Note G gives a machine procedure for Bernoulli numbers

The Brazilian mathematician known as Souzinha became the first Brazilian awarded a doctorate in mathematics.

His work sought solutions and general methods in areas then central to European mathematical research.

Souza struggled to secure evaluation and publication of memoirs in European institutions that controlled international recognition.

His career linked scientific ambition, education and nation-building in a former Portuguese colony.

Her translation of Menabrea's account appeared with notes much longer than the original and explained the unrealized machine's operations.

She argued that the Engine could follow operations supplied to it but could not originate ideas on its own.

Lovelace compared punched-card control with the Jacquard loom, linking patterns in textiles with patterns in symbolic computation.

Noether became a foundational figure in abstract algebra and mathematical physics despite institutional discrimination against women and Jews.

She shifted attention toward structural relationships among rings, ideals and modules, influencing much of twentieth-century mathematics.

Her result established a deep mathematical relationship between continuous symmetries and conserved quantities in physics.