50 Mathematical Ideas You Really Need to Know

the theory of curves and a conjecture put forward by two Japanese mathematicians Yutaka Taniyama and Goro Shimura. In 1993 Andre ...

50 The Riemann hypothesis The Riemann hypothesis represents one of the stiffest challenges in pure mathematics. The Poincaré con ...

is called the harmonic series. The harmonic label originates with the Pythagoreans who believed that a musical string divided by ...

In this last series the power of the terms is 2. In the harmonic series the power of the denominators is silently equal to 1 and ...

The Riemann zeta function has an infinity of zeros, that is, an infinity of values of s for which ξ(s) = 0. In a paper presented ...

7, 11 and so on, the numbers only divisible by 1 and themselves. Using primes, we can form the expression and this turns out to ...

Glossary Algebra Dealing with letters instead of numbers so as to extend arithmetic, algebra is now a general method applicable ...

for example, the derivative represents the velocity. The derivative of the expression for velocity represents acceleration. Diop ...

the square root of 2). Iteration Starting off with a value a and repeating an operation is called iteration. For example, starti ...

Square number The result of multiplying a whole number by itself. The number 9 is a square number because 9 = 3 × 3. The square ...

Index Bold page numbers indicate a glossary entry A Abel, Niels 58 , 154 adding fractions 13 –14 imaginary numbers 33 –4 matrice ...

base 10 8 , 10 , 11 , 204 base 60 8 , 204 Bayes’s theory 128 –31 Benford, Frank 136 , 138 Bernoulli, Jacob 24 , 89 binary system ...

continuum hypothesis 75 corollary 204 correlation 144 –6 counterexample 69 , 204 counting 4 , 28 –9, 30 , 119 , 164 –7 cubed num ...

E e 24 –7 Egyptians 8 , 15 , 165 Einstein, Albert 97 , 111 , 113 , 177 , 192 , 194 –5 ellipse 88 , 89 , 115 empty set 7 , 204 en ...

converting to decimals 14 –15 counting 30 Riemann hypothesis 200 –3 square roots 18 –19 Franklin, Benjamin 170 fuzzy logic 67 G ...

hexadecimal system 204 hieroglyphs 15 highest common factor 61 Hilbert, David 75 , 99 , 203 Hindu-Arabic numbers 4 , 8 hyperbola ...

limaçon 90 linear equations 56 –7 linear programming 182 –3 logarithm 24 logarithmic spiral 89 logic 64 –7, 68 Lo Shu square 168 ...

number systems 8 –11 numerator 12 , 205 numerology 39 , 42 O octahedron 93 one-to-one correspondence 28, 30 , 205 optimum soluti ...

proof 68 –71, 85 , 123 Pythagoras 16 , 40 , 41 , 89 , 200 theorem 18 , 84 –5, 205 Q quadratic equations 57 –8 quaternions 58 –9, ...

statistics connecting data 144 –7 normal curve 140 –3 probability 128 , 136 –8 Steiner Triple System (STS) 115 Stokes, George Ga ...