Mathematical Beauty

To make difficult things simple,
that’s the ultimative riddle.

To convert the unknown
to the known
in a way no one has ever thought before,
that’s the most beautiful lore.

Can you dare to think the impossible,
to solve the things
they told you
were unsolvable?

Originality;
or merely the combination of thoughts
that were thought before,
they become beautiful, even more…

Generality
and individuality;
Holism
and reductionism…

But, my friends,
what is (mathematical) beauty
even supposed
to be?

Starting with as few assumptions
as possible,
generating solutions
as easy as solvable;

Generalizing solutions
to solve similar issues;
shaping conclusions;
the implication continues…

That, my dear friends,
is why mathematics never ends;
Driven by beauty;
that’s the mathematician’s most joyful duty.

Misconception of Chaos

You may say
I’m random,
but, my dear,
that’s not the case!

I follow rules
like in your deterministic views.
But you have to know
I’m very sensitive to change.

I’m a complex system
of my own,
not as easy
as in your simplified view.

Can you see the structures
deep within?
Can you recognize the patterns
deep inside my heart?

I am chaos;
I am not randomness;
I am order
in a very twisted sense!

Platonic Thoughts in Non-Euclidean Space

How can my thoughts
be
so utterly simple,
yet so complex
at its own?

My thoughts form
platonic solids
in a non-euclidean space,
a space of curvature
and wonders.

The sphere,
my perfect little ball of paradoxes;
You are so simple,
yet so complex
like platonic solids themselves…

I’m living in hidden hemispheres;
how can I escape my personal horizons
if my thoughts are
perfect platonic solids
dancing on spheres?

Multi-dimensional Fractals

What we observe
is three-dimensional shadows
of four-dimensional actions.

We don’t know
about the complexity of reality,
yet it’s full of the purest simplicity…

(…that we can only grasp as such
if we are able to see
beyond the borders of our understanding.)

We’re living in a multi-dimensional world
of fractal-like patterns
and utterly intertwined connections
between relationless-seeming points.

We use lines to connect these dots,
zero-dimensional objects,
to form one-dimensional constructions.

Connecting these constructions
creates planes,
objects of two dimensions.

And if we add further dimensions
our dots become connected even more.

That’s all I wanted to say;
Because you have to know
that everything is connected to everything else
in this very intertwined and nested world.

Beyond the Borders of our Understanding

Can you see
beyond the complexity
of simplicity?

Beyond the borders
of our understanding
lie orders
far beyond our reasoning.

Sine and cosine – Sequences
that never end;
How can you even comprehend
their nature of helices?

Beyond the borders
of our limited view
lie uncountable wonders
that always grew.

How can you even grasp
what lies beyond our imagination?
How can you dare to fill the gap
of a very intertwined contradiction?

That, my dear,
means trying something new,
taking another view
and killing one’s own fear.