Charles Darwin's book On the Origin of Species shattered a vast collection of cherished myths. The truths he showed us are so difficult to consider that we still haven't got round to taking them on board. Instead, we have created a new mythology to cover up the gaping hole Darwin has left in our species-pride.

It was Freud who suggested that history had given three insupportable blows to human self-esteem. The first was the revelation that the Earth was not the centre of the Universe after all. The second was Darwin's: that humans are just one more species of animal. The third, Freud modestly suggested, was his own work, which robbed humans even of the consolation that we at least possess rational minds.

It is precisely because of our less than fully rational natures that we have created the false Darwinian myth. Yes, all right, evolution exists, but it is a ladder, a form of progression in which good leads to better, while better, with serene inevitability, leads to best. The myth is best explained visually: the creeping monkey, the knuckle-walking ape, the stooping proto-hominid and at last, wondrously, triumphantly, fully erect Man. (Fully erect Woman is never shown on this diagram; no doubt she fails the test of perfection.)

The life of Darwin

It has been said with truth that we must go back to Newton before we meet with Darwin's peer

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• Darwin at the NHM

Perfectibility. The purpose of evolution is to produce the supreme animal, an animal so wonderful that he is hardly an animal at all. We may be part of creation, but we are its crown.

This is a pleasing bit of mythology, but it's got nothing to do with Darwin. It was with wonder, then, that in the Natural History Museum I gazed at the open page of one of Darwin's notebooks. It's a nice notebook, a sort of policeman's notebook, like the one I use for jotting notes in the field.

But Darwin jotted down the explanation of life. The page towards me was the one of the most significant doodles in the history of science, in the history of human thought. There are two words: “I think.” Underneath is a rough sketch of a branching tree. This is how life works: the stem is the common ancestor, the branches are different species. Not a ladder: a bush.

There is no purpose, no great goal, no race for perfection: just the one ambition of all living things, which is to become an ancestor. Every living thing on the planet is the result of this process: every single living thing, then, is equally triumphant, equally perfect. Humans are just one of the crowd, created not by Nature's crazed ambitions but by Nature's reliance on chance.

The Natural History Museum is one of London's and the world's great buildings, and, in the place of honour, looking down across the great Central Hall, Darwin offers his mild gaze in stone across to the prancing dinosaur Diplodocus. On Friday the museum is opening an exhibition on Darwin that will take in his 200th birthday, February 12, and end on the 127th anniversary of his death. Next year is also the 150th anniversary of the publication of Origin, the book that shook the world - and is still shaking it.

It is a marvellous exhibition, not least in that it is full of marvels. Another Darwin myth: he went to the Galapagos Islands and shouted “Eureka.” But no, the process took years. The first inkling came with two mocking birds: and there they are, just as you go in, flat on their backs on a cushion, each bearing a little hand-written label, very much alike but subtly and unquestionably different. Separate bits of divine creation? Or do they share a common ancestor?

Thus the worm of questioning entered Darwin's mind. The exhibition tracks the worm's progress and catches some of his extraordinary meticulousness, his certainty that God dwells in the details - and if you are about to give voice to a heresy, you need all the details you can muster.

I was particularly glad to see a collection of the pigeons he worked with so painstakingly. Darwin became a pigeon fancier, breeding pouters and tumblers and fantails at Down House, his home in Kent. If humans can change the shape of a bird by selective breeding - artificial selection - then nature can do the same thing by means of natural selection. These stuffed birds are as eloquent to the visitor as they were to Darwin: a hymn to the polymorphous powers of life.

Once Darwin had cracked it, he did the oddest thing: he did nothing at all. He was silent until he was forced into going public because some one else had caught up with him. There are a million suggestions as to why he did so - out of fear of the furore he would create, because he was tender of his wife's untroubled faith; because he was always ill; because he wanted to perfect his theory; because he wanted more and more evidence; because he was waiting until he had got it right about human evolution, or because he needed to establish his own scientific street-cred. But sit on it he did, occasionally taking fellow scientists into his confidence, “like confessing to a murder”, as he said. He added, with the confidence and the modesty that marked him: “I think I have found out (here's presumption!) the simple way by which species become adapted to various ends”.

There was one species in particularly that troubled the world: one species in particular that is notable by its absence in Origin. It is humans. Darwin was at pains not to mention the war, as it were, but the implications for humans shouted from every page. By the time he published The Descent of Man 12 years later, however, the controversy had burnt itself out. Our apishness was now established.

The exhibition displays hominid skulls against a timeline, again demonstrating that life is not an irreversible tide of progress. Homo sapiens co-existed with the Neanderthals - there we are, on the exhibition wall, one among many. Our kinship with our ancestors, with all primates, all mammals, all vertebrates, all animals, all life, is incontrovertible. You can bring God into it anywhere you like, because God is outside the scope of science, unless you are Richard Dawkins. What is not in the realms of scientific doubt is the validity of the concept of evolution by means of natural selection.

The man that brought this about did so mostly by sitting at home at Down House in his armchair, scribbling away with his notebooks resting on a board across his knees. The chair had wheels so he could whizz about the room and examine specimens and consult volumes. This intimate and unpretentious study is lovingly reproduced at the exhibition: you feel he might drop in at any moment for a soothing chat about earthworms or barnacles, two of his major areas of work.

This exhibition is a vivid experience for anyone who has an interest in life. You can gaze on stuffed specimens of the animals that were part of the subtle and cumulative process of reaching his eureka. You can see demonstrations of its unquestionable validity in, for example, the bones of a human hand and arm, the wing of a fruit bat and the foot of a Komodo dragon: all showing their staggering similarities, their incontrovertible kinship.

The man - his life, his thoughts, the long process that led to his revelation - are presented for us to wonder at. The real implication of his work is something we have to work out for ourselves. Me, I cherish my kinship with the wild world, feel honoured to be a species among millions, and am greatly the richer for realising this. Far from feeling that Darwin's truth makes the world a bleak and depressing place, I believe with Darwin that there is grandeur in this view of life.

Darwin is at the Natural History Museum, SW7 (020-7942 5000) from Fri to Apr 19

HIGHLIGHTS OF THE SHOW

Darwin's notebooks chart the germination of an idea that changed the world Live iguana and frogs represent the creatures Darwin saw during his voyage on the Beagle

Darwin's study - the perenially sickly scientist preferred to work in his comfortable armchair

Glyptodont fossil cast - the similarity of this ancient creature to the modern armadillo gave credence to Darwin's theory of evolution

Annie's box - containing the effects of his late daughter - is a poignant reminder of Darwin as a man, not just a scientist

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