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Who's your favourite artist? I hate the question. At first my brain always turns utterly blank. And then suddenly, as if some valve has just been hit a mighty blow with a hammer, the name of every artist I've ever heard of - from Leonardo to Rolf Harris - is gushing into my head. And trying to choose any one of them is like clutching at a straw in a flood. Because how can one compare such utterly disparate contenders? How can one possibly decide who to put at the top?

Well, that is precisely what we are about to ask you to do. Today The Times teams up with Saatchi Gallery to launch a search for the nation's favourite modern artists.

For the past few months, times2 has been running a weekly Modern Art Explained column. Readers have been asked to offer their opinions and insights on a series of works.

Now the newspaper, taking as its starting point a longlist of artists compiled in partnership with the Saatchi Gallery, asks you to go online and cast your vote for your “top” modern artist - ie, artists working since the turn of the 20th century.

All that we want is for you to make a completely impossible choice. Artists are not like pedigree dogs. There is no breed standard. And how can you rank passions and emotions and visions? Just a glance at the list of contenders that appears online today is enough to dazzle anyone. How can you possibly select between the vast zig-zagging lightning field of Walter de Maria, its electricity flickering and forking across the deserts of New Mexico, and Carl Andre's famous pile of bricks in the Tate; between the subtle patience of Georgio Morandi and Jeff Koon's brash kitsch; between Francis Bacon's impetuous individualism and Andy Warhol's mass-produced Marilyns?

Picasso is bound to attract a huge number of fans, but even if you have decided that he should be the top artist, which Picasso do you mean? Is it the melancholy painter of lyrical blue canvases, or the creator of the rose-tinted saltimbanques, or the Cubist who smashed the world into shards?

Your choice will depend on your mood. One day Marcel Duchamp's anarchic wit might feel as if it fits; another you might find that Claude Monet's deliquescent lilies suit. Are you looking for a work to hang over your fireplace, in which case you probably won't go wrong with a pretty little Édouard Vuillard interior; or perhaps are you hoping to stir up feelings and go for the tempestuous Chaïm Soutine instead. Is this the top work for public display, a familiar Henry Moore, for instance, to lounge about lazily in the town square, or are you looking at the more secretive and sometimes decidedly dodgy sexual scrutiny of artists such as Balthus or Egon Schiele? This survey will double up as a portrait of our tastes.

Will the golden greats of Gustav Klimt beat Paul Cézanne's landscapes? Or, to put it another way, will decorative cliché turn out to be more popular than the founding father of Modernism? Will Mark Rothko make it into the Top 20, given the superlative show that for the past few months has been running at Tate Modern? And will Frida Kahlo turn out to be the highest-ranking female artist on the list?

There may be artists on the longlist whom you have never heard of. Can you picture the work of Bernd and Hiller Becher, for example, the photographers brought together by a shared passion of the shapes of German industrial architecture? Compiling this list will hopefully turn into a learning process. Or there may be an artist for whom you would like to vote but who doesn’t appear. The selection is far from comprehensive: we invite readers to nominate artists who have not been included and every week or so new names will be added to — or subtracted from — the list.

We know that even contemplating the question is enough to put anyone into the most appalling quandary. But then that is precisely the point. Ever since Cézanne first set out to challenge the fundamental conventions of image-making and so to create a new modern vision, art has been all about confusing and provoking, baffling and challenging. Hoping to discover any one final answer is impossible in the constantly shifting, multifaceted modern world.

But just thinking about the question should return you to works afresh, help you to engage with them as their creators first intended, as they appeared before their place in the cultural canon was fixed.

Today, over these pages, just a few of the candidates and their art are presented for your consideration. And over the next few months, works by the artists you vote for will become the focus of theTimes’Modern Art Explained column.

That will be your chance to canvas for your favourite.

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