The Principia drew on global observations

The machine sought to transfer routine calculation from human operators to a device, anticipating later debates about automation.

Instrument makers, metalworkers and workshop techniques were essential to realizing designs often credited only to a philosopher-mathematician.

The Mathematical Principles of Natural Philosophy presented laws of motion and universal gravitation in a geometric mathematical framework.

Edmond Halley encouraged Newton, managed the printing and paid costs when the Royal Society could not.

The work argued that the same quantitative laws could explain falling bodies, planetary paths and tides.

Seki's death provides an exact date for a body of independent Japanese work in algebra, determinants, elimination and numerical calculation.

Seki developed procedures for systems of equations independently of contemporary European approaches.

His notation and teaching shaped wasan, the mathematical tradition cultivated during the Edo period.

His career demonstrates simultaneous innovation in a society with restricted direct exchange with Europe.

Euler showed that the requested walk was impossible by reducing the city to land regions and connecting bridges.