Departure question
Catch change and accumulationPort 1 of 18Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
"A machine that takes an input and gives an output." The most fundamental and most flexible tool across mathematics and science. "How does y change as x changes?" — that single question is the seed of calculus, analysis, machine learning, and signal processing.
A rule assigning exactly one output to each input. The notion grew from quantities attached to curves into a central language for mathematical relations and computation.
Q.f(x) = 2x + 1, f(3) = ?
Q.sin(0) = ?
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
Leibniz used functio for quantities associated with a curve, an early step toward treating dependence itself as a mathematical object.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearEuler’s Introductio in analysin infinitorum defined functions through analytic expressions, a conception that became standard in the 18th century.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearDirichlet broadened the idea of a function beyond a single formula: each allowed input is assigned a definite output by some rule.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearChurch’s lambda calculus showed how computation could be expressed through functions and application alone, laying theoretical groundwork for functional programming.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearFunctions in programming, machine-learning models as vast functions, graphics shaders, and database queries. Functional programming makes the concept itself the center of computation.
Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.
No concept belongs to one person
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
Open the number voyage
Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
Open the number voyage
Follow the languages built to calculate a world that will not stand still, from planets and fluids to waves, optimization, and chaos.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
Function
Concepts opened from here
Only direct editorial links are shown; this is not a complete learning order or historical influence line.
