Welcome to mikematics
Hello and welcome to my personal mathematics website. My name is Mike Winkler, also known as mikematics. I am a mathematician living on a horse farm on the German North Sea coast.
My work focuses mainly on number theory, combinatorics, and discrete geometry, including graph theory. On this website, I present some of my research in the form of articles, ideas, conjectures, and proofs on selected topics from both my academic and personal work. My favorite subjects include the 3x+1 problem, regular matchstick graphs, nonperiodic tilings, and Heesch’s problem.
Beyond mathematics, I love horses and cycling, play the piano and guitar, enjoy swimming, and occasionally paint.
I hope you enjoy reading and exploring this website.
Mike Winkler
Latest research, articles and preprints
Der Mythos der tödlichen Münze: Physik im freien Fall (March 2026, German)
Die Recamán-Folge (February 2026, German)
The best current approximation of a 4-regular matchstick graph with 64 vertices (February 2026)
Thinned Wallis-type prime products in residue classes modulo 2^m (February 2026)
Deterministic Structures in the Stopping Time Dynamics of the 3x+1 Problem (February 2026, Update from 2017)
On the existence of 4-regular matchstick graphs (February 2026, Update from 2017)
A Quartic Identity Related to Fermat-Type Equations (February 2026, Update from 2014)
The two best current approximations of 4-regular matchstick graphs with 62 vertices (February 2024)
Two new 4-regular matchstick graphs with 66 vertices (January/February 2024)
The two best current approximations of 4-regular matchstick graphs with 61 vertices (June 2023)
