Back in 1972, he was driving a cab around New York City. But he had dreams. He had plans. He had talent. Three years later, Tim Hauser, Laurel Massé, Janis Siegel, and Alan Paul had their first national hit as The Manhattan Transfer. In 1978, Massé had a car accident and decided not to return to the group. Enter Cheryl Bentyne. Two years ago, Hauser went to join a heavenly choir and Trist Curless took his place. And forty-one years after their first hit, they played to a packed audience of all ages at Müpa here in Budapest and they’re still giving it welly.

At least three of them are in their 60s with the vim and vigour of people half their age. They put on a fantastic show, one where equal play is given to the three musicians – all of whom are excellent in their own right. And while their dress style may be stuck in the 1970s, their music – their four-part harmonies – is something timeless.

It’s easy to forget that those in the public eye have personal stories. For all their fame and fortune, they, too, are human, with everyday issues to deal with.

Bentyne was diagnosed with Non-Hodgkins Lymphoma in 2011 and with Hodgkins Lymphoma in 2013. But now, after a successful stem cell transplant, she is in remission. Seeing her move around the stage with such agility and such enthusiasm was nothing short of inspiring.

Paul started out as a 12-year-old Oliver on Broadway and has been on stage since. He released a solo album this year Shu Bop that gives  a nod to classic doo-wop from the 1950s and 1960s. The song he did from it last night – My Heart Swings – was one of the highlights of the gig.

Siegel is quite the fireball. She rapped to Jungle Book’s I wanna be just like you: I can pick the lice from my lady’s head and feed her a banana … in bed. Brilliant. Like the others, Siegel does fantastic instrument impressions. Her double bass is right up there with her trumpet. And I learned something:

Vocalese is a style or musical genre of jazz singing wherein words are sung to melodies that were originally part of an all-instrumental composition or improvisation.

This is brilliant to listen to and shows how gobsmackingly talented these people are. Their album, Vocalese, was nominated for a host of Grammy awards and won three. Last night, they did a few numbers in this style with Sing Joy Spring the one that did the most for me. Classic. A history of the world in just over 7 minutes. Not bad going.

Arguably the youngest member of the group, Trist Curless joined full-time in 2014 to replace Houser. He had stood in for Houser a few years earlier when he had spinal surgery so was no stranger.  It can’t have been easy though, coming into a tight group who had worked and played together for decades. He, too, has an impressive voice. And the four of them together are quite a formidable talent. And so very appreciative of each other’s style, if the high-fives on stage were anything to go by. It really was a joy to watch.

Pianist Yaron Gershovsky is also the musical director and the speed at which his fingers pass over the keys is mesmerising. I’d like to see Havasi take him on. Boris Karlov plays my all-time favourite instrument, the double bass. It has to have the sexiest sound around. Not exactly portable, but for me, it’s an essential part of any jazz ensemble. Steve Hass on drums was having way too much fun and again, his speed and dexterity were mind-blowing. I don’t think I’ve heard as much applause at a concert – ever. And it was constant.

Apparently 20 years ago, when they played a gig in the city, the audience refused to leave. They came back on, in their street clothes, and did another set. They did an encore last night, too, but hey, 90 minutes of giving it welly will take it out of the best of us. I know I couldn’t have lasted the pace.

It was an experience to see them in action. And it was inspiring to think that they’re still going strong. They’re poster children for living life to the full. And they get around. In 2012, Paul and Siegel were judges China’s online talent show – Rock the Web. Now there’s a concept.

And all this for the princely sum of 3500 ft (about £9, €11, $12). Not the best seats in the house, admittedly, but in Müpa they work. What’s not to love about Budapest?