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Mathematics is
often referred to as the search for patterns.
In the film Pi, the mathematician Max Cohen begins
his day by chanting his mantra of what it means
to be a mathematician:
"11:15. Restate my assumptions.1. Mathematics
is the language of nature.2. Everything around
us can be represented and understood through numbers.3.
If you graph these numbers, patterns emerge. Therefore:
there are patterns everywhere in nature."
How good a pattern searcher are you?
Here are some sequences of numbers. Can you find
the next number in the sequence:
| 1,1,2,3,5,8,13… Give
up? |
| 1,3,6,10,15,21… Give
up? |
| 1,2,3,5,7,11,15,22,30…
Give up?
|
| 2, 12, 1112, 3112, 132112,
1113122112, 311311222112, 13211321322112,
1113122113121113222112, 31131122211311123113322112,
... Give up?
|
| 13, 17, 31, 37, 71, 73,
79, 97, 107, 113, ... Give
up? |
But here is what the famous eighteenth century
mathematician Euler had to say about the primes:
"There are some mysteries that the human
mind will never penetrate. To convince ourselves
we have only to cast a glance at tables of primes
and we should perceive that there reigns neither
order nor rule".
Despite Euler’s pessimism, mathematicians
have found ways to understand the primes. To find
out more visit the $1,000,000
problem section of the site.
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Are there formulas that
produce some of the primes? |
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