't like meeting people at all. I find myself uncomfortable in most social situations and typically try to avoid socializing more than the standard small talk.

Now in regards to your example, this arranged meeting could be on friendly terms or romantic terms. Maybe this other person had confided in the professor of their interest in you and is trying to arrange a meeting. Maybe the professor has graded both your work and seen how similar your thought patterns are and thought you'd make good friends. Maybe the professor thought you or the other person looked upset or depressed and was trying to encourage another person to break the other out of the funk. Or maybe even the professor is playing the matchmaking game. I know some teachers who put a pool together to see which students end up with which.

There are plenty reasons the professor might be doing this, if this type of behavior bothers you, the biggest thing I would do is find out why they are doing it. Or in the very least find out what their intentions are.