Raphael M. Robinson

Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an <a href="/facts/United_States_of_America/P0sCdLe5">American</a> <a href="/facts/Mathematician/eaFSR8Fx">mathematician</a>.
Born in <a href="/facts/National_City%2c_California/RNfXNQLd">National City</a>, <a href="/facts/California/zLW2vdQJ">California</a>, Robinson was the youngest of four children of a lawyer and a teacher. He was awarded from the <a href="/facts/University_of_California%2c_Berkeley/MXVEjklr">University of California, Berkeley</a> in mathematics: the BA (1932), MA (1933), and Ph.D. (1935). His Ph.D. thesis, on <a href="/facts/Complex_analysis/hgCoQlH0">complex analysis</a>, was titled Some results in the theory of <a href="/facts/Schlicht_function/PXKcc8un">Schlicht functions</a>.
In 1941, Robinson married his former student <a href="/facts/Julia_Robinson/HgGWeuFU">Julia Bowman</a>. She became his Berkeley colleague and the first woman president of the <a href="/facts/American_Mathematical_Society/fr5gotCt">American Mathematical Society</a>.
Robinson worked on <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a>, <a href="/facts/Set_theory/1ptfsvUP">set theory</a>, <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, and <a href="/facts/Combinatorics/k14xUoKT">combinatorics</a>. In 1937 he set out a simpler and more conventional version of the <a href="/facts/John_von_Neumann/aUk6urof">John von Neumann</a> 1923 <a href="/facts/Von_Neumann%25E2%2580%2593Bernays%25E2%2580%2593G%25C3%25B6del_set_theory/5wLhAIMz">axiomatic set theory</a>. Soon after <a href="/facts/Alfred_Tarski/7h6NySAj">Alfred Tarski</a> joined Berkeley's mathematics department in 1942, Robinson began to do major work on the <a href="/facts/Foundations_of_mathematics/yjpbbUkt">foundations of mathematics</a>, building on Tarski's concept of <a href="/facts/Decidability_(logic)/17SHPMo0">essential undecidabilility</a>, by proving a number of mathematical theories <a href="/facts/Decision_problem/cQNWjbdE">undecidable</a>. In 1950 Robinson proved that an essentially undecidable theory need not have an infinite number of <a href="/facts/Axiom/mLjP14Mc">axioms</a> by coming up with a counterexample: <a href="/facts/Robinson_arithmetic_Q/FAFPDus0">Robinson arithmetic Q</a>. Q is finitely axiomatizable because it lacks <a href="/facts/Peano_arithmetic/DhhDnNug">Peano arithmetic</a>'s axiom schema of <a href="/facts/Mathematical_induction/KxAPqNrH">induction</a>; nevertheless Q, like Peano arithmetic, is <a href="/facts/G%25C3%25B6del%2527s_Incompleteness_Theorem/du8PRu8g">incomplete</a> and undecidable in the sense of <a href="/facts/Kurt_G%25C3%25B6del/P14DqKqK">Gödel</a>. Robinson's work on undecidability culminated in his coauthoring Tarski et al. (1953), which established, among other things, the undecidability of <a href="/facts/Group_theory/NfowcI5H">group theory</a>, <a href="/facts/Lattice_theory/5ak6ufky">lattice theory</a>, abstract <a href="/facts/Projective_geometry/rHKSaEbx">projective geometry</a>, and <a href="/facts/Closure_algebra/TYhpHoYN">closure algebras</a>.
Robinson worked in <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, even employing very early computers to obtain results. For example, he coded the <a href="/facts/Lucas%25E2%2580%2593Lehmer_primality_test/P6sD2wv8">Lucas–Lehmer primality test</a> to determine whether 2n − 1 was prime for all prime n < 2304 on a <a href="/facts/SWAC_(computer)/kBJEN7s8">SWAC</a>. In 1952, he showed that these <a href="/facts/Mersenne_number/IyF3sBNf">Mersenne numbers</a> were all composite except for 17 values of n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281. He discovered the last five of these <a href="/facts/Mersenne_prime/IyF3sBNf">Mersenne primes</a>, the largest ones known at the time.
Robinson wrote several papers on <a href="/facts/Wang_tile/639AJElj">tilings of the plane</a>, in particular a clear and remarkable 1971 paper Undecidability and nonperiodicity for tilings of the plane simplifying what had been a tangled theory.
Robinson became a full professor at Berkeley in 1949, retired in 1973, and remained active in his educational interests for the duration of his life having published late in his life:

<ul><li>(age 80 years) <a href="/facts/Marvin_Minsky/HTU5MYLL">Minsky</a>'s small universal Turing machine, describing a <a href="/facts/Universal_Turing_machine/2klpb1qQ">universal Turing machine</a> with four symbols and seven states;</li>
<li>(age 83 years) Two figures in the <a href="/facts/Hyperbolic_plane/DjTMKdgy">hyperbolic plane</a>.</li></ul>

Raphael M. Robinson open-in-new

Raphael M. Robinson