Posts Tagged ‘Personal Way’

About Understanding Mathematics

Thursday, July 1st, 2010

When I was a student I made some money by helping young people to understand Mathematics. I Listened to the way they tried to Solve the Puzzles their Teachers gave them and tried to find out their Personal Way of Reasoning. 

When I found their reasoning problem I gave them a new Way to Think.

This approach was very effective. Sometimes I just needed one hour and the highly frustrated pupil transformed into a Lover of Mathematics. They saw that Mathematics is the Art of Beauty and Harmony.

The main problem most of these pupils had was the Why-Question. They wanted to know what was “behind” mathematics. In Mathematics there is no Why. Mathematics is “Just the Way it is“. It is a System of Rules you have to Apply.

When you are a Highly Creative Person Mathematics is a Highly Frustrating Science.

Highly Creative Persons are Highly Associative.  They See Links between Every-Thing. They Build Bridges between Islands almost nobody knows they exist.

Mathematics is about creating Abstractions.

Highly Creative Persons Think with their Imagination. They Jump from Images to Image.

The Images of the Mathematicians are Abstract Symbols and most of the time the Mathematical Symbols are chosen without any relationship to the Situation they want to represent.

If Creative, Associative, Persons are not able to See what Mathematics is trying to represent they are Lost in Space.

When we go back in History the Imagination (and not Thinking/Reasoning) was the most important “Thinking-Tool“. The meaning of the word “Think” originally meant “to See“. 

The Art of Reasoning was based on detecting Correspondences.

The Ancient Scientists observed Nature and found out that certain situations “looked alike“. They used and linked Visual Metaphors to explain what they observed. 

Abstract Concepts were always represented by something others could See.

The interesting point is that New Scientists are founding out what the Old Scientists already knew. Our Basic Reasoning System is based on Images.

When we move to the Abstract Domain we use Images (called Prototypes) to Reason. Abstract terms like Furniture are always represented by a prototype we have Seen.

This explains why most of the People are not able to See Mathematics and why most of the People have a big problem Understanding Ancient Knowledge.   

They try to Map the Ancient Visual Landscape of Knowledge to the Modern Space of  Abstract Terms they don’t understand.

They are looking for something that is already there.

They are asking the Why-Question while the  Ancient Knowledge is Visible All Around Us.


About the Foundation of Mathematics

About Old Fashioned Thinking

About Topology, the Art of Seeing

About the Art of Creation