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: Where is the white king? <ref>on c3, capturing a pawn from b3, which took on c3 [[En passant|en passant]] after 1... Bd5+ 2. c4</ref>

* <span id="Video"></span>[https://vimeo.com/127338218 A Mathematical Mystery Tour] - [https://en.wikipedia.org/wiki/Horizon_%28BBC_TV_series%29 BBC Horizon Documentary] (1984), edited 1985 [https://en.wikipedia.org/wiki/Nova_(TV_series) Nova] version, [https://en.wikipedia.org/wiki/Vimeo Vimeo] Video: featuring [[Mathematician#Dieudonne|Jean Dieudonné]], [[Mathematician#Atiyah|Michael Atiyah]], [[Mathematician#GWMoore|Greg Moore]], [[Mathematician#Erdos|Paul Erdős]], [[Mathematician#Thom|René Thom]], [[Raymond Smullyan]], and [https://en.wikipedia.org/wiki/Ivor_Grattan-Guinness Ivor Grattan-Guinness] - [[White Knight]] at 3642:25{{#evu:45https://vimeo.com/127338218|alignment=left|valignment=top|dimensions="640"}}

** [https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem Fermat's Last Theorem] 01:3040** [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Goldbach's conjecture] 01:3949** [https://en.wikipedia.org/wiki/Riemann_hypothesis Riemann hypothesis] 02:5202** [https://en.wikipedia.org/wiki/4-manifold#Special_phenomena_in_4-dimensions Classification Problem for 4-D Manifolds] 12:0212** [https://en.wikipedia.org/wiki/P_versus_NP_problem P versus NP problem] 12:1626** [https://en.wikipedia.org/wiki/Invariant_subspace_problem Invariant Subspace Problem] for [https://en.wikipedia.org/wiki/Hilbert_space Hilbert Spaces] 12:2838* '''A Mathematical Mystery Tour''' 13:5000# '''Proof Beyond Doubt''' 25:5106** ## [https://en.wikipedia.org/wiki/Mathematical_proof Proof]5:45** ## [https://en.wikipedia.org/wiki/Euclid%27s_theorem Euclid's theorem] 36:3258** ## [https://en.wikipedia.org/wiki/Twin_prime Are there infinitely many twin primes?] 37:5525** [https://en.wikipedia.org/wiki/Paul_Erd%C5%91s#Erd.C5.91s.27_problems Erdős' problems] 4:23** # [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Goldbach's conjecture] 57:0750** ## [https://en.wikipedia.org/wiki/Mertens_conjecture Mertens conjecture] 58:3517** ## [https://en.wikipedia.org/wiki/EuclidFermat%27s_Elements Euclid27s_Last_Theorem Fermat's ElementsLast Theorem] 69:1510** ## [https://en.wikipedia.org/wiki/Chinese_mathematics Chinese mathematicsPaul_Erd%C5%91s#Erd.C5.91s.27_problems Erdős' problems] 612:4239** [https# '''The Foundations of Mathematics''' 13://en.wikipedia.org/wiki/Egyptian_mathematics Egyptian mathematics] 7:0221** ## [https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem Fermat's Last TheoremChinese_mathematics Chinese mathematics] 813:3025# '''The Language of Abstraction''' 12:20** # [https://en.wikipedia.org/wiki/Nicolas_Bourbaki Bourbaki GroupEgyptian_mathematics Egyptian mathematics] 1213:2442** ## [https://en.wikipedia.org/wiki/Abstract_structure Abstract structureEuclid%27s_Elements Euclid's Elements] 15:3000** ## [https://en.wikipedia.org/wiki/Euclidean_geometry Euclidean geometryParallel_postulate Parallel postulate] 16:1204** ## [https://en.wikipedia.org/wiki/Non-Euclidean_geometry Non-Euclidean geometry] 16:4510** ## [https://en.wikipedia.org/wiki/Hypercube Hypercube] 1716:0824** ## [https://en.wikipedia.org/wiki/Klein_bottle Klein bottle] 1817:0800# '''Discovery or Invention''' 19:1821** [https://en.wikipedia.org/wiki/History_of_mathematics History of mathematics] 19:20** ## [https://en.wikipedia.org/wiki/Platonism Platonism] 2019:1549** ## [https://en.wikipedia.org/wiki/Pythagorean_theorem Pythagorean theorem] 2019:2157** ## [https://en.wikipedia.org/wiki/Golden_rectangle Golden rectangle] 20:35** [https://en.wikipedia.org/wiki/Golden_ratio Golden ratio]48# '''Playing the NumbersA Question of Infinity''' 2224:1320** ## [https://en.wikipedia.org/wiki/Pi PiInfinity Infinity] 2224:1820** ## [https://en.wikipedia.org/wiki/Mersenne_prime Mersenne primePi Pi] 24:0750# '''The Taming of the Infinite''' 25:37** # [https://en.wikipedia.org/wiki/Infinity InfinityMersenne_prime Mersenne prime] 2526:3736** ## [https://en.wikipedia.org/wiki/Countable_set Countable set] 2627:0858** ## [https://en.wikipedia.org/wiki/Uncountable_set Uncountable set] 2730:2500** ## [https://en.wikipedia.org/wiki/Aleph_number Aleph number] 2830:1750# '''Contradictions and ParadoxesCracks in the Foundation''' 2932:2206** ## [https://en.wikipedia.org/wiki/Mathematical_logic Mathematical logic] 2932:4006** ## [https://en.wikipedia.org/wiki/Russell%27s_paradox Russell's paradox] 3132:2332** ## [https://en.wikipedia.org/wiki/Principia_Mathematica Principia Mathematica] 3336:26# '''Back to Basics''' 38:5032## [https://en.wikipedia.org/wiki/Nicolas_Bourbaki Bourbaki Group] 38:40** ## [https://en.wikipedia.org/wiki/Hilbert%27s_program Hilbert's program] 3541:25## [[White Knight]] 42:25# '''The Uncertain Future''' 44:4046** ## [https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Gödel's incompleteness theorems] 3944:0352# '''Incomplete Future''' 40# [https://en.wikipedia.org/wiki/Continuum_hypothesis Continuum hypothesis] 46:2030** ## [https://en.wikipedia.org/wiki/Four_color_theorem Four color theorem] 4446:0038** ## [https://en.wikipedia.org/wiki/Computer-assisted_proof Computer-assisted proof] 4450:5004