31:
446:
173:
Professor of
Mathematics. Between 1997 and 2006, he was a professor at Stanford, and before that worked at Ohio State University between 1987 and 1999. His research interest is in
506:
451:
286:
Rubin, Karl (1989). "Tate-Shafarevich groups of elliptic curves with complex multiplication". In Coates, John; Greenberg, Ralph; Mazur, Barry; et al. (eds.).
481:
476:
322:
456:
486:
461:
338:
496:
491:
295:
359:
166:
124:
426:
389:
228:
217:
334:
213:
178:
240:
408:
257:
146:
501:
471:
422:
318:
290:. Advanced Studies in Pure Mathematics. Vol. 17. Boston, MA: Academic Press, Inc. pp. 409–419.
177:. He was the first mathematician (1986) to show that some elliptic curves over the rationals have finite
206:
112:
466:
190:
108:
76:
232:
120:
116:
80:
291:
267:
131:
57:
305:
301:
170:
360:"Karl Rubin, acclaimed mathematician, named Edward and Vivian Thorp Chair in Mathematics"
363:
174:
440:
319:
Fermat's Last
Theorem - The Theorem and Its Proof: An Exploration of Issues and Ideas
224:
202:
162:
262:
198:
136:
385:
236:
220:
90:
252:
194:
30:
431:
181:. It is widely believed that these groups are always finite.
216:
386:"List of Fellows of the American Mathematical Society"
142:
130:
104:
86:
72:
64:
40:
21:
335:"Putnam Competition Individual and Team Winners"
321:- Rubin's talk in 1993 about elliptic curves at
239:. Rubin is brother to astronomer and physicist
447:Institute for Advanced Study visiting scholars
8:
507:Fellows of the American Mathematical Society
18:
452:University of California, Irvine faculty
278:
161:(born January 27, 1956) is an American
231:. Rubin's parents were mathematician
193:in 1976, and obtained his Ph.D. from
7:
482:21st-century American mathematicians
477:20th-century American mathematicians
227:. In 2012 he became a fellow of the
339:Mathematical Association of America
14:
197:in 1981. His thesis advisor was
167:University of California, Irvine
125:University of California, Irvine
29:
1:
457:Ohio State University faculty
427:Mathematics Genealogy Project
390:American Mathematical Society
229:American Mathematical Society
218:American Mathematical Society
487:Princeton University alumni
462:Columbia University faculty
214:National Science Foundation
523:
212:In 1988, Rubin received a
497:American number theorists
492:Harvard University alumni
152:
97:
28:
258:Torus-based cryptography
147:Cristian Dumitru Popescu
288:Algebraic Number Theory
179:Tate–Shafarevich groups
432:Karl Rubin's Home page
16:American mathematician
207:Sloan Research Fellow
189:Rubin graduated from
113:Ohio State University
366:on September 9, 2006
191:Princeton University
185:Education and career
109:Princeton University
77:Princeton University
233:Robert Joshua Rubin
121:Stanford University
117:Columbia University
35:Karl Rubin in 2009.
81:Harvard University
423:Karl Cooper Rubin
268:Stark conjectures
159:Karl Cooper Rubin
156:
155:
143:Doctoral students
99:Scientific career
23:Karl Cooper Rubin
514:
411:
409:Vera Rubin obit.
406:
400:
399:
397:
396:
382:
376:
375:
373:
371:
362:. Archived from
356:
350:
349:
347:
345:
331:
325:
316:
310:
309:
283:
132:Doctoral advisor
58:Urbana, Illinois
54:
51:January 27, 1956
50:
48:
33:
19:
522:
521:
517:
516:
515:
513:
512:
511:
437:
436:
419:
414:
407:
403:
394:
392:
384:
383:
379:
369:
367:
358:
357:
353:
343:
341:
333:
332:
328:
317:
313:
298:
285:
284:
280:
276:
249:
235:and astronomer
205:in 1974, and a
187:
175:elliptic curves
123:
119:
115:
111:
79:
73:Alma mater
60:
55:
52:
46:
44:
36:
24:
17:
12:
11:
5:
520:
518:
510:
509:
504:
502:Putnam Fellows
499:
494:
489:
484:
479:
474:
469:
464:
459:
454:
449:
439:
438:
435:
434:
429:
418:
417:External links
415:
413:
412:
401:
377:
351:
326:
311:
296:
277:
275:
272:
271:
270:
265:
260:
255:
248:
245:
186:
183:
154:
153:
150:
149:
144:
140:
139:
134:
128:
127:
106:
102:
101:
95:
94:
88:
84:
83:
74:
70:
69:
66:
62:
61:
56:
42:
38:
37:
34:
26:
25:
22:
15:
13:
10:
9:
6:
4:
3:
2:
519:
508:
505:
503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
475:
473:
472:Living people
470:
468:
465:
463:
460:
458:
455:
453:
450:
448:
445:
444:
442:
433:
430:
428:
424:
421:
420:
416:
410:
405:
402:
391:
387:
381:
378:
365:
361:
355:
352:
340:
336:
330:
327:
324:
320:
315:
312:
307:
303:
299:
297:0-12-177370-1
293:
289:
282:
279:
273:
269:
266:
264:
261:
259:
256:
254:
251:
250:
246:
244:
242:
238:
234:
230:
226:
225:number theory
222:
219:
215:
210:
208:
204:
203:Putnam Fellow
200:
196:
192:
184:
182:
180:
176:
172:
168:
164:
163:mathematician
160:
151:
148:
145:
141:
138:
135:
133:
129:
126:
122:
118:
114:
110:
107:
103:
100:
96:
92:
89:
85:
82:
78:
75:
71:
67:
63:
59:
53:(age 68)
43:
39:
32:
27:
20:
404:
393:. Retrieved
380:
368:. Retrieved
364:the original
354:
344:December 13,
342:. Retrieved
329:
314:
287:
281:
263:Euler system
241:Judith Young
211:
199:Andrew Wiles
188:
158:
157:
137:Andrew Wiles
105:Institutions
98:
467:1956 births
201:. He was a
65:Nationality
441:Categories
395:2016-08-22
370:August 28,
274:References
237:Vera Rubin
221:Cole Prize
91:Cole Prize
47:1956-01-27
209:in 1985.
247:See also
68:American
425:at the
306:1097625
253:CEILIDH
195:Harvard
304:
294:
93:(1992)
87:Awards
171:Thorp
372:2006
346:2021
323:MSRI
292:ISBN
165:at
41:Born
223:in
169:as
443::
388:.
337:.
302:MR
300:.
243:.
49:)
398:.
374:.
348:.
308:.
45:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
