Fermat's enigma: the quest to prove Fermat's last theorem
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
RBA
2012
|
| Series: | Everything is mathematical
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | 151 S. Ill., graph. Darst. |
Staff View
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Record in the Search Index
| _version_ | 1804149693986373633 |
|---|---|
| adam_text | Contents
Preface
......................................................................................................................................................... 9
Chapter
1.
Light in the Mansion of Mathematics
................................................... 11
Monday, Tuesday
................................................................................................................................ 14
...
and Wednesday
................................................................................................................................ 15
A mathematician in the headlines
.............................................................................................. 16
Chapter
2.
It all Began in
Sumeria
...................................................................................... 19
The Plimpton
322
tablet
.................................................................................................................. 19
The Babylonian base-60 number system
.............................................................................. 20
From the decimal metric system to the sexagesimal number system
......... 23
Mixing populations, merging systems
............................................................................. 23
Astronomical theories and degrees
.................................................................................... 24
Ways of counting
........................................................................................................................... 25
Language and counting
............................................................................................................. 26
Two symbols to count the world
................................................................................................ 26
The additive system
..................................................................................................................... 27
The positional system
................................................................................................................. 27
Decimals
.............................................................................................................................................. 28
Translating the Plimpton
322
tablet into decimal notation
...................................... 29
Otto Neugebauer s hypothesis
.............................................................................................. 32
R. Creighton Buck s explanation
....................................................................................... 33
The interpretation of Eleanor Robson
........................................................................... 35
Pythagoras theorem in
Sumeria
......................................................................................... 36
Indian mathematics takes centre stage
..................................................................................... 38
Harappa culture
.............................................................................................................................. 38
Vedic
culture
.................................................................................................................................... 39
Sulbasutras and altars
.................................................................................................................... 39
Chapter
3.
Fermat,
a Lawyer to be Reckoned With
............................................. 45
Place of birth, family and education
......................................................................................... 46
Mathematical circles
............................................................................................................................ 47
Political and administrative career
.............................................................................................. 50
CONTENTS
The prince
of
amateurs and Pierre de Carcavy
.............................................................. 53
Marin Mersenne
.................................................................................................................................... 54
Correspondence with
Fermat
............................................................................................... 58
The cycloid problem
.................................................................................................................. 60
The
maximums
and
minimums
method
............................................................................... 62
Multiplicity of interests
..................................................................................................................... 64
A strange way of working
............................................................................................................... 66
The dispute with Descartes
............................................................................................................ 69
The theory of refraction
........................................................................................................... 71
Chapter
4.
The Birth of the Last Theorem
.................................................................. 73
Euclid s Elements
................................................................................................................................... 73
Perfect numbers
.............................................................................................................................. 75
The generation of perfect numbers
.................................................................................. 75
Conjectures regarding perfect numbers
......................................................................... 77
Diophantus Arithmetica
.................................................................................................................... 80
Importance of the work
........................................................................................................... 82
Diffusion of Diophantus legacy
.......................................................................................... 84
The problems from Diophantus Arithmetica
..................................................................... 88
Problem
32
of Book II
.............................................................................................................. 88
The solution to problem
32 ................................................................................................... 89
Characteristics of the problem
.............................................................................................. 90
Parallel reasoning
........................................................................................................................... 91
Problem
29
of Book IV
............................................................................................................ 92
An enigmatic annotation
.......................................................................................................... 94
Back to Book II: problem
8 ................................................................................................... 95
Fermat
s
contributions
............................................................................................................... 97
An unpublished genius
...................................................................................................................... 99
Chapter
5.
The Ingredients for a Tasty Dish
................................................................ 103
Fermat
s
Grand Prix
............................................................................................................................ 103
The first two hundred years
................................................................................................. 104
An unexpected protagonist
................................................................................................... 106
Lames demonstration
................................................................................................................. 109
Ideal solutions
..................................................................................................................................
Ill
A question of genus
............................................................................................................................. 113
CONTENTS
A bridge between two worlds
...................................................................................................... 116
The first world: elliptic curves
.............................................................................................. 117
The second world: modular forms
.................................................................................... 120
The bridge: the Taniyama-Shimura conjecture
......................................................... 122
The
epsilon
conjecture
...................................................................................................................... 125
From conjecture to theorem
................................................................................................. 127
So, now what?
......................................................................................................................................... 128
Chapter
6.
The Proof
....................................................................................................................... 129
The boy who dreamed of proving Fermat s last theorem
.......................................... 129
Counting infinities
............................................................................................................................... 131
Flach, Katz
and flickers of light
.................................................................................................... 134
An early morning email
................................................................................................................... 137
I m still not satisfied, Andrew
................................................................................................. 137
Revelation
................................................................................................................................................. 141
The medal he never received
...................................................................................................... 142
Epilogue. Life after
Fermat?
........................................................................................................... 143
Appendix. Polygonal Numbers
............................................................................................... 145
Bibliography
............................................................................................................................................ 147
Index
............................................................................................................................................................. 149
Fermaťs
Enigma
The quest to prove
Fermaťs
last theorem
No other conjecture in the history of mathematics has caused
such widespread debate as that stated by the brilliant French
mathematician Pierre
de Fermât
in
1637.
The simplicity of its
formulation contrasts with the great mathematical depths to
which its study leads, and the quest to prove it introduces us
to some extraordinary mathematical minds.
|
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| institution | BVB |
| language | English |
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| physical | 151 S. Ill., graph. Darst. |
| publishDate | 2012 |
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| publisher | RBA |
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| series2 | Everything is mathematical |
| spelling | Violant i Holz, Albert Verfasser aut Fermat's enigma the quest to prove Fermat's last theorem Albert Violant i Holz London RBA 2012 151 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Geschichte gnd rswk-swf Fermatsche Vermutung (DE-588)4154012-8 gnd rswk-swf Fermatsche Vermutung (DE-588)4154012-8 s Geschichte z DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025430914&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025430914&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Violant i Holz, Albert Fermat's enigma the quest to prove Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd |
| subject_GND | (DE-588)4154012-8 |
| title | Fermat's enigma the quest to prove Fermat's last theorem |
| title_auth | Fermat's enigma the quest to prove Fermat's last theorem |
| title_exact_search | Fermat's enigma the quest to prove Fermat's last theorem |
| title_full | Fermat's enigma the quest to prove Fermat's last theorem Albert Violant i Holz |
| title_fullStr | Fermat's enigma the quest to prove Fermat's last theorem Albert Violant i Holz |
| title_full_unstemmed | Fermat's enigma the quest to prove Fermat's last theorem Albert Violant i Holz |
| title_short | Fermat's enigma |
| title_sort | fermat s enigma the quest to prove fermat s last theorem |
| title_sub | the quest to prove Fermat's last theorem |
| topic | Fermatsche Vermutung (DE-588)4154012-8 gnd |
| topic_facet | Fermatsche Vermutung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025430914&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025430914&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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