The artist: Charlotte Cory, 56
I met Kevin on an internet-dating site. I'd walked out of a long marriage and been rattling around on my own for 18 months. The fact that he was a mathematician... well, I'd wept through my O-level maths and I can't even write phone numbers down correctly. In fact, I think I went to meet him out of sheer perversity.
We went to the British Library for a coffee, and he told me he had studied astronomy, so we ended up having a conversation about the stars and planets. I was out of my depth but it was just so magical to be with somebody who talked in such a learned and open way - it was what I'd been looking for all my life.
I'm louder, whereas Kevin has a serenity, which I find very endearing. Sometimes he'll just sit gazing into space working out a formula and I've learnt to leave him to it. I've also learnt not to use language so casually, as it causes him genuine pain. We'll be out shopping and I'll say, "Oh god, we don't need butter, there's millions of packs in the fridge," and I can see him start to think, because he's looking in his head at the millions.
He's got a fantastic eye: if I'm working on a picture, he'll look over my shoulder and quietly say something and is always spot-on. He's always been interested in the intellectual basis of my art.
But at the same time, we have our own takes on everything. For example, last summer we went to the Olympics dressage. I was obsessed with the beauty of the riders dancing with the horses, but he was picking up on the mathematics of how horses actually run.
The mathematician: Professor Kevin Parrott, 62
Charlotte said she was a photographer on her dating profile, and that drew my eye: I'd done astronomy at university, which at that time was mostly concerned with photographic observations. She said to me from the start, "I think I'm a bit wild for you" - which is true, but everyone's more flexible than they think they are.
One of the main differences between us is that Charlotte notices so much: she picks up about 10 times more than I do, in terms of where we are and what the people around us are doing. But she's also totally unembarrassed by things I appreciate; as a mathematician, if you see something, you say it. And I enjoy her sense of humour: I don't know anyone else who'd claim to have had a séance with my dead mother, but she [will joke that] she has; she'll offer genuine insight into my behaviour based on what she reckons my mother would have said.
If I didn't like her artwork, I don't think I would have married her. She works with taxidermy and I've had to get used to having it around the house. I'm currently staring at a monkey. I go to the odd [art function], but they're a bit difficult, to be honest. People talk at each other, and I never have anything to say.
The key to our relationship is a sense of freedom, of being able to go on a bicycle ride together and be kids again, say. The older you get, the fewer answers you have, but you have to have fun.
The butcher: Des Whyman, 72
It was almost 50 years ago: I was working in a butcher's shop in Kentish Town in north London, and Vicky came in. The chap who worked next door to me lived in her road, and he did say, "She won't go out with you - she's stuck up. She walks with her nose in the air."
The first time I saw her getting off the bus, I didn't have the nerve to say anything. The second time I called out to her. She didn't look left or right. So I crossed the road, and she said, "I don't answer men shouting at me in the street." But we went to a pub and I thought I'd make a good impression on her.
We decided we'd get married within the first week. There was uproar with the mother-in-law. We got married at the registry office, which shocked our parents, because it wasn't done then.
It was a couple of weeks after that when I found out she was vegetarian. I got meat from work, a nice couple of steaks. She told me, "There is one thing... I'm a vegetarian." And I said, "Well, why didn't you say earlier?" And she explained that she didn't like to, in case it put me off marrying her...
We don't argue about it, but I have tried to persuade her to eat meat sometimes. I brought a heart home once; she ran out of the kitchen.
When we first went on holiday, I'd want to traipse round butcher's shops. We had more photographs of butcher's shops than holiday snaps! She's very nice about it. When we go abroad now she says, "Why don't we get it over with..."
The vegetarian: Victoria Whyman, 70
Love over the pork chops... I went in to the shop with my mum; I noticed this guy looking at me - I thought, "What a fool!" But I didn't tell him that till much later.
I had him running after me - start as you mean to go on! - and it just developed from there. We'd known each other just under a month when we got married. We just knew; at 21, you do tend to think you know everything.
I don't like eating meat. But while I lived with my parents, it was a case of you must at least try a bit. When I left home I thought, I shall do what I want. And I don't want to ever eat meat.
But when you're newly married, you don't want to say you don't like something - so I ate little bits still. I left it a little while and then I had to tell him - and he thought it was ridiculous that I hadn't set him straight before.
I do the cooking, but if it's something like liver, it gets cooked from the end of a fork. I have all the windows open; I'd rather freeze than smell it. I don't like the texture, the taste, or anything else about meat. I don't like it, even on telly, when you see all the blood coming out of it.
Des used to take the calves from the farms to the abattoir - I just couldn't. He made the mistake of showing me the calf once, and these two brown eyes looked up at me... I wouldn't talk to Des for weeks after - murderer!
Tolerance is the key to our relationship. It's thinking of each other and being able to make allowances.
The atheist: Jeremy Teague, 48
I met Lynda through my work: I had a garden-fencing business in Cardiff, and I put one in for her, because she had a new puppy who kept going next door and nicking the washing off the line. Our first date was walking our dogs; we both liked camping and being outdoors and our relationship was just easy.
She says she was religious when we got together, but I had no idea about the seriousness of her conviction. I started to notice it five or so years ago: it started off with reading the Bible, then she started going to church more and more. She'll go through phases where she's out every other night at a prayer club or talk and she also gets a lot of religion online, like Thought for the Day emails.
I think it's all crazy, personally - my own belief is that religion was created as a system for the rich to control the menials - and I do wind her up about it. For example, the cat brought in a rat the other day and I said, "There can't be a God because why would he invent rats?" She'll also say to me, "You need to find your faith or you won't go to heaven," and I say, "Just in case, I'll repent on my deathbed and then I will!"
She thinks she's going to convert me, but I think her Christianity has just made my atheism stronger. Our differences are something to talk about, I suppose, and it's not like she's getting drunk every night: the results of the way she lives her life aren't that bad. And one good thing is that she's secure in her own world - she doesn't worry about anything, because the good Lord will look after it all.
The Christian: Lynda Frayling, 49
I consider that God brought me and Jeremy together. I had just got a little Samoyed puppy, who kept escaping from the garden, so I phoned a few contractors for a quote but Jeremy was the only one who turned up. A few days previously, I'd prayed about men and relationships, as I'd never had a relationship before.
At the point I met Jeremy, I read my Bible, but I wasn't going to church and didn't talk too much about my religion to him. But my faith grew through time: when my daughter was born in 2006, she was in intensive care, and I really turned to God. [Soon after] Jeremy wanted to move to Carmarthen - I was dead against it at first, but I think God wanted to take me out of my comfort zone and that's when I really got strong in my belief. I think our relationship has got better as a result. I always used to do what he wanted; now I feel like I do what I want to do: I'll go to a service on a Sunday, and a prayer meeting once a week, and sometimes other church groups as well.
We have three children, and I'll talk to them about Jesus, but I usually wait till I'm alone with them, because Jeremy will say the opposite. But Christianity is a choice for them to make.
Jeremy has often said, "The men in white coats will take you away." But we can make light of it: I know at some point Jeremy's going to see [the way] and it's going to be quite funny.