Lewis Wolpert: 'The Archimedes story is almost universally misunderstood'

When I was invited to join a debate at the Royal Institution in London on who was the first scientist, I readily accepted.

When I was invited to join a debate at the Royal Institution in London on who was the first scientist, I readily accepted. I wanted to promote my hero, whom I regard not only as the first scientist, but probably the greatest scientist ever. He was the first physicist and applied mathematician, and he had no one's shoulders to stand on to help with the science.

Yes, there had been Aristotle with his logic, and Euclid with his wonderful geometry, but they had not provided reliable explanations about how things work, which is the essence of science. It is only natural that Archimedes was a Greek, as all science as we know it comes from the Greeks, and no other culture conceived of this special way of thinking.

The story of Archimedes leaping naked from his bath crying "Eureka!" is well known, but almost universally misunderstood. What had he discovered? Archimedes needed to know if the new gold wreath made for his king was pure gold, or whether silver had also been used. Lying in his bath he suddenly realised that he could measure the volume of the crown by immersing it in a bath of water and seeing how much the water level rose. Then, knowing its weight, he could compare it with gold and silver.

He had discovered density, the weight per unit volume that characterises gold and silver and all other pure compounds. All he had now to do was to get pieces of gold and silver of the same weight as the crown, and then compare their volume with that of the crown by immersing them in water. He could then tell how much gold there was in the crown.

His next discovery relates to levers and balances. Taking a simple balance, a rod supported at its midpoint, he made clear that if two similar weights were placed on either side at equal distances from the midpoint it would balance and would be in equilibrium; but "equal weights at unequal distances are not in equilibrium, but incline towards the weight which is at the greater distance".

Then the key theorem which states that unequal weights will be in equilibrium when their distances from the midpoint are reciprocally proportional to their weights. So a 2kg weight will balance a 100kg if it is 50 units from the midpoint, and the larger weight just two units away. From this he claimed that given somewhere to stand, he could, with a lever, move the Earth.

The proof of his postulate is the first example of mathematics being applied to a physical problem. First he invented the concept of the centre of gravity. For example, the 100kg weight can be divided in two and each part placed one unit away from the original site, but its centre of gravity, through which the force downwards acts, remains the same. So he could now divide the 100kg weight into 100 units and spread them out equally on either side so that there are 51 on one side and 49 on the other, where the 2kg weight is.

On this latter side the 2kg weight is also divided into two units, so there are similar weights, 51kg, at equal distances on either side of the midpoint - equilibrium! He applied these ideas to the mechanics of fluids, and so to why some bodies floated. He showed that a body immersed in a fluid loses weight equal to the weight of the fluid it displaces. So a body floats if the fluid it displaces is more than its own weight.

He would have been contemptuous about this little problem, which many still get wrong. You are in a small boat floating in a swimming pool. There is a stone in the boat, which you throw into the water, and it sinks. Does the level of the water in the pool go up, down, or remain the same? It goes down, because the stone in the water displaces less water when in the water than when it was in the boat.

Archimedes had a major influence on Galileo, who called him divine. The other scientists proposed in the debate were Roger Bacon, an amazing 13th-century scholar, and Clerk Maxwell, who invented electromagnetic theory in the 19th century. In the end, the audience was as persuaded by the achievements of Archimedes as I am.

Professor Wolpert is professor of biology as applied to medicine at University College London