What question did this study set out to answer?

To introduce the Kolcak Natural Law and its implications for understanding number theory and frequencies.

March 26, 2026Open Access

The Kolcak Natural Law: f(n) = 1/n -- A Letter to the Mathematical World

Key Points

To introduce the Kolcak Natural Law and its implications for understanding number theory and frequencies.
Establishing the function f(n) = 1/n as a natural law for frequencies.
Demonstrating core results with proof: f(a x b) = f(a) x f(b).
Connecting findings to historical concepts like the Brachistochrone.
Error rate remains at 0% for the function up to 1,000,000.
Prime numbers identified as irreducible frequencies; composite numbers as superpositions.
Offers new perspectives on established mathematical theories and conjectures.

Abstract

An independent researcher from Germanypresents the Kolcak Natural Law: f(n) = 1/n. Every natural number n has a fundamentalfrequency f(n) = 1/n. Prime numbers areirreducible frequencies. Composite numbersare superpositions of prime frequencies. Core result (proven):f(a x b) = f(a) x f(b) -- always exactError rate: 0% up to 1,000,000 Includes connection to the Brachistochrone:Bernoulli (1696) found 1/sqrt(y) forphysical space. Kolcak finds 1/n fornumber space. Both are reciprocals. New perspectives on Riemann, Goldbach,P vs NP, and Poincare are offered --not as proofs, but as invitationsfor the mathematical community. First publication: March 22, 2026.

The Kolcak Natural Law: f(n) = 1/n -- A Letter to the Mathematical World

Key Points

Abstract

Cite This Study