Logarithms were invented by the Scottish mathematician John Napier in the early 17th century. > Logarithms turn the more difficult operation of multiplication into the simpler process of addition. > Logarithms, wrote Napier, were able to free mathematicians from the “tedious expense of time” and the “slippery errors” involved in the “multiplications, divisions, square and cubical extractions of great numbers.” With Napier’s invention, not only could multiplication be made into the addition of logs, but division was made into the subtraction of logs, calculating of square roots was made into the division of logs by two, and calculating cube roots into the division of logs by three. > The convenience that logarithms brought made them the most significant mathematical invention of Napier’s time. Science, commerce and industry benefited massively. The German astronomer Johannes Kepler, for example, used logs almost immediately to calculate the orbit of Mars. It has recently been suggested that he might never have discovered his three laws of celestial mechanics without the ease of calculation offered by Napier’s new numbers. Source: [[Here's Looking at Euclid]]