The Number Mysteries: A Mathematical Odyssey through Everyday Life

Marcus Du Sautoy
CIA 3 (Part 2)
Name- Khushboo Kothari
Registration no.- 2140880
Submitted to- Fr. Joseph Varghese

About the Author

Summary
Human civilization is directly proportional to growing complexity and sweeping structures of
the environment. Communication has led to the need of asking questions which in turn has
resulted in generating better solutions for the society as a whole. There are many people in
the world who think in a certain and curious manner that why might catching an icosahedron
kill you, what is the shape of the universe, what are the odds that your telephone number is
prime, how can I beat the lottery system and the list goes on. The subject of mathematics is
the best tool that has been developed by human beings to try to look and predict the future.
According to Marcus Du Sautoy, Mathematics is the beautiful science of pattern search
which enables us to read into the future. Mathematics has the immense power to make
unequivocal assumptions.

Marcus Du Sautoy discusses various popular number series such as the Fibonacci Numbers,
The Circle of Division and Prime numbers.

 Fibonacci Numbers are nature’s favourite numbers as they appear in biological settings
such as fruit sprouts of pineapple, banana, trunks of trees, pinecone bracts etc. In
mathematical terms, each number is the sum of two preceding numbers.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

 The Circle of Division is a method which determines the number of regions a circle can
be divided into for a given number of cuts.
 Prime numbers are the building blocks of mathematics. They are referred to and given
importance as hydrogen and oxygen in mathematics. The sequence of prime numbers is
very complex as they don’t follow any formula or pattern. Showing that there is no
pattern is much more difficult than establishing a definite pattern. Hence, prime numbers
are a true mystery to the mathematicians till this date.

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 2,3,5,7,11,13,17,19,23

The author takes up Prime Numbers as ‘Mystery 1’. He elucidates the history of prime
numbers and how different cultures from the Chinese to the Greeks have tried to survey the
relationship of primes also how musicians and poets played an important role in unveiling
primes using their syncopated rhythms.

Million-dollar question: Are the dice fair or not? Are the dice distributing prime numbers
fairly through the universe of numbers or are there regions where they are biased?

The 2nd mystery takes us through ‘The Story of Elusive Shape’. This chapter talks about the
diverse shapes available in our environment from snowflakes to the radial symmetry of
diamonds. The author emphasises on the uncanny importance of the sphere. He takes up the
example of bubbles to show that everything starting as a different shape collapses into a
sphere. He described the sphere as nature’s laziest and the strongest shape by citing the
examples of helmets, eggs, raindrops, viruses, football etc. It was an Ancient Greek
mathematician called Plato who first started to investigate what sort of shapes you can make
for footballs and we’ve got some of them here. Another Greek mathematician, Archimedes,
proved that you can make spheres using various symmetrical shapes. A total of thirteen
footballs can be made using this procedure in addition to Plato’s. The author mentioned the
great American artist, Jackson Pollock’s work as fractal geometry. Pollock used wrist flicking
technique to paint his beautiful art pieces, he was actually doing something unique while he
flicked to form a fractal shape unknowingly.

Million-dollar question: What are the possible shapes of the universe?

The 3rd mystery reveals ‘The Secret of the Winning Streak’. Playing games is one of the best
ways to revive the brain areas which are responsible for memory function and problem-
solving skills. Games inculcate various skills such as planning and plotting, risk assessment
and critical thinking. It also teaches us about the nature of probability and unpredictability,
and allows us to explore real life problems in a better way. The games have come a long way
from the ancient civilization to the present day, from ancient mancala to monopoly, from
mah-jong to rummy and from pachisi to ludo. Games are unalterably won by the person who
gets a hold of mathematical and analytical approach. The author explains that the path to win
Rock, Paper and Scissors is spotting patterns. But sometimes the rhythm is just random,
hence, along with mathematics, a large amount of psychology goes in to make further
predictions. The strategy of randomizing things is the only way which gives you an even
chance of winning. In the case of the lottery system, one thing that is common to all is their
desire to spread out numbers evenly. This habitual spacing of numbers isn’t essentially a
characteristic of randomness; rather clumped up numbers. The powerful aspect of
mathematics is that, by looking at things from the right angle, we can explore other
perspectives which makes the solution transparently obvious.

Million-dollar question: Is trial and error the only method to find the combination of boxes or
perhaps there is some efficient way to crack this problem?

The 4th mystery reveals ‘The Case of the Uncrackable Code’. Communication has developed
avenues for codes and secrecy, but during wartime code became a necessity for soldiers and
higher authorities. History proves that since ancient times, codes have been used by spies and

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messengers to carry out plans and information in the enemy's territory. The code makers and
code breakers are always engaged in a tense battle. One of the most sophisticated encoding
machines invented was the ‘Enigma’ which was developed by the Germans during World
War II to protect diplomatic, military and commercial communications. Another coding
language which was popularly used was the ‘Substitution Cipher’. It was used by renowned
Julius Caesar and graceful Mary Queen of Scots. In substitution cipher any character of plain
text is substituted with another text or symbol. The sender and receiver must have knowledge
of the translations, so it becomes convenient to decode it. But to others, it looks completely
gibberish. Well, unfortunately, the Substitution Cipher has a really big flaw: its security
crumbles in the face of a statistical technique called Frequency Analysis. In the ninth century,
an Arab mathematician, Al-Kindi, wrote down the first procedure to try and crack these
codes. It worked on a simple principle, the fact that some letters occur more often than others.

Million-dollar question: To understand the mathematics and crack the code behind the elliptic
curves?

The 5th mystery is about ‘The Quest to Predict the Future’. To be able to look into future has
always been a source of interest and strangeness to us. Loads of research and conclusions on
time travelling have fascinated students from across the globe. But it is not possible, not yet
at least. Mathematics the ultimate fortune teller, it helps us to predict when is it going to rain,
the flight of the ball and whether population will grow or not. Galileo Galilei, an Italian
polymath, studied the concepts of free fall, velocity and gravity. He conducted various
experiments from the top of Leaning Tower of Pisa and realised that the weight of the objects
didn’t matter but the air resistance. Another important theory, called Chaos theory, was
discovered by a French mathematician, Henri Poincare, over a hundred years ago. Chaos
theory states that complex structures may follow laws but their overall future nature remains
unpredictable. Hence, future cannot be predicted on the basis of past events. Lastly,
mathematics is the only tool which allows to describe and examine nature precisely,
henceforth, helps to predict future.
Million-dollar question: Identify and solve the equations behind the concept of turbulence?