All mathematics is is a language that is well tuned, finely honed, to describe patterns; be it patterns in a star, which has five points that are regularly arranged, be it patterns in numbers like 2, 4, 6, 8, 10 that follow very regular progression.
I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.
What humans do with the language of mathematics is to describe patterns... To grow mathematically children must be exposed to a rich variety of patterns appropriate to their own lives through which they can see variety, regularity, and interconnections.
Epidemics follow patterns because diseases follow patterns. Viruses spread; they reproduce; they die.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
Every place is given its character by certain patterns of events that keep on happening there. These patterns of events are locked in with certain geometric patterns in the space. Indeed, each building and each town is ultimately made out of these patterns in the space, and out of nothing else; they are the atoms and molecules from which a building or a town is made.
Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
There are only patterns. Patterns on top of patterns, patterns that affect other patterns, patterns hidden by patterns, patterns within patterns.
There are only patterns, patterns on top of patterns, patterns that affect other patterns. Patterns hidden by patterns. Patterns within patterns. If you watch close, history does nothing but repeat itself. What we call chaos is just patterns we haven't recognized. What we call random is just patterns we can't decipher. what we can't understand we call nonsense. What we can't read we call gibberish. There is no free will. There are no variables.
One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.
Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive.
We must look towards societies that set a high value on nonaggression and noncompetitive ness, and therefore handle conflicts by nonviolent means. We can see how child rearing patterns produce nurturing adult behaviors.
[Pleasure is what suggested] which behaviors, emotions, social patterns and patterns of taste served us well during our evolutionary history. They were experienced as pleasures and encoded into our formative genetic codes . . . deep in the past, from about 100,000 years ago and beyond.
Walk a little slower, Dad
Cos I am only small.
I'm following in your footsteps,
And I don't want to fall.
Someday when I'm all grown up.
You're what I want to be;
Then I will have a little child,
Who'll want to follow me.
And I would want to lead just right,
And know that I was true;
So, walk a little slower, Dad,
For I must follow you.
A very very very Happy Birthday Dad
If you record things, you're going to find, patterns of things, and patterns are important, because you can then see the patterns form before it happens.