Logic Theorist: The program that rewrote the foundations of mathematics (bigthink.com)

In 1956 Allen Newell and Herbert Simon’s Logic Theorist became the first program to convincingly demonstrate that a computer could perform symbolic reasoning and prove mathematical theorems — in fact it proved 38 of the first 52 theorems from Whitehead and Russell’s Principia Mathematica and even discovered shorter, novel proofs. Rather than numeric computation, the program navigated an implicit graph of mathematical states: starting from axioms and derived facts it searched paths in this infinite “map” until reaching a target proposition, effectively acting as an artificial mathematician and challenging conceptions of intelligence and creativity. The Logic Theorist crystallized a core AI idea still central today: reduce problems to search over symbolic representations. That paradigm underpins everything from solving the 8‑puzzle to autonomous navigation. Later systems like Shakey (1968) paired symbolic maps with A* search — a method that is complete, optimal and optimally efficient — to plan real-world robot routes, and that same search logic powers modern GPS routing and many AI solvers. Technically, the lasting implication is that manipulating symbols via structured search (explicit or implicit state spaces, heuristics, and optimal graph-search algorithms) remains a foundational approach for reasoning, planning, and problem-solving in AI/ML.