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The Great Mathematical Problems
About this book
There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincaré Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries.Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.
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Information
Table of contents
- Cover Page
- Title Page
- Copyright Page
- Dedication
- Contents
- Preface
- 1 Great problems
- 2 Prime territory Goldbach Conjecture
- 3 The puzzle of pi Squaring the Circle
- 4 Mapmaking mysteries Four Colour Theorem
- 5 Sphereful symmetry Kepler Conjecture
- 6 New solutions for old Mordell Conjecture
- 7 Inadequate margins Fermatâs Last Theorem
- 8 Orbital chaos Three-Body Problem
- 9 Patterns in primes Riemann Hypothesis
- 10 What shape is a sphere? Poincaré Conjecture
- 11 They canât all be easy P/NP Problem
- 12 Fluid thinking Navier-Stokes Equation
- 13 Quantum conundrum Mass Gap Hypothesis
- 14 Diophantine dreams Birch-Swinnerton-Dyer Conjecture
- 15 Complex cycles Hodge Conjecture
- 16 Where next?
- 17 Twelve for the future
- Glossary
- Further reading
- Notes
- Index