The theoretical
aspects of the computation were developed by mathematicians as J. von
Neumann and A. Turing.
The development of a motor, of an electric circuit or of a
computer chip need an enormous amount of mathematical calculations and
of Mathematical Theories, as well as most of the electric
apparels.
The industrial era was only possible due
to the
Physics development and of the Mathematics due by Newton, Lagrange,
Fourier, Cauchy, Gauss and other cientists.
The fractal groups appear in the
mathematicians
Hausdorff's and Besikovich's works, and later they were popularized by
B. Mandelbrot. The illustrations that appear in the Microsoft Encarta
Enciclopedy are made by compactifications of images
obtained by adaptation of mathematical ideas of fractal auto-similarity
due by the mathematician M. Barnsley. The physical explanation of the
phenomenon of the water to become ice at zero degrees and of the
magnetization of objects to low temperatures, demands aplicattions of
the Mathematical Theory of Probability. This Theory, in the beginning,
was just devoted to calculate chances of to win or to lose in the
roulette games. This before penetrating in the Statistical and Quantum
Mechanics as irreplaceable tool. It suits to remind that the
mathematician W. Gibbs was one of the cientists that established the
beginnings of the Statistical Mechanics.
The understanding of the Theory of the
Relativity of
Einstein and of the "black holes" of S. Hawking owes to the development
of the Non Euclidian Geometries (The Axiom of the Parallels of Euclides
- century IV B.C.) due by Gauss, Riemmann and Poincaré. The
subject, if
it was or not possible to deduce the Axiom of the Parallels ones
starting from other, extended for more than 20 centuries to be denied
by Lobachewski in the century XIX. Then appear the Riemmann's and
Hyperbolic Geometries. The phenomenon that the light had constant speed
independently of the observer's referencial that measured it, pointed
for the direction that the space-time should have some curvature.
Einstein, that learned the Riemmann's Geometry, found a mathematical
model for the phenomena in subject, through a convenient Non Euclidian
Geometry.
Several Mathematical Theories resulted,
later, in
tools for the understanding of models of the natural science with the
ones which at first they didn't seem to have any
relationship.
The complex numbers, introduced to give
sense to the
existence of solutions of polynomial equations, they led to the study
of the diferencial calculus with complex numbers. This Theory resulted
to be, later, extremely useful to explain the drainage of
incomprehensible fluids. S. Hawking theory to explain the
"black
holes" needs results involving complex numbers and Quantum Mechanics
(therefore, it requests results of the Theory of the Probability). The
formalization of the Quantum Mechanics was only possible road the
fundamentation given by the mathematician J. von Neumann, using the
theory of spaces of functions largely developed by the mathematician D.
Hilbert, that would never imagine that your mathematical theory of the
beggining of the century XX would apply the such subject.
The mathematical Theory of the wavelets,
developed
mainly about 1970, allowed considerable progresses in computerized
tomography.
The text-book of Biology, Economy,
Agronomy, etc,
used nowadays in the Universities, contain very more mathematical and
statistical formulas that used them 20 years ago.
The tendency of all the Sciences is more
and more to
use and to develop Mathematical Models to describe natural phenomena in
an appropriate way.
The intense rhythm of the technological
development
of the current times produces the following phenomenon: it is every
times shorter the current time between the development of a
mathematical theory and your practical use.
In the social sciences, the Statistics
is, nowadays,
extremely useful tool for any professional of the area. Even to invest
in the financials market we need mathematical and
probabilistic
theories that make possible to maximize the gained profit
exist.
In summary, we can affirm that the
domain of the use
of the Mathematics, nowadays, is a necessary condition for the success
in an enormous amount of professions. The projections for the close
future indicate that this tendency should intensify if. To the United
States it projected that already at this beginning of the century XXI
the white-collars (workers that need some study of undergraduate level)
they will be in larger number than the blue-collars (manual workers).
The automation and the computer will also produce the occurrence of the
same phenomenon in the rest of the world in a reasonably close future.
In most of the undergraduate level
programs in the
United States, the student should take some courses of Mathematics. In
a modern society in that the "efficiency" is one of the larger
objectives, to maximize benefits and to minimize losses is
essential. In these cases, invariably, some mathematical
model
should enter in scene.
Now, after that we believed to have
become aware the
visitor of the importance of the Mathematics in the current world, we
will talk a little about the professionals that act in this
area.
Some times it is ignored by the common
citizen that
the Mathematics is an alive Science and that an intense research work
is developed nowadays in this area.
"In the last thirty years the
amount of written pages of works published in Mathematics
is larger than the number of pages written on Mathematics from old
Greece up to thirty years ago".
A. Odlyzko, of the ATTN & T Bell Laboratories
A lot of reasons compete for
the ignorance of
the research in Mathematics.
The first of them is that for your own
nature, a
mathematical result uses other previous results and so on so that it is
difficult to describe for a lay one the importance of the current
results obtained by the mathematicians. Thus, the common citizen
doesn't have knowledge, in general, of the current research in
Mathematics. It also suits to remind that the Mathematics that is
learned today at the high school and at the undergraduate levels, that
is applied in an enormous amount of practical situations, was
considered mathematical research at some time ago.
The second reason, perhaps it is the
fact that the
Nobel Prize doesn't exist in Mathematics. A. Nobel (1833-1896) a
Swedish cientist that created a foundation was that annually presses
cientists of several areas of the knowledge as Physics, Chemistry,
Medicine, Literature, etc. As a Nobel Prize doesn't exist in
Mathematics, many think mistakenly that doesn't exist current
researches in this area. The prize corresponding to the Nobel Prize, in
the area of the Mathematics is the Fields Medal that is granted by
International Mathematical Union every 4 years to 4 mathematicians
distinguished that are less than 40 years old. Recently, the french
mathematician J.C. Yoccoz of the University of Paris-Sud
received
this prize. He passed great part of your life in Brazil working and
developing mathematical researches with Brazilian researchers.
Intense research work is develop today
in the
central areas of the Mathematics.
Fractals, the Chaotic Systems, Cellular
Automata,
the Theory of the Catastrophes, the Geometry of the Minimum Varieties,
the Applications of Algebraic Topology to problems of Quantum
Mechanics, the Theory of the wavelets, the Mathematical Applications to
the Theory of the Computation are some of the topics that more became
popular.
Other equally important and deep themes
are being
developed by mathematicians, although it is difficult to explain your
importance for lay people.
Nothing impedes that these topics pass
suddenly to
be mentioned in papers of larger popularization, when somebody finds a
real model in that such theories can be applied.
Recently an English mathematician solved
the
celebrated last Fermat's conjecture.
The Riemmann's conjecture concerning the
zeros of a
certain function is the more famous of the still not resolved
conjectures of the current Mathematics. A series of other important
subjects in Geometry, Analysis, Algebra and in Quantum
Mechanics
would be mathematically resolved if such conjecture is true.
Ricardo Mañé
(1948-1995), a
mathematician working in
IMPA (Rio de Janeiro), solved in 1987 the conjectures of the structural
stability that was considered one of the most important results of the
Theory of the Chaotic Systems.
Celso Costa in your doctoral thesis in
IMPA (Rio de
Janeiro), exhibited in 1982 an example of a minimum surface with
certain special properties. This example also answers negatively one
famous conjecture. This surface, that is known in the whole world as
the surface of Costa, was inspired, according to the author, for a hat
of one samba school personate of Rio de Janeiro.
The universe of the mathematical
problems which we
don't have the smallest idea of how to solve them is inexhaustible. At
the same time, at all times, the natural science, collaborating with
the Mathematics, suggests a series of new mathematical problems whose
solution is important and still ignored.
The mathematician develops the
Mathematical Theories
by following his intuition of what is fundamental and deep in
Mathematics. The Mathematics is fundamentally "resolution of
mathematical" problems.
The renowned botanical Sir Arcy Thompson
said that
everything that is beautiful in Mathematics, earlier or later will be
of importance in some natural phenomenon.
When a mathematician finds the solution
for some
mathematical problem and this result seems him interesting, he wants
your friends to appreciate it. The fruit of this work is published then
in an article of Mathematics of international circulation, the so
called papers. Later, some of these results (in general that have more
importance of the mathematical point of view) become used by cientists
of other more applied areas.
The Mathematics, in a certain sense, is
an art. The
analysis and the ingeniousness in the obtaining of the solution of a
mathematical problem possess an intrinsic aesthetic value. A series of
results they insert "magicianly" in a final result that, or it
surprises, or it enchants, or it places us a flea behind the ear: will
it be really truth?
The mathematical proof is what finally
will decide
if the result is right or wrong. The proof in Mathematics plays the
same part that the experience carries out in the Physics. It is the
referencial of the truthfulness or not of the mathematical result.
Many times, when one need to use a certain
technique, the
real situation is not so equal to that was learned in the university.
It is necessary to do small fittings in the model that was taught. At
this time, to understand the mathematical result (and sometimes until
your proof) it can be of great usefulness.
Exactly due to your mathematical proof,
a
mathematical result is eternal. It is today valid as well as it will be
from here to thousands of years; in other words, assumed certain
hypotheses, it proceeds of the mathematical proof that such and such
properties are valid.
Finally, let us say some about the
research in
Algebra.
The last quarter of the century XX went
of
unprecedented accomplishments to the Algebra. All heard to speak of the
proof of the Last Theorem of Fermat. Although not so
commented,
not less important it was the obtaining of the classification of the
simple finite groups. However, which few know, it is that the own
existence of World Wide Web is only possible due to efficient codes
brokers of errors and to simple and trusted methods of cryptography,
all based on algebraic systems. Other implications of the Algebra would
be: digital media (CD, DVD, etc.), cellular telephony, theory of
information (transmission and correction of digital data), etc. the
amount of subjects that we don't know how to answer is horribly larger
than the number of established results. Therefore, we participated in
the
