In the begining of 20th century there were a plenty of philosophies each one giving its own definition. Nowadays, there are foundations of mathematics giving reducionistic definitions of mathematics.
Math is what often absent me when I am going to solve some problems :-)
Mathematics is the beginning of thinking, whether it be logical, intuition, formal or predicative.
Abstract mind devlopment trough signs and symbols language.
In a practical manner,
we have agreed to manipulate numericals
in specific sequences and processes.
Dear Romer Castillo,
I do not think that "Mathematics is the beginning of thinking".
The beginning of thinkink is '(by my opinion) most simple - hungry, love, fear, hatred, etc. Just the simplest human situation.
Only then comes some math :-)
Romer and Josef
As I read it, Romer's proposition is that
Math is the (Beginning) BASIS for Rational Thinking.
However,
I do NOT find that verbal and social reasoning is well described in Math terms.
Mathematics is just an international language ;-)
We use this language to setup models for our observations !
We are all very lonely in this wonderful world !
Each of us will never be able to observe our surrounding world the same way !
To Erik,
I would suggest :
Math is logical language by which we describe our experiments,
and by which we can predict alternative results of our experiments.
Without common Math Descriptions,
we would be in the world of "Babel",
unable to talk with each other and unable to predict the future.
To Josef,
Indeed, even Barrie has spoken about "putting on the robes of the electron" during mind experiments, somewhat devoid of math.
... and ...
Einstein did "mind experiments"
and described he process like an "intuitive approach",
not calculating forward but rather "imagining" forward.
In my own experiments, I most frequently model in my mind,
then model in Spice, which helps me to write Math descriptors,
which I can manipulate to predict alternative results.
I do enjoy reading other engineers thinking about thinking.
Just My Own Humble Opinion
Math is an excellent tool for hiding the human mediocrity:) In technical area, math is frequently used as Latin in medicine:)
https://en.wikibooks.org/wiki/Circuit_Idea/Formulas
Mathematics is another human language that is symbolic and connected with nature.
Mathematics can have several definitions, according to our prefered foundation of mathematics. It can be the logical theory that deals with sets or the algebraic theory that deals with categories. There is a plenty of alternative foundations, I will refer a theory mentioned before: type theory.
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