10 Mathematical Equations That Changed the World
Mathematical equations that rocked our world. Mathematics (from Greek
μάθημα máthēma , “knowledge, study, learning”) is the study of topics such
as quantity( numbers ), structure , space and change . There is a range of
views among mathematicians and philosophers as to the exact scope and
definition of mathematics.
Mathematicians seek out patterns and use them to formulate new
conjectures . Mathematicians resolve the truth or falsity of conjectures by
mathematical proof . When mathematical structures are good models of
real phenomena, then mathematical reasoning can provide insight or
predictions about nature. Through the use of abstraction and logic,
mathematics developed from counting , calculation, measurement , and the
systematic study of the shapes and motionsof physical objects. Practical
mathematics has been a human activity for as far back as written records
exist. The research required to solve mathematical problems can take
years or even centuries of sustained inquiry.
Below are 10 of the greatest
mathematical equations that changed
our world forever:
Mathematics arises from many different kinds of problems. At first these
were found in commerce, land measurement , architecture and later
astronomy ; today, all sciences suggest problems studied by
mathematicians, and many problems arise within mathematics itself. For
example, the physicist Richard Feynman invented the path integral
formulation of quantum mechanics using a combination of mathematical
reasoning and physical insight, and today’s string theory , a still-developing
scientific theory which attempts to unify the four fundamental forces of
nature , continues to inspire new mathematics.
Some mathematics is relevant only in
the area that inspired it, and is applied
to solve further problems in that area.
But often mathematics inspired by one
area proves useful in many areas, and
joins the general stock of mathematical
concepts. A distinction is often made
between pure mathematics and applied
mathematics. However pure
mathematics topics often turn out to
have applications, e.g. number theory in
cryptography. This remarkable fact, that
even the “purest” mathematics often
turns out to have practical applications,
is what Eugene Wigner has called “ the
unreasonable effectiveness of
mathematics“. As in most areas of
study, the explosion of knowledge in the
scientific age has led to specialization:
there are now hundreds of specialized areas in mathematics and the latest
Mathematics Subject Classification runs to 46 pages. Several areas of
applied mathematics have merged with related traditions outside of
mathematics and become disciplines in their own right, including statistics ,
operations research , and computer science .
For those who are mathematically inclined, there is often a definite
aesthetic aspect to much of mathematics. Many mathematicians talk
about the elegance of mathematics, its intrinsic aesthetics and inner
beauty . Simplicity and generality are valued. There is beauty in a simple
and elegant proof , such as Euclid ‘s proof that there are infinitely many
prime numbers , and in an elegant numerical method that speeds
calculation, such as the fast Fourier transform. G.H. Hardy in A
Mathematician’s Apology expressed the belief that these aesthetic
considerations are, in themselves, sufficient to justify the study of pure
mathematics. He identified criteria such as significance, unexpectedness,
inevitability, and economy as factors that contribute to a mathematical
aesthetic. Mathematicians often strive to find proofs that are particularly
elegant, proofs from “The Book” of God according to Paul Erdős. The
popularity of recreational mathematics is another sign of the pleasure
many find in solving mathematical questions.