Archimedes showed how exponents could be used to write bigger numbers than had ever been thought of before. To do this he introduced a new classification of numbers. Archimedes proved that to multiply numbers written as exponents, the exponents should be added together.

Archimedes calculated pi to the most precise value known. His upper limit for pi was the fraction 22⁄7. This value was still in use until electronic calculators took over.

Archimedes discovered and mathematically proved the formulas for the volume and surface area of a sphere.

Archimedes helped invent the science of physics by establishing the center of gravity. He invented the lever and the compound pulley, which allowed us to move heavy objects using small forces. These are inventions we still use today.

Archimedes invented the sciences of mechanics and hydrostatics. The finest example of this achievement is the Archimedes screw, which is still in use today to pull water out of the ground.

Archimedes inspired Galileo Galilei and Isaac Newton to investigate the mathematics of motion. He also invented war machines such as a highly accurate catapult, which stopped the Romans conquering Syracuse for years. It’s now believed he may have done this by understanding the mathematics of projectile trajectory.