When In Our Time first joined the Radio 4 lineup, host Melvyn Bragg didn't expect it to last long. "I gave In Our Time about six months," he recalls. "We were asking top-class academics to talk at the top of their form about a single subject – no book plugs allowed."

That was 13 years and 499 episodes ago. On Thursday, the programme reaches its 500th episode and does so with a subject – free will – that is suitably complex and bewildering for most of us, certainly at 9am on a Thursday morning. Last week's programme was an intellectual canter through almost 14bn years of history, as guests debated The Age of the Universe. I listened in my pyjamas, rooted to the spot in awe and wonder, delaying the morning's routines to hear a programme that began with Bragg saying: "Hello, in 1654 the Anglican Bishop of Armagh..." Imagine pitching that to TV executives.

After more than a decade, and with a small tweak to the format – three guests over 45 minutes instead of two over half an hour – In Our Time remains one of Radio 4's quiet jewels in its crown, quite possibly its finest programme. It shouldn't work, even on a pretty highbrow speech network – academics tussling with mind-bogglingly chewy issues, shepherded by Bragg who never bothers to hide when he's bored or frustrated, or the talk goes off topic. But it does, with its unrivalled range of subjects and uncluttered format in which clever people simply talk about fascinating ideas and concepts.

There are other key ingredients in the hugely successful mix, and I love these quirky elements almost as much as the content. Bragg now says "hello" at the top of the programme so quickly that it attaches itself to whatever word follows, so keen is he to dodge presenting niceties and move onto the subject. There is always a battle for the most authentic pronunciation of foreign words, and a similar tussle over who can say the word "Renaissance" in the poshest, most learned way (that is: absolutely not as "Renaaaysonce", but as a shuddered near-monosyllabic utterance). I also like the regular muted chortles, and the moments at which it's obvious that Bragg considers a guest either a particular genius or twerp.

The other reason to love In Our Time is its online presence: every episode is archived, and on the Radio 4 blog at the moment, the IoT team are asking for suggestions for future topics (which include a Danish attack on Canterbury, human sacrifice, and molecular biology). The interactivity – which might seem to run counter to a programme featuring experts on complicated topics – continues with Bragg's programme newsletter. The latest of those has him in devastatingly bright flaneur mode, witnessing fisticuffs on the streets of London, and is worth a peek.

Most of all, though, In Our Time exemplifies what Radio 4 is all about, and what makes it world class. When the network is attacked for being too metropolitan, too old, too white, or too inward-looking, I always think: listen to that programme, and hear how ideas, well handled, do more than transcend such labels. They blow them into smithereens.