The cheeky smile is not the only similarity between the veteran TV children's presenter and maths whizz, who brought us the BBC series Think Of A Number, and his celebrity daughter.

Both have a zany sense of humour - according to Zoe, he'd answer the door dressed as a caveman when she used to bring boyfriends home as a teenager.

They both also have boundless enthusiasm and an amiable quirkiness which have endeared them to the masses.

Yet Ball senior, 71, whose latest book Mathmagicians aims to inspire children to take an interest in science, numbers and measurement, can be quite grumpy about certain subjects.

Ask him about the way maths is taught in this country, global warming, children's television today and a variety of other issues, and the smile disappears. He's quite a tub-thumper, our Johnny.

"Our kids are being scared to death by the whole idea of climate change. We are losing our scientists but producing more environmental scientists than actual scientists in engineering and technology," he blusters.

"Of course there's climate change, but it's totally overstated, it's scaring people out of science."

His exasperated tone continues on the subject of maths teaching. "In the last 20 years, the push has been to improve numeracy, but that's only one small aspect of maths. Without geometry, you can't work out how much wallpaper you need or how much carpet you have to lay."

And while he claims not to watch children's TV today, he still has an opinion on it. "I've watched Brainiac and I think it's garbage," he declares. "It teaches nothing. They only go for the bang. Why do we need to know how to blow a caravan up? When you become a scientist, it's not flash, bang."

However, move on to the subject of his family and the big smile returns. His charming wife, Di, has just planted some beautiful hanging baskets to give to his two grown-up sons, although she doesn't do them for Zoe, she explains, because they just dry up in the sea air of Brighton.

Back in the chintzy sitting room of his house in south Buckinghamshire, he plucks a framed photograph off a shelf - a happy family shot with Zoe in the middle. Clearly they are close, but he admits that at one point he feared that she was going off the rails.

She couldn't handle the media attention she received while she was doing the Radio 1 breakfast show, he recalls.

"She coped terribly and we lost her because she was totally besotted by it. She was clubbing all the time and drinking too much. We lost her during the Radio 1 years, because we were in a different generation.

"She became a ladette because she was the first girl to get this job. On the first morning after her show, a reporter at the press conference said, 'Do you think that was a good enough standard for you to keep the job?' She kept her chin up, said she had a lot to learn, then went into the corridor and burst into tears.

"But Zoe realised that the lads all talked about being lads and being out on the town and she thought, 'I've got to do the same'. She had become an envoy, a spokesperson, for teenage girls, so she became a ladette, saying anything the boys could do, girls could do.

"I understood what she was trying to do. We've never fallen out, but there are periods you know you're not in the equation when it comes to discussion."

He didn't read the newspapers which reported her wild nights and later her ups and downs with her husband, DJ Fatboy Slim, aka Norman Cook, and encouraged Zoe not to read them either.

"I remember going to her flat and she said, 'Look what they've written about me!' and I said, 'Well, don't read the f***ing stuff because nobody will remember it tomorrow'."

It must be hard for him to ignore the rocky times in his daughter's marriage to Cook, who recently came out of rehab where he was treated for alcohol addiction. Yet Ball speaks of his son-in-law with huge fondness.

"He's just done his first gigs as a new man, an abstainer," he enthuses. "I asked him what it was like and he said, 'God, I was nervous. It wasn't as much fun in a way and it was harder work', but then he normally had half a bottle of vodka in him.

"But, do you know, they are so happy now. In all marriages, especially showbiz marriages, there have been slightly rocky times."

Ball's own marriage to his first wife, Julia, ended after she walked out when Zoe was two. He then married Di when Zoe was six.

He believes his first wife's desertion is a legacy which may have prompted his daughter's marriage to flounder when she had a brief fling with DJ Dan Peppe in 2003.

"When she left for that silly DJ, I know exactly why that was. (Her son) Woody was exactly the same age as Zoe was when her mother left. She was thinking, 'I'm like my mother, I'm going to let us all down'. It was a cry for help."

It's all water under the bridge and Ball is the first to enthuse about Zoe's new Saturday early morning Radio 2 slot.

"Zoe is on the threshold of a more substantial career, one that will take her further than before. She's had to have a rest from her early career while she becomes re-invented as a different age base."

She has kept a lower profile since her son Woody, now eight, was born, apart from her Strictly Come Dancing appearance in 2005 and a steady trickle of radio and TV presenting work.

Ball says he didn't open doors for his daughter when she chose a broadcasting career, although he tried to help her in other ways.

"I wasn't saying, 'You follow me, I'll open doors for you'. All I bought her was a Marks & Spencer's outfit that would look good for interviews and give her an air of poise, and a briefcase. And she got an in to The Big Breakfast."

Born in Bristol and later moving to Bolton, Ball always had an aptitude for maths yet left school with only two O-levels.

He went on to become a Butlin's redcoat and, as a late 60s comedian, appeared in Val Doonican and Harry Secombe TV shows, later making his name on children's TV, appearing in Play School for 17 years.

Today he spends his time travelling the country giving presentations on maths and science to schools and businesses - and is busier than ever.

Despite his grumbles about climate change, maths teaching and other issues, he remains an upbeat, cheerful character.

"Have we really screwed the world up?" he asks. "Well, it hasn't been perfect previously. I'm a total optimist."