Seki's school strengthens symbolic Japanese mathematics

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.

Astronomical and geographic data came through imperial and maritime networks; its achievement was mathematical but not socially isolated.

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 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.

Ignoring distances and shapes allowed Euler to focus on connections, a foundational move toward graph theory and topology.

The four land areas each had an odd number of incident bridges, preventing a trail that used each bridge exactly once.

Euler's publication is a conventional origin point, while continuous-line traditions in Africa and Oceania show other culturally embedded studies of paths and networks.