Largely lifted from Wikipedia - this needs summarising and then a reference given.

• Archimedean Screw
• Approximating Pi
• Volumes of solids
• Array of mirrors
• Apparently the first to regard 0 as a true number.
• Law of the lever
• Archimedes principle of displacement

Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. We know little of his life, but he is regarded as one of the leading scientists in classical antiquity. His advances in physics include the foundations of hydrostatics, statics and the explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water, and setting ships on fire using an array of mirrors.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi. He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.

One of the Famous People on this site.