Why bother with Plato? Isn't this bearded man from ancient Athens ancient history? It is true that AN Whitehead declared European philosophy to be "a series of footnotes to Plato". But why should that matter? Modern physics originates in the work of Isaac Newton and, though we read about him, few read his actual words, and no one expects the future of physics to flow from his centuries-old pen.

Well, for one thing, philosophy is not like physics. It does not contribute to the accumulation of knowledge, an essentially linear, progressive activity. Rather, it seeks wisdom, and that – as Plato stressed time and time again – is a circular activity, mostly focused on asking better questions. To put it another way, as Plato himself did, wisdom is not like water that can be poured from one vessel into another; it is more like the seed that sprouts afresh in each generation. Or, as Bertrand Russell wrote:

Philosophy is to be studied not for the sake of any definite answers to its questions, since no definitive answers can, as a rule, be known to be true, but rather for the sake of the questions themselves.

Something else that is key, though routinely forgotten by professional philosophers: Plato wrote dialogues, and no work of philosophy that is indisputably his own contains a single word written in his own voice. He always speaks through the mouths of others. It's a literary strategy with far-reaching implications for what we make of him, not least that it allows him to be his own best critic. As a thinker, he is as much like Shakespeare as your typical philosophical great. In fact, Plato arguably reigns supreme when it comes to asking good questions, and pursuing the equally important task of searching out flaws in possible answers. That is why he sets an agenda that philosophers broadly still follow to this day.

And there are other reasons to attend to him now. For one thing, opinion about Plato is changing. Until recently, the way scholars read Plato focused primarily on seeking to put his rational arguments to the test and, from that, struggling to discern what Plato himself might have believed. In short, it's an approach that tries to read the dialogues as treatises.

There is much value in that, but it risks distorting what Plato himself probably took philosophy to be. And that different sensibility is now beginning to re-emerge, through the work of individuals like Pierre Hadot. Hadot might be said to understand Plato's dialogues as invitations to philosophy, rather than as the work of philosophy itself. The dialogues set you thinking, as you track the intellectual and psychological tussles between the characters concerned. But crucially, they force you to address the same questions in your own life. That is the primary locus for philosophy.

Further, Plato increasingly looks not just like a generator of footnotes, but a philosopher whose time is coming again. We live in an age of religious pluralism, secular innovation and ideological searching. Reading him encourages us to delve deep and refashion a way of life that can speak truth to our own times.

So what of Plato's own life? There are two ways we know something about him: facts and myths. The facts are relatively sparse. The myths are plentiful.

It seems likely that the name we know him by was a nickname, his real name being Aristocles. "Plato" resonates with the Greek platus, meaning "broad". It might suggest he was a wrestler at one point, or more lyrically, that he could write across a broad range of styles. It's interesting to reflect on the possibility that his named changed, whether he changed it himself or whether others changed it for him. For that dynamic of change is surely one that fits with his philosophy too: Plato wanted his philosophers to be changed by seeing things more clearly, by understanding what's at stake more sharply.

He was born in 427 BC, into an old Athenian family, and died in 347 BC. This meant that he grew up during the long and bloody Peloponnesian war, and then lived much of his adult life during times of political upheaval and civil war – as democrats were replaced by tyrants, who then, a few years later, found themselves usurped.

Of course, the single most important fact about him is that he was the pupil of Socrates. It is said that on the day he first heard Socrates speak, when he was 20 years old, he was on his way to deliver a tragedy to the great theatre festival of Dionysius. He was a young literary star. But there and then, he stopped, burnt his manuscript, and turned to follow the sage. Apart from the light that the life of Socrates poured into his philosophy, and the shadow that the death of Socrates cast across it, he was also influenced by the Pythagorians, who were themselves probably influenced by philosophy from the east, and possibly Egyptian lines of thought too.

The other thing that is certain is that he founded a philosophy school, the Academy. It included such luminaries as Aristotle, who did philosophy with Plato for 20 years. His followers did not make their way to the park outside the walls of Athens where it was located to gain philosophy degrees, neither to learn about the system of doctrines we now call Platonism. Mostly, the Academy was a place for profound discussion: it was a community of people who were committed to each other not because they agreed, but because they had a love of wisdom, the quality that made them philosophers.

Mark Vernon's new book, out in October, is Plato's Podcasts: The Ancients' Guide to Modern Living (Oneworld).

This is the first in a series of eight blogs on Plato which will appear each Monday morning on Comment is free: belief