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Alan Turing and Number Theory
Published on Jul 10, 201211809 Views
Beside well-known revolutionary contributions, Alan Turing had a number of significant results in "traditional" mathematics. In particular he was very much interested in the famous Riemann Hypothesis.
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Chapter list
Alan Turing and Number Theory00:00
Recognition of Merits (1)01:14
Recognition of Merits (2)01:20
Recognition of Merits (3)01:25
Distribution of Prime Numbers (1)02:06
Distribution of Prime Numbers (2)02:15
Distribution of Prime Numbers (3)02:22
Distribution of Prime Numbers (4)02:34
Distribution of Prime Numbers (5)03:01
Distribution of Prime Numbers (6)03:04
Distribution of Prime Numbers (7)03:08
Distribution of Prime Numbers (8)03:25
Distribution of Prime Numbers (9)03:47
Numerical Values04:06
Riemann's formula for (x) (1)04:15
Riemann's formula for (x) (2)04:17
Riemann's formula for (x) (3)04:54
Riemann's formula for (x) (4)05:20
Riemann's formula for (x) (5)05:34
Ingham's Book06:09
Riemann's zeta function (1)07:03
Riemann's zeta function (2)07:06
The Riemann Hypothesis (1)07:20
The Riemann Hypothesis (2)07:23
The Riemann Hypothesis (3)07:49
The Riemann Hypothesis (4)08:40
The Riemann Hypothesis (5)08:49
Numerical checking of RH08:55
Riemann's formula for (x) (6)09:19
Riemann's formula for (x) (7)09:23
Riemann's formula for (x) (8)10:05
Application for a grant of Royal Society11:22
"Turing Machine"12:14
The cost13:19
Tide-predicting Machine (1)13:48
Tide-predicting Machine (2)15:37
Tide-predicting Machines15:49
March, 1939 (1)16:39
March, 1939 (2)16:47
Methods for the calculation of the zeta-function (1)17:10
Methods for the calculation of the zeta-function (2)17:15
Methods for the calculation of the zeta-function (3)17:18
Methods for the calculation of the zeta-function (4)17:26
Methods for the calculation of the zeta-function (5)17:40
Proceedings of the London Mathematical Society (1)18:50
Proceedings of the London Mathematical Society (2)19:13
Proceedings of the London Mathematical Society (3)19:26
Proceedings of the London Mathematical Society (4)19:46
Proceedings of the London Mathematical Society (5)20:14
Proceedings of the London Mathematical Society (6)20:29
Proceedings of the London Mathematical Society (7)20:35
Proceedings of the London Mathematical Society (8)20:55
Cauchy integral (1)21:49
Cauchy integral (2)22:04
Alongside the Critical Line (1)22:53
Alongside the Critical Line (2)23:10
Alongside the Critical Line (3) 23:34
Alongside the Critical Line (4)23:52
Alongside the Critical Line (5)24:04
Alongside the Critical Line (6)24:40
Alongside the Critical Line (7)24:42
Classical Method for Checking Riemann's Hypothesis (1)24:48
Classical Method for Checking Riemann's Hypothesis (2)24:56
Classical Method for Checking Riemann's Hypothesis (3)25:03
Classical Method for Checking Riemann's Hypothesis (4)25:16
Gram Points (1)25:39
Gram Points (2)25:51
Gram Points (3)26:08
Gram Points (4)26:14
Gram Points (5)26:18
Gram Points (6)26:25
Gram Points (7)26:30
Gram's "law" (1)26:39
Gram's "law" (2)26:40
Gram's "law" (3)27:06
Violation of Gram's "law" (1)27:54
Violation of Gram's "law" (2)28:09
Violation of Gram's "law" (3)28:14
Violation of Gram's "law" (4)28:19
Violation of Gram's "law" (5)28:26
Violation of Gram's "law" (6)28:29
Violation of Gram's "law" (7)28:38
Violation of Gram's "law" (8)28:46
Violation of Gram's "law" (9)28:49
Violation of Gram's "law" (10)28:56
Classical Method for Checking Riemann's Hypothesis (1)29:00
Classical Method for Checking Riemann's Hypothesis (2)29:06
Classical Method for Checking Riemann's Hypothesis (3)29:11
Classical Method for Checking Riemann's Hypothesis (4)29:26
Proceedings of the London Mathematical Society (9)30:37
Proceedings of the London Mathematical Society (10)30:56
Function S(t) (1)31:37
Function S(t) (2)31:46
Function S(t) (3)31:49
Function S(t) (4)31:52
Function S(t) (5)31:55
Function S(t) (6)32:02
Function S(t) (7)32:20
Function S(t) (8)32:53
Function S(t) (9)33:16
Example Turing33:41
Turing's Method (1)33:54
Turing's Method (2)34:46
Turing's Method (3)35:16
Turing's Method (4)35:22
Turing's Method (5)35:28
Turing's Method (6)35:32
Turing's Method (7)35:37
Turing's Method (8)35:44
Turing's Method (9)35:45
Turing's Method (10)35:49
Turing's Method (11)35:51
Turing's Method (12)36:27
Turing's Method (13)36:31
Turing's Method (14)36:33
Turing's Method (15)36:36
Turing's Method (16)36:42
Turing's Method (17)36:46
Turing's Method (18)36:49
Turing's Method (19)37:07
Proceedings of the London Mathematical Society (11)38:13
Proceedings of the London Mathematical Society (12)39:33
Proceedings of the London Mathematical Society (13)39:57
Proceedings of the London Mathematical Society (14)40:41
Numerical checking of RH (continued)41:44
Turing's papers on Riemann's Hypothesis (1)43:03
Turing's papers on Riemann's Hypothesis (2)44:20
Systems of logic based on ordinals (1)44:45
Systems of logic based on ordinals (2)44:47
Systems of logic based on ordinals (3)44:54
Systems of logic based on ordinals (4)45:12
Systems of logic based on ordinals (5)45:33
RH in the Arithmetical Hierarchy (1)46:19
RH in the Arithmetical Hierarchy (2)46:20
RH in the Arithmetical Hierarchy (3)46:32
RH in the Arithmetical Hierarchy (4)46:36
RH in the Arithmetical Hierarchy (5)46:38
RH in the Arithmetical Hierarchy (6)46:40
RH in the Arithmetical Hierarchy (7)46:41
RH in the Arithmetical Hierarchy (8)47:42
RH in the Arithmetical Hierarchy (9)47:49
RH in the Arithmetical Hierarchy (10)49:34
RH in the Arithmetical Hierarchy (11)49:35
RH in the Arithmetical Hierarchy (12)49:36
RH in the Arithmetical Hierarchy (13)49:38
RH in the Arithmetical Hierarchy (14)50:11