Addition and Multiplication Alone Suffice to Simulate Turing Machines

A series of posts explains how Peano arithmetic, using only addition and multiplication, can simulate Turing machines by encoding the tape as natural numbers via Gödel's β function, showing that mathematics is inherently Turing-complete and revealing the often-overlooked flip side of Gödel's incompleteness theorem.

2026-10-17 ~ 2026-10-18 · 4 related posts

• Gödel's flip side: addition and multiplication alone make math Turing complete — jessi_cata · 2026-10-17
• How addition and multiplication alone encode logic: Gödel encoding makes math Turing complete — PoniesModus · 2026-10-18
• Simulating a Turing machine with addition and multiplication by encoding the tape as a number — jessi_cata · 2026-10-18
• Encoding Turing machine tapes in Peano Arithmetic via Gödel's beta function — jessi_cata · 2026-10-18