Mathematical Bold Small R

The formula identifies its role; boldface separates it from an ordinary variable.

Many physics and applied-math texts use bold r in vector notation: a bold lowercase letter marks a vector, a quantity with magnitude and direction. The author's definitions still decide what 𝐫 denotes.

Math boldface developed as a printing convention, not as a letter with one fixed meaning. In 1881, mathematician J. Willard Gibbs used small Greek letters for vectors and small Latin letters for scalars (single-number quantities). Edwin B. Wilson's 1901 textbook made Clarendon, a heavy bold type, influential for vectors and ordinary type for scalars; ordinary A could also mark the length of bold A. In mathematician Hermann Weyl's 1921 book, bold x marked a vector while a subscripted x marked one component. The role followed each book's conventions.

Why can bold r become plain r?

Compatibility normalization can turn 𝐫 into plain r.

Unicode treats mathematical alphabets as distinct roles in formulas, not decoration. But NFKC, a compatibility form used for loose matching, maps mathematical bold letters back to ordinary Latin letters, so 𝐫 becomes r and loses its style distinction. For ordinary prose, use text formatting; Unicode reserves these styled alphabets for mathematical and technical notation.