"Are you going to the top?" asks Park Ki Soo. When I say yes, he invites me to walk up with him and his two sons.

Bright shades of red and gold line the mountain trail, and the misty breath of my fellow hikers signals the approach of winter. The sky above Seoul was clear blue this morning, so I decided to visit Bukhansan National Park. But several thousand city residents had the same idea, and if I am to have so much company I am happy to share a conversation as well as a climb.

Park is an engineer and embodies the uncomplicated diligence that has powered the economy of this small nation to unprecedented heights. His English is functional and rarely used. He tells me that he once visited Germany, but remembers nothing about it because he was preoccupied with learning how to manufacture car parts. I ask simple questions about the city and the mountain, but he brushes them aside, saying: "It's not my expertise." And he is bemused by my reasons for hiking around his country: "If I had 10 days' vacation, I would sleep and watch TV."

At 12 years old, San Yong, his elder son, proves more forthcoming. His language skills are at least the equal of his father's and he seems more culturally adept. He studies English three evenings a week at one of Seoul's many private schools. I am peppered with questions about my dietary habits and favourite football players, and he says he is looking forward to a solo trip to visit an aunt in Australia next year. The men of the Park family are climbing the 837 meters of Baekundae today, San Yong explains, to "train" his younger brother.

Ten-year-old San Un is less athletic and outgoing than his brother. Clearly not a regular climber, he grumbles about video games as we reach the bare rock of the upper slopes. The sections become larger and smoother, and my lack of preparation proves embarrassing; my worn soles mean that I slip and slide as I try to clamber up. As the path turns, we hear muffled screams and see a small group of people congregate by the edge of a lower trail. "What happened?" Park senior shrugs and replies: "Someone flew."

Disregarding the many no smoking signs dotted around the mountainside, Ki Soo frequently disappears and rejoins us with an unapologetic smile and an acrid aroma. Despite this habit, and his admitted lack of recent exercise, he is immensely strong. On one occasion he bounds up a huge boulder that I cannot see any route over, reaches down and easily pulls my entire body weight up the rock. Such assistance is not extended to his children; he apparently sees the climb as a character-building experience.

At the crowded summit we share hot tea and gimbap, a kind of sushi with squid, kimchi (spicy pickled cabbage) and vegetables rolled in dried seaweed. Park's mobile phone unexpectedly broadcasts "Hotel California" - it is his wife calling to see how the boys are bearing up.

From this peak we have a fine view down upon northern Seoul and across to other hills and mountains, all of which are swarming with people. Neighbouring Insubong, far too steep to walk up, is strung with ropes from which dangle dozens of climbers. One particularly adventurous man raises cheers by somehow free climbing up a high vertical incline and performing victorious one-handed push-ups on the tiny, precariously balanced rock at the top.

The temperature drops as the sun blends into the city haze. We join the hundreds of hikers waiting patiently for their turn to descend the narrow path to the forest below, and decide to take the long route down to avoid the worst of the congestion. Mrs Park is waiting for us, and the family gives me a ride to the nearest bus station. I certainly didn't find solitude on Baekundae, but as we say our goodbyes I know that I will remember this Sunday more fondly than exhausted San Un.