They begin in chaos, 75 miles or more beneath Earth's surface, as carbon transformed into crystals by extreme heat and pressure. As volcanic eruptions drive the crystals upward, they can revert to free carbon atoms, or vaporize into carbon dioxide, or become the graphite that's used in lead pencils. The survivors retain their original form only if they make it to a point near Earth's surface where they can cool down rapidly. Here, under large plates of Earth called "cratons," they form into diamonds.

The movements of land masses, glaciers and water have transported diamonds thousands of miles from their origins. It is believed that the first diamonds were discovered in riverbeds of India in around 800 B.C., yet their volcanic birthplace was never found. These abundant alluvial deposits supplied the world until the 1700s, when further exploration revealed diamonds in Brazil.

For centuries, people mined diamonds only from riverbed sands and gravel. Then in 1870, they found diamonds in the South African earth far from any river, and the era of dry-digging for diamonds began.

Ever-better techniques led to mining at greater depths. In South Africa, diamonds were found more than 150 miles deep in conical rocks called "kimberlite pipes." And when one of the world's richest diamond deposits was found on the beaches near Namibia, marine mining came into play, yielding diamonds that had been carried to Atlantic Ocean resting places by South African rivers eons ago.

For centuries, rough diamonds were used only as talismans, and they were rarely worn. They were thought to magically produce an immense variety of powerful benefits ranging from medicinal cures and protection in storms to punishment for lying. Possibly the earliest use of diamonds for jewelry was when a Hungarian queen's crown was set with uncut diamonds in approximately 1074.

It's believed that diamond polishing began in India during the 1300s, followed by the first diamond cutting in Antwerp, Belgium during the mid-1500s. While India remained the world's central diamond source until more deposits were found elsewhere, Antwerp became the leading diamond center.

The 58-facet round-brilliant cut was invented by Vincent Peruzzi in the 1700s, but the man whose name would become synonymous with the modern round-brilliant cut diamond was born in 1898 to a renowned family of diamond cutters and dealers in Antwerp. His name was Marcel Tolkowsky.

By age 21 he had long mastered the many skills of diamond cutting. Now he developed a mathematical formula for the round brilliant cut as his doctoral thesis for the University of London.

The formula was calculated to maximize the refraction and dispersion of light through a diamond for optimum fire and brilliance with the least loss of material. It involved a precise combination of cutting angles and relative measurements. The result was a more beautiful stone than the European cuts of that time. Soon it replaced the old cuts, and became known as the "Tolkowsky cut" or the "ideal cut."

Tolkowsky moved to the United States in 1940, retired in 1975 and lived until 1991. But meanwhile, starting in the late 1940s, diamond cutters had evolved variations of his formula and the industry became engaged in debate that remains unresolved.

Regardless of the controversy, Tolkowsky's disciplined approach to a standard formula inspired the diamond cutting industry to reach new heights of competence and skill, shining forever through the countless diamonds that rise from chaos to be treasured as precious jewels.