Is mathematics discovery
or invention ?
From the problems of everyday life to the mystery
of existence
Part One
By Marco Dal Prà – Venice - Italy
May 2013
1
Foreword
This document is intended as a starting point for
serious reflection on a problem: the existence of
physics.
The aim is to open a debate, because the topic
is much more interesting and profound than you
might think.
Suggestions & feedback:
[email protected]
2
Preface / 1
Was mathematics discovered or invented of humans ?
Apparently it seems a very banal question, but on the
contrary the answer has surprising consequences.
In fact, physics is based on mathematics, so if you find
answers to existential problems of mathematics, you
can find answers to questions about the existence of the
humans and the universe.
3
Preface / 2
Similar questions have been asked by some scientists of
the early '900, in particular by the discoverers of
quantum physics, as Einstein, Schroedinger, Bohr.
On the contrary, the philosophers do not seem to have
ever asked this question, and even contemporary
scientists.
Perhaps that some men consider it "uncomfortable"?
Now, we start our reflection trying to analyze the
problem to 360 degrees.
4
Problems of definition
Before you begin, it is necessary to make a
clarification on terminology.
That is, it is essential to clarify what it means
discovery and what it means invention,
otherwise you risk getting lost in a thousand
opinions without concluding anything.
5
From Dictinoary “Merriam-Webster”
To INVENT - to produce as something useful
for the first time through the use of the
imagination or of ingenious thinking and
experiment.
INVENTION – a product of the imagination.
6
From Dictinoary “Merriam-Webster”
To Discover – to obtain sight or
knowledge of for the first time
Discovery – disclosure, display,
exploartion.
From Italian vocabulary :
To discover : Identify, find, acquire human experience
facts, concepts, places previously unknown.
Discovery : Locating a subject of considerable interest
(scientific, social, economic, cultural).
7
A bit of history
To begin our analysis, it is
necessary to analyze briefly
the history of mankind and
mathematics.
Let us briefly.
8
Where is the origin of mathematics ?
Mathematics is a tool
developed in ancient
times to solve everyday
problems as trade,
commerce, construction,
measurements and many
other human activities.
9
Where is the origin of mathematics ?
Then from addition and
subtraction has
passed, to
multiplication and
divisions.
And then squaring,
square roots, etc..
etc...
Pythagoras...
10
Mathematics follow the evolution
As with all scientific and technical
disciplines, also mathematics was
developed with the help of so
many men.
Archimedes, Euclid, Fourier,
Lagrange, Laplace, Euler, Cantor,
Hilbert and many others, each is
contributing to the advancement
of the discipline.
11
Meanwhile, someone look over ...
Eratosthenes, librarian of
Alexandria in Egypt, is one of the
first to use mathematics and
geometry for "scientific“ purpose.
In about 200 BC, he was able to
calculate the circumference of the
earth using the shadows of the sun
inside the wells of two Egyptian
cities.
(with an error very small: about
1,5% !!!)
12
Then came Newton
Isaac Newton, to solve the problems
of the motion of objects, realized
how essential it was mathematics to
solve them.
In practice, he could not approach the problem in a
scientific manner without first was endowed of the
appropriate mathematicians "tools".
And since these tools for this problem did not exist, He
had to "invent” them.
(eg. infinitesimal calculus)
13
Physics and mathematics
At this point, without further historical
quotations, it is quite clear that the
physics to exist, needs mathematics !
Instead, the opposite is not true :
mathematics does not need the physics to
exist.
In fact ... the mathematics doesn’t need
no other discipline to exist !
14
Physics and mathematics
The dependence of physics from
mathematics is not essential to solve our
initial question.
But will subsequently be used to analyze
the consequences to which port the
answer.
15
What do they say mathematicians ?
We now move in the early 1900s.
In this age we find some mathematicians
who express opinions about mathematics
and its role, its foundations.
16
David Hilbert
German mathematician (1862-1943),
father of the Formalist school.
About mathematics, Hilbert said “One of
the supreme achievements of purely
intellectual human activity”.
In other words, according to this
discipline, mathematics is an activity of
free thought.
17
Godfrey Harold Hardy
English mathematician (1862-1943),
author of the fundamental contributions
that we will see later.
In his book A Mathematician's Apology is
written:
"I am interested in mathematics only as a
creative art“
“A mathematician, like a painter or a poet, is
a maker of patterns. If his patterns are more
permanent than theirs, it is because they are
made with ideas.”
18
Alan Touring
English Mathematical and logical (19121954), father of computer science.
He about the mathematics said :
“Mathematical reasoning may be
regarded rather schematically as the
exercise of a combination of two
facilities, which we may
call intuition and ingenuity ”
19
The race ends....
At this point, are the mathematicians
to tells us that mathematics is an
invention.
Its formulas in fact stems from the
human’s mind, by his free thoughts.
20
A foregone conclusion !
In fact, the mathematical formulas were
not discovered such example was with
vaccines, DNA, chemical elements,
electricity.
They are the result of reflections of the
human intellect as were the inventions:
the phone, the press, the light bulb, the
steam engine, etc..
21
But what happens ?
Everything seems to be
resolved, but only apparently.
The answer generates a new
question, much more
complicated than the first.
If mathematics is a logical exercise of the
human imagination,
how can it explain the phenomena of the
universe?
22
This creates a mathematical short-circuit
If mathematics is born in the human's mind, how can we
explain the existence of the physics ?
23
Part One - End
Continues in the second part:
“Consequences of the invention of
mathematics”
Marco Dal Prà
[email protected]
24