Knowledge (XXG)

Andrey Markov Jr.

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315: 141:. Embedding implies failure to create a correspondence between algorithms and indexing (naturally uncountably infinite, but even larger) of the four-manifolds structure. Failure is in Cantor's sense. Indexing is in Godel's sense. This result has profound implications for the limitations of mathematical analysis. 137:: no general algorithm exists for distinguishing two arbitrary manifolds with four or more dimensions. This is because four-dimensional manifolds have sufficient flexibility to allow us to embed any algorithm within their structure. Hence, classifying all four-manifolds would imply a solution to Turing's 165: 400: 420: 395: 410: 405: 390: 385: 356: 177: 68: 415: 450: 123: 189: 349: 425: 440: 31: 303: 145: 445: 171: 111: 455: 342: 84: 435: 72: 95: 91: 430: 380: 375: 253:
Glukhov, M. M.; Nagornyĭ, N. M. (2004). "Andreĭ Andreevich Markov (on the centenary of his birth)".
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In 1960, Markov obtained fundamental results showing that the classification of four-dimensional
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obtained the same result independently at about the same time. In 1953 he became a member of the
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and logic. He made outstanding contributions to various areas of mathematics, including
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Kushner, Boris A (2006). "The constructive mathematics of A. A. Markov".
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Medal "For Valiant Labour in the Great Patriotic War 1941–1945"
114:. An important result that he proved in 1947 was that the 330: 67:, and one of the key founders of the Russian school of 401:
Corresponding Members of the USSR Academy of Sciences
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Recipients of the Order of the Red Banner of Labour
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Academic staff of Saint Petersburg State University
411:Recipients of the Order of the Badge of Honour 350: 8: 406:Communist Party of the Soviet Union members 357: 343: 90:His name is in particular associated with 30:For other people with the same name, see 202: 63:, the son of the Russian mathematician 7: 391:Mathematicians from Saint Petersburg 311: 309: 178:Medal "For the Defence of Leningrad" 386:20th-century Russian mathematicians 329:. You can help Knowledge (XXG) by 25: 190:Order of the Red Banner of Labour 416:Recipients of the Order of Lenin 313: 27:Soviet mathematician (1903–1979) 144:His doctoral students include 1: 304:Mathematics Genealogy Project 451:Burials at Kuntsevo Cemetery 172:Order of the Badge of Honour 112:theoretical computer science 116:word problem for semigroups 472: 308: 267:10.1515/156939204774148776 85:foundations of mathematics 46:Андре́й Андре́евич Ма́рков 29: 52:– 11 October 1979, 45: 38:Andrey Andreyevich Markov 69:constructive mathematics 98:in mathematical logic, 426:Mathematical logicians 73:differential equations 441:Soviet mathematicians 321:This article about a 48:; 22 September 1903, 446:Mathematician stubs 255:Diskrete Math. Appl 212:Amer. Math. Monthly 456:Russian scientists 92:Markov's principle 81:mathematical logic 18:Andrey Markov, Jr. 338: 337: 300:Andrey Markov Jr. 160:Awards and honors 16:(Redirected from 463: 436:Soviet logicians 359: 352: 345: 317: 310: 287: 286: 250: 244: 243: 224:10.2307/27641983 207: 118:was unsolvable; 108:Markov algorithm 100:Markov's theorem 65:Andrey Markov Sr 50:Saint Petersburg 47: 21: 471: 470: 466: 465: 464: 462: 461: 460: 366: 365: 364: 363: 296: 291: 290: 252: 251: 247: 209: 208: 204: 199: 162: 150:Gennady Makanin 139:halting problem 124:Communist Party 35: 28: 23: 22: 15: 12: 11: 5: 469: 467: 459: 458: 453: 448: 443: 438: 433: 428: 423: 418: 413: 408: 403: 398: 393: 388: 383: 378: 368: 367: 362: 361: 354: 347: 339: 336: 335: 318: 307: 306: 295: 294:External links 292: 289: 288: 245: 218:(6): 559–566. 201: 200: 198: 195: 194: 193: 187: 184:Order of Lenin 181: 175: 169: 161: 158: 154:Nikolai Shanin 120:Emil Leon Post 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 468: 457: 454: 452: 449: 447: 444: 442: 439: 437: 434: 432: 429: 427: 424: 422: 419: 417: 414: 412: 409: 407: 404: 402: 399: 397: 394: 392: 389: 387: 384: 382: 379: 377: 374: 373: 371: 360: 355: 353: 348: 346: 341: 340: 334: 332: 328: 324: 323:mathematician 319: 316: 312: 305: 301: 298: 297: 293: 284: 280: 276: 272: 268: 264: 260: 256: 249: 246: 241: 237: 233: 229: 225: 221: 217: 213: 206: 203: 196: 191: 188: 185: 182: 179: 176: 173: 170: 167: 164: 163: 159: 157: 155: 151: 147: 146:Boris Kushner 142: 140: 136: 132: 127: 125: 121: 117: 113: 109: 105: 101: 97: 96:Markov's rule 93: 88: 86: 82: 78: 74: 70: 66: 62: 61:mathematician 59: 55: 51: 43: 39: 33: 32:Andrei Markov 19: 331:expanding it 320: 258: 254: 248: 215: 211: 205: 143: 128: 89: 37: 36: 431:Topologists 381:1979 deaths 376:1903 births 135:undecidable 104:knot theory 370:Categories 261:(1): 1–6. 283:120486293 131:manifolds 232:27641983 83:and the 77:topology 56:) was a 302:at the 275:2069985 240:2231143 42:Russian 281:  273:  238:  230:  192:(1963) 186:(1954) 180:(1946) 174:(1945) 168:(1945) 152:, and 58:Soviet 54:Moscow 325:is a 279:S2CID 228:JSTOR 197:Notes 327:stub 106:and 94:and 263:doi 220:doi 216:113 133:is 110:in 102:in 372:: 277:. 271:MR 269:. 259:14 257:. 236:MR 234:. 226:. 214:. 156:. 148:, 126:. 87:. 79:, 75:, 44:: 358:e 351:t 344:v 333:. 285:. 265:: 242:. 222:: 40:( 34:. 20:)

Index

Andrey Markov, Jr.
Andrei Markov
Russian
Saint Petersburg
Moscow
Soviet
mathematician
Andrey Markov Sr
constructive mathematics
differential equations
topology
mathematical logic
foundations of mathematics
Markov's principle
Markov's rule
Markov's theorem
knot theory
Markov algorithm
theoretical computer science
word problem for semigroups
Emil Leon Post
Communist Party
manifolds
undecidable
halting problem
Boris Kushner
Gennady Makanin
Nikolai Shanin
Medal "For Valiant Labour in the Great Patriotic War 1941–1945"
Order of the Badge of Honour

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