Bunyakovsky's inequality

A recent review of the volume Saint Petersburg Mathematicians and Their Discoveries (also available in Russian, Математики Санкт-Петербурга и их открытия. Сборник статей

asks whether Bunyakovsky’s name should appear in what is usually called the Cauchy–Bunyakovsky–Schwarz inequality.

For a deeper historical perspective, see S. Kichenassamy’s lecture “The Cauchy-Bunyakovsky inequality and its mathematical interpretations,” complete with slides.

Kichenassamy develops these ideas further in his article “Apodictic discourse and the Cauchy-Bunyakovsky-Schwarz inequality” published in Gaṇita Bhāratī 42 (1), 2020, 1–19.

“The various interpretations of Bunyakovsky’s inequality are therefore not logical developments of a single idea. Unlike nested Matryoshka dolls, each of which is a copy of the next one, only smaller, the sequence of these inequalities rather resembles Fabergé eggs, each containing a ‘surprise’ entirely different from the outer shape… Historical investigation provides a deeper understanding of modern mathematics that cannot be inferred from the modern stage alone.”

This evocative Fabergé-egg metaphor is one of the most striking images in the paper and captures the layered—but not necessarily nested—evolution of the inequality over time.