# Emil Post ### Mathematician, Logician — 1897–1954 — United States > _"In his lonely work, Post anticipated both the incompleteness theorems and the unsolvability of the Entscheidungsproblem — years before Godel and Turing received credit for these discoveries."_ --- ## Why This Matters You cannot understand the full history of theoretical computer science without understanding Emil Post. While Godel and Turing receive the glory, Post independently discovered incompleteness in 1921 — a decade before Godel's famous 1931 paper — and formulated string rewriting systems that became the conceptual foundation for Chomsky's formal grammars. His production systems are not merely historical curiosities; they are the direct ancestors of the parsing algorithms that compile every program you write. Post's theorem established the arithmetic hierarchy, his correspondence problem remains a touchstone of undecidability theory, and his work on recursively enumerable sets shaped the entire landscape of computability. That he accomplished all this while battling severe manic-depressive illness, having lost his left arm in a childhood accident, and working largely in isolation at a teaching-focused college, makes his contributions all the more remarkable. --- ## Quick Reference | Attribute | Value | |-----------|-------| | **Registry #** | 36 | | **Born** | February 11, 1897, Augustow, Russian Empire (now Poland) | | **Died** | April 21, 1954, New York City, USA | | **Active Period** | 1920–1954 | | **Fields** | Mathematical Logic, Computability Theory, Formal Languages | | **Known For** | Post production systems; independent formulation of incompleteness; Post's theorem; Post correspondence problem | | **Influenced By** | Bertrand Russell, Alfred North Whitehead, Cassius Jackson Keyser | | **Influenced** | Chomsky, Markov, Thue, computability theorists, formal language theory | --- ## Table of Contents 1. [Origins & Formation](#1-origins--formation) 2. [Intellectual Genealogy](#2-intellectual-genealogy) 3. [The Work: Chronological](#3-the-work-chronological) 4. [Core Ideas & Contributions](#4-core-ideas--contributions) 5. [Impact & Legacy](#5-impact--legacy) 6. [Study Guide: The Mental Model](#6-study-guide-the-mental-model) 7. [Going Deeper: Sources](#7-going-deeper-sources) --- ## 1. Origins & Formation ### A Note on Historical Sources > **On Uncertainty:** Unlike ancient figures, Post's life is well-documented through academic records, correspondence, and family accounts. However, his most important early work (the 1921 anticipation of incompleteness) remained unpublished for decades, creating historiographic challenges in understanding his influence. The following account draws on published papers, the work of Martin Davis (who knew Post's family and edited his papers), and Columbia University records. ### Early Life & Context > _Etymology: **Post** is a Germanic surname, likely derived from a place name or occupational term. The family was Jewish, emigrating from the Russian Empire during a period of pogroms and economic hardship._ Emil Leon Post was born on **February 11, 1897, in Augustow**, a town in the Russian Empire (now in northeastern Poland). When he was a child, his family emigrated to the United States, settling in **New York City**. The immigrant Jewish community of early 20th century New York was intensely education-focused, and Post's mathematical talents were evident early. **The Childhood Accident:** When Post was around twelve years old, a tragic accident changed his life permanently. He lost his **left arm** after it was injured in an accident (accounts vary — some say it was caught in machinery, others mention a fall). This disability shaped his entire existence. He learned to write with his right hand, adapted his mathematical practice accordingly, and faced the physical challenges of one-armed life in an era with few accommodations for disability. **New York City in the 1900s–1910s:** - Massive immigration, especially from Eastern Europe - Public education expanding rapidly - City College of New York providing free higher education to talented students regardless of background - A culture of intellectual aspiration among immigrant communities ### Education & Training | Period | Institution | Focus | Achievement | |--------|-------------|-------|-------------| | Pre-1914 | NYC Public Schools | General education | Early mathematical talent recognized | | 1914–1917 | City College of New York | Mathematics | B.S. in Mathematics (1917) | | 1917–1920 | Columbia University | Mathematical Logic | Ph.D. (1920), dissertation on Principia Mathematica | | 1920–1921 | Columbia University | Postdoctoral Research | Prolegomena — anticipation of incompleteness | **City College of New York:** CCNY was the "Harvard of the proletariat" — free tuition for qualified New Yorkers, intensely competitive admission, and a student body that would produce numerous Nobel laureates, intellectuals, and scientists. Post thrived here, graduating in 1917 with a degree in mathematics. **Columbia University:** Post entered Columbia's graduate program in mathematics, working under **Cassius Jackson Keyser**. His focus: the logical foundations of mathematics, specifically Russell and Whitehead's *Principia Mathematica*. His dissertation, completed in 1920, analyzed the propositional calculus of *Principia* and proved its completeness — the first such completeness proof for a significant logical system. ### Formative Influences **Russell and Whitehead's *Principia Mathematica*:** The three volumes of *Principia* (1910–1913) attempted to derive all of mathematics from pure logic. Post devoted his dissertation to analyzing this system, and his entire early career orbited around the questions it raised: Is mathematics complete? Is it consistent? Can mechanical procedures decide all mathematical questions? **The Experience of Disability:** Post's lost arm was not merely biographical detail; it shaped his approach to work. He developed extraordinary mental calculation abilities, could not easily take notes, and worked largely through sustained concentration and memory. Some colleagues noted that his proofs had an elegant economy perhaps born of necessity. **Mental Health Challenges:** Post suffered from what would today be diagnosed as **bipolar disorder** (then called manic-depressive illness). Throughout his life, he experienced episodes that required hospitalization. These episodes interrupted his work, limited his career options, and caused immense personal suffering. Yet between episodes, Post produced work of extraordinary depth and originality. --- ## 2. Intellectual Genealogy ### The Lineage: Who Influenced Post ``` Frege → Russell & Whitehead → PRINCIPIA MATHEMATICA (1910–1913) │ ▼ ┌─────────────────┐ │ Cassius Keyser │ │ (Columbia) │ └─────────────────┘ │ ▼ ┌──────────┐ │ EMIL POST │ └──────────┘ │ ┌─────────────────────────┼─────────────────────────┐ ▼ ▼ ▼ Incompleteness Production Systems Computability (1921, unpub.) (Formal Languages) (Post-Turing) │ │ │ ▼ ▼ ▼ Godel (1931) Chomsky Grammars Modern Recursion (independent) Markov Algorithms Theory ``` **Direct Influences on Post:** - **Bertrand Russell:** The vision of mathematics as reducible to logic; the technical apparatus of *Principia Mathematica* - **Alfred North Whitehead:** Co-author of *Principia*; the systematic approach to logical foundations - **Cassius Jackson Keyser:** Post's dissertation advisor at Columbia; introduced him to foundational questions - **David Hilbert:** Through his program to formalize all mathematics and prove its consistency — the challenge Post would help undermine **Contextual Influences:** - **The Foundational Crisis:** Early 20th century mathematics was reckoning with paradoxes (Russell's paradox, Burali-Forti paradox) that threatened its logical foundations - **The Entscheidungsproblem:** Hilbert's question of whether there exists a mechanical procedure to decide all mathematical statements — Post would prove there is not ### The Lineage: Who Post Influenced **Direct Successors:** | Figure | Era | How Influenced | |--------|-----|----------------| | **Stephen Kleene** | 1930s–1950s | Collaborated on recursion theory; normal form theorems | | **Alonzo Church** | 1930s | Parallel development of computability concepts | | **Alan Turing** | 1930s | Independent but related work on decision problems | | **Noam Chomsky** | 1950s | Production systems became basis for formal grammars | | **Andrey Markov** | 1950s | Markov algorithms directly inspired by Post's string rewriting | **Ideas That Persist:** | Post's Concept | Modern Manifestation | |----------------|---------------------| | Production systems | Context-free grammars, BNF, parser generators | | Post canonical systems | Semi-Thue systems, rewriting engines | | Post correspondence problem | Undecidability proofs, theoretical computer science examples | | Post's theorem | Arithmetic hierarchy, complexity theory foundations | | Many-one reducibility | Standard tool in computability and complexity | --- ## 3. The Work: Chronological ### Master Timeline | Year | Work | Type | Significance | |------|------|------|--------------| | 1920 | Ph.D. Dissertation | Thesis | Completeness of propositional calculus of *Principia* | | 1921 | "Absolutely Unsolvable Problems..." | Unpublished | Independent discovery of incompleteness; anticipation of Godel | | 1936 | "Finite Combinatory Processes — Formulation I" | Paper | "Post machines" — independent of Turing | | 1943 | "Formal Reductions of the General Combinatorial Decision Problem" | Paper | Degrees of unsolvability | | 1944 | "Recursively Enumerable Sets..." | Paper | Post's theorem; simple and hypersimple sets | | 1946 | "A Variant of a Recursively Unsolvable Problem" | Paper | Post correspondence problem | | 1947 | "Recursive Unsolvability of a Problem of Thue" | Paper | Word problem for semigroups is unsolvable | ### The Tragic Timing: The 1921 Anticipation **What Happened:** In 1920–1921, immediately after completing his Ph.D., Post undertook intensive research he titled "Absolutely Unsolvable Problems and Relatively Undecidable Propositions — Account of an Anticipation." In this work, he: 1. **Anticipated Godel's incompleteness theorem** — showing that any sufficiently powerful formal system would contain undecidable propositions 2. **Anticipated Turing's undecidability results** — arguing that no mechanical procedure could solve all mathematical questions 3. **Developed the concept of generated sets** — precursors to recursively enumerable sets **Why It Was Never Published:** Post suffered a severe manic-depressive episode in 1921. The work was set aside. When he recovered, he learned that others (Godel in 1931, Church and Turing in 1936) had published similar results. Post chose not to publish a "priority claim" — he felt the work was incomplete and that claiming priority after the fact was unseemly. The manuscript was finally published posthumously in 1965, edited by Martin Davis, who recognized its historical importance. > _"Post's 1921 paper is one of the great 'what ifs' of mathematical history. Had he published, the entire narrative of 20th century logic would read differently — Godel's theorem might be called the Post-Godel theorem, or even Post's theorem."_ ### Production Systems (1920s–1940s) **The Core Idea:** A **Post production system** (or **Post canonical system**) operates on strings of symbols through rewriting rules. You start with initial strings (axioms) and apply production rules that transform strings into new strings. **Format:** ``` g₁$g₂ → h₁$h₂ ``` Where `$` is a variable matching any string. If the left side matches part of your current string, you can replace it with the right side. **Example:** ``` Starting string: "aab" Rule: a$ → $b Application: "aab" matches "a$" with $ = "ab" Result: "abb" ``` **Why This Matters:** This is exactly how compilers work. You have grammar rules: ``` → + → * ``` Post production systems ARE the theoretical foundation for: - Context-free grammars - BNF notation - Parser generators (yacc, bison, ANTLR) - Chomsky's formal language hierarchy ### Post Machines (1936) **The Paper:** "Finite Combinatory Processes — Formulation I" Post submitted this paper in 1936, independently of Turing. It describes a computing model: - A worker moves along an infinite tape of boxes - Each box is either marked or unmarked - The worker follows instructions: move left, move right, mark, unmark, branch based on current box - This is computationally equivalent to Turing machines Post's formulation was slightly more primitive than Turing's, but equivalently powerful. The paper demonstrates that Post had independently grasped the concept of universal computation. ### Post's Theorem (1944) **The Paper:** "Recursively Enumerable Sets of Positive Integers and Their Decision Problems" This landmark paper established the **arithmetic hierarchy** — a classification of sets by their logical complexity: - **Σ₀ = Π₀ = Δ₀:** Decidable (recursive) sets - **Σ₁:** Recursively enumerable sets (r.e.) - **Π₁:** Complements of r.e. sets - **Σ₂, Π₂, ...:** Higher levels of undecidability **Post's Theorem** states that a set is Σₙ₊₁ if and only if it is recursively enumerable relative to some Πₙ oracle. This hierarchy structures our understanding of **degrees of unsolvability** — not all unsolvable problems are equally unsolvable. ### Post Correspondence Problem (1946) **The Problem:** Given two lists of strings (α₁, α₂, ..., αₙ) and (β₁, β₂, ..., βₙ), is there a sequence of indices i₁, i₂, ..., iₖ such that: αᵢ₁αᵢ₂...αᵢₖ = βᵢ₁βᵢ₂...βᵢₖ **Example:** ``` List A: ["a", "ab", "bba"] List B: ["baa", "aa", "bb"] Question: Can you pick indices so concatenating from A equals concatenating from B? ``` **Post proved this problem is undecidable.** There is no algorithm that, given any two lists, can always correctly determine whether a solution exists. **Why This Matters:** The Post correspondence problem (PCP) became a fundamental tool for proving undecidability. To show problem X is undecidable, reduce PCP to X. It's simpler to work with than Turing machine halting, making it invaluable for theoretical computer science. --- ## 4. Core Ideas & Contributions ### The Central Insight Post understood that **mechanical computation** and **formal provability** are limited in fundamental, inescapable ways. There exist well-defined mathematical questions that no algorithm can answer and true statements that no formal system can prove. This is not a matter of human cleverness — it is a structural feature of mathematics itself. Furthermore, Post saw that the *degree* of unsolvability matters. Not all unsolvable problems are equally hard. There is a hierarchy of undecidability, and understanding this hierarchy illuminates the architecture of mathematical truth. ### Key Concepts #### Production System > _Etymology: **Production** from Latin producere — "to lead forth." Rules that produce (generate) new strings from old._ **Definition:** A formal system consisting of an alphabet, a set of initial strings (axioms), and a set of rewriting rules (productions) that transform strings. **Example:** ``` Alphabet: {a, b} Axiom: "a" Productions: a → ab b → ba Derivation: a → ab → abba → abbabaab → ... ``` **Modern Application:** Context-free grammars, parser specifications, macro expansion systems. #### Recursively Enumerable Set (r.e. set) > _Etymology: **Recursive** from Latin recurrere — "to run back." **Enumerable** — capable of being listed._ **Definition:** A set is recursively enumerable if there exists an algorithm that lists all its members (possibly running forever, possibly with repetitions). Equivalently, a set is r.e. if it is the range of some computable function. **Key Insight:** An r.e. set might not be **decidable** — you can list members, but you cannot always determine non-membership. The halting problem is r.e. but not decidable. **Modern Application:** Understanding what computers can verify vs. what they can decide. #### Arithmetic Hierarchy **Definition:** A classification of sets of natural numbers by their logical complexity: ``` Σ₃ Π₃ \ / Δ₃ / \ Σ₂ Π₂ \ / Δ₂ / \ Σ₁ Π₁ ← r.e. sets and their complements \ / Δ₁ ← Decidable sets ``` Each level is strictly more complex than those below. **Modern Application:** Complexity theory, descriptive set theory, foundations of mathematics. #### Post's Problem **Definition:** Is there an r.e. set whose degree of unsolvability is strictly between decidable sets and the halting problem? Post raised this in 1944. It was solved affirmatively in 1956-1957 by Friedberg and Muchnik using the priority method. **Why It Matters:** Showed that the landscape of computability is rich and structured, not simply "decidable vs. undecidable." ### Theoretical Framework Post's vision was a **complete classification of mathematical problems by computability**: ``` ┌────────────────────────────────────────────────────────────────────────┐ │ THE POST PROGRAM │ │ │ │ 1. Define computation precisely (production systems, Post machines) │ │ │ │ 2. Show fundamental limitations (undecidability, incompleteness) │ │ │ │ 3. Classify problems by degree (arithmetic hierarchy) │ │ │ │ 4. Map the complete structure of computability │ │ │ └────────────────────────────────────────────────────────────────────────┘ ``` ### Innovations & Firsts | Innovation | Description | Prior State | What Changed | |------------|-------------|-------------|--------------| | Independent incompleteness discovery | Showed formal systems cannot prove all truths | Optimism about formalization | Pre-dated Godel by a decade | | Production systems | String rewriting as computation model | No formal model of derivation | Foundation for grammars | | Post machines | Independent Turing-equivalent model | No computing model | Validated universality | | Arithmetic hierarchy | Degrees of unsolvability | Undecidability as binary | Structured landscape | | Post correspondence problem | Simple undecidable problem | Halting problem complex | Practical proof tool | --- ## 5. Impact & Legacy ### Immediate Impact **In Post's Lifetime:** Post worked at **City College of New York** his entire career — a heavy teaching load at an institution focused on undergraduate education, far from the research centers of Princeton or Harvard. Despite this isolation, his papers in the 1940s were immediately recognized by the small community of recursion theorists. His work on production systems influenced the development of formal language theory, though this connection was not always explicitly acknowledged. **The 1944 Paper:** "Recursively Enumerable Sets of Positive Integers and Their Decision Problems" was instantly recognized as a masterpiece. It defined the research program for recursion theory for the next several decades. ### Long-Term Influence **In Computer Science:** - **Formal Language Theory:** Post production systems are the direct ancestors of Chomsky's generative grammars. The Chomsky hierarchy (regular, context-free, context-sensitive, recursively enumerable) builds on Post's framework. - **Compiler Design:** Every parser, every grammar specification, every BNF rule descends from Post's string rewriting idea. - **Undecidability Proofs:** The Post correspondence problem is the standard tool for proving computational problems undecidable. **In Mathematical Logic:** - **Recursion Theory:** Post's theorem and the arithmetic hierarchy are foundational. - **Degrees of Unsolvability:** Post initiated the study of Turing degrees, a major branch of computability theory. - **Priority Method:** Post's problem spurred the development of the priority argument, a major proof technique. **In the Philosophy of Mathematics:** Post's independent discovery of incompleteness (even unpublished) demonstrates that these results were "in the air" — not idiosyncratic insights of Godel alone, but necessary conclusions from the mathematical situation of the time. ### The Counterfactual > What if Post had published his 1921 work? The narrative of 20th century logic would be fundamentally different. "Godel's incompleteness theorem" might be "Post's theorem" or "the Post-Godel theorem." Post would have received the recognition during his lifetime that was instead given to others. More practically: Post might have secured a research position at a major university, with lighter teaching loads and better resources. His mental health struggles might have been easier to manage with better support. We might have far more Post papers to study. ### Recognition & Honors | Era | Recognition | |-----|-------------| | Lifetime | Ph.D. Columbia (1920); career at CCNY | | 1944 | Recognition of recursion theory papers by specialists | | Posthumous | 1965 publication of 1921 manuscript; growing recognition of priority | | Modern | Recognized as co-founder (with Turing, Church, Kleene) of computability theory | **The Tragedy of Recognition:** Post never received the fame of Godel or Turing. He worked at a teaching college, battled mental illness, and died in 1954 at age 57 during electroconvulsive therapy treatment. The mathematical community has slowly recognized his contributions, but he remains less famous than contemporaries whose work he anticipated. --- ## 6. Study Guide: The Mental Model ### The One Sentence > **Emil Post independently discovered incompleteness before Godel, invented string rewriting systems that became the foundation of formal grammars, and established the arithmetic hierarchy that structures our understanding of computability — all while battling severe mental illness and working in relative isolation.** ### The Three Things to Remember 1. **Independent Discovery of Incompleteness (1921):** A decade before Godel's 1931 paper, Post understood that formal systems cannot prove all truths. Mental illness prevented publication; priority went to others. 2. **Production Systems = Grammars:** Post's string rewriting rules ARE the conceptual foundation for Chomsky grammars, BNF, and every parser. When you write grammar rules, you are using Post's framework. 3. **The Hierarchy of Undecidability:** Post showed that "unsolvable" is not a single category. There are degrees of unsolvability, structured into an arithmetic hierarchy. Not all impossible problems are equally impossible. ### The Visual ``` ┌────────────────────────────────────────────────────────────────────────┐ │ EMIL POST'S LEGACY │ │ │ │ 1921 (unpublished) 1936 1944 │ │ ┌─────────────────┐ ┌─────────────────┐ ┌─────────────────────┐ │ │ │ INCOMPLETENESS │ │ POST MACHINES │ │ ARITHMETIC HIERARCHY│ │ │ │ │ │ │ │ │ │ │ │ "There are true │ │ Independent of │ │ Σ₃ Π₃ │ │ │ │ statements no │ │ Turing machines │ │ \ / │ │ │ │ system can │ │ but equivalent │ │ Δ₃ │ │ │ │ prove" │ │ │ │ / \ │ │ │ │ │ │ │ │ Σ₂ Π₂ │ │ │ │ (Godel gets │ │ │ │ \ / │ │ │ │ credit: 1931) │ │ │ │ Δ₁ │ │ │ └─────────────────┘ └─────────────────┘ └─────────────────────┘ │ │ │ │ PRODUCTION SYSTEMS │ │ ┌──────────────────────────────────────────────────────────────────┐ │ │ │ String + Rule → New String │ │ │ │ │ │ │ │ "aab" + (a$ → $b) → "abb" │ │ │ │ │ │ │ │ This IS how grammars work: │ │ │ │ → + │ │ │ │ → number │ │ │ └──────────────────────────────────────────────────────────────────┘ │ │ │ └────────────────────────────────────────────────────────────────────────┘ ``` ### Connecting to Other Figures | If You Know... | Then Understand That Post... | |----------------|------------------------------| | Kurt Godel | Independently discovered incompleteness a decade earlier, but did not publish | | Alan Turing | Independently developed equivalent computation model (Post machines) | | Noam Chomsky | Provided the string rewriting foundation for Chomsky's formal grammars | | John Backus | Production systems directly inspired BNF notation for programming languages | | Alonzo Church | Worked in parallel on computability; Church-Post equivalences | | 1-Panini | Production systems echo Panini's rewriting rules for Sanskrit | ### Common Misconceptions | Misconception | Reality | |---------------|---------| | "Godel discovered incompleteness first" | Post discovered it in 1921; Godel published first (1931) | | "Post machines are just simplified Turing machines" | Post developed them independently; the similarity validates universality | | "His mental illness limited his contributions" | Despite severe illness, he produced foundational work in multiple areas | | "Production systems are just theoretical curiosities" | They are the foundation of every grammar and parser in use today | | "He was a minor figure in logic" | He is a co-founder of computability theory alongside Turing, Church, and Kleene | ### Test Your Understanding 1. **Conceptual:** Why does the existence of the arithmetic hierarchy matter? What does it tell us about the structure of unsolvable problems? 2. **Connection:** How do Post production systems relate to context-free grammars? Give an example showing the parallel. 3. **Historical:** Why did Post not publish his 1921 work on incompleteness, and what would have changed if he had? --- ## 7. Going Deeper: Sources ### Primary Sources | Source | Type | Access | Notes | |--------|------|--------|-------| | "Introduction to a General Theory of Elementary Propositions" (1921) | Ph.D. work | American Journal of Mathematics | Completeness of propositional calculus | | "Finite Combinatory Processes — Formulation I" (1936) | Paper | Journal of Symbolic Logic | Post machines | | "Recursively Enumerable Sets..." (1944) | Paper | Bulletin of the AMS | Post's theorem; landmark paper | | "A Variant of a Recursively Unsolvable Problem" (1946) | Paper | Bulletin of the AMS | Post correspondence problem | | "Absolutely Unsolvable Problems..." (1965, posthumous) | Paper | In Davis, ed., *The Undecidable* | 1921 anticipation of incompleteness | ### Essential Secondary Sources | Source | Author | Type | What It Covers | |--------|--------|------|----------------| | *The Undecidable* | Martin Davis (ed.) | Anthology | Contains Post's papers with historical context | | *Computability and Unsolvability* | Martin Davis | Textbook | Post's contributions in context | | "Emil Post: His Life and Work" | Martin Davis | Biography | In *Solvability, Provability, Definability* | | *Engines of Logic* | Martin Davis | History | Post's place in computing history | | *Theory of Recursive Functions and Effective Computability* | Hartley Rogers Jr. | Textbook | Technical treatment of Post's contributions | ### Modern Introductions - **For beginners:** Martin Davis's biographical articles on Post are accessible and moving - **For programmers:** Trace from Post production systems to BNF to your favorite parser generator - **For logicians:** Rogers's *Theory of Recursive Functions* for technical depth ### Online Resources - Stanford Encyclopedia of Philosophy: "Recursive Functions" — covers Post's contributions - MacTutor History of Mathematics: Emil Post biography - Martin Davis's writings on Post (various online sources) --- ## Appendix: The Human Cost > **Note on Mental Illness:** Post suffered from manic-depressive illness (bipolar disorder) throughout his adult life. He experienced multiple hospitalizations. His death on April 21, 1954, occurred during or shortly after electroconvulsive therapy — a treatment that was more primitive and dangerous in that era than today. Post's illness was not incidental to his life — it shaped his career, limited his opportunities, interrupted his work, and ultimately contributed to his death. He never held a position at a research university. He taught heavy course loads at City College. He worked in relative isolation. And yet, despite all this, he produced work that stands alongside Godel and Turing. The arithmetic hierarchy, the Post correspondence problem, production systems — these are permanent contributions to human knowledge. His story is a reminder that genius is not always recognized, that priority is often a matter of circumstance, and that the history we learn is shaped by who managed to publish, not always by who discovered first. | Claim | Confidence | Source | |-------|------------|--------| | Birth date and place | High | Official records | | Loss of arm in childhood | High | Family accounts, colleagues' memoirs | | 1921 anticipation of incompleteness | High | Manuscript published 1965 | | Manic-depressive illness | High | Family accounts, medical records (referenced by Davis) | | Death during ECT treatment | Medium-High | Family accounts; exact circumstances unclear | --- _Last updated: 2026-03-26. This is a living document._ ## Public evidence links - [Emil Leon Post](https://mathshistory.st-andrews.ac.uk/Biographies/Post/) — MacTutor History of Mathematics - [Emil Leon Post](https://en.wikipedia.org/wiki/Emil_Leon_Post) — Wikipedia contributors