Short answers, pulled from the story.
Mineralogy is a branch of geology that specializes in the scientific study of the chemistry, crystal structure, and physical properties of minerals and mineralized artifacts. Its specific areas include the origin and formation of minerals, their classification, geographical distribution, and practical uses.
The modern study of mineralogy built on the work of several figures. René Just Haüy, called the father of modern crystallography, established that crystals are periodic and that crystal face orientations follow rational numbers. Georgius Agricola's De re metallica (1556) and De Natura Fossilium (1546) began the systematic scientific approach to the subject.
The Mohs scale ranks ten reference minerals from 1 (talc) to 10 (diamond) by increasing hardness. An unknown mineral is placed on the scale by determining which reference minerals it scratches and which scratch it. The scale is nonlinear compared to absolute hardness measured by a sclerometer.
X-ray diffraction works because X-rays have wavelengths on the same order of magnitude as the distances between atoms. When X-rays scatter off atoms in a crystal, they produce distinctive intensity patterns that reveal the crystal's geometry. In powder diffraction, the mineral is ground so X-rays sample all orientations at once, allowing identification of minerals that look identical by eye, such as quartz and its polymorphs tridymite and cristobalite.
There are over 6,000 named and unnamed minerals recognized in the scientific literature. Approximately 100 new mineral species are discovered each year. A 2015 analysis by Robert Hazen and colleagues noted that Earth has over 4,800 known minerals incorporating 72 elements, and the model predicts thousands more may remain undiscovered.
The Mineral Evolution Database was begun in 2011 and combines Mindat.org's more than 690,000 mineral-locality pairs with the International Mineralogical Association's approved mineral list and geological age data. Analysis of the database found that 34 percent of known minerals have been found at only one or two locations, suggesting both a role of chance in rare mineral formation and that thousands of species may still await discovery.