This document discusses the history and importance of mathematics. It notes that mathematics has become essential in fields like robotics, space research, sports, biology, and information technology. It then discusses some key developments in mathematics throughout history, including how it became integrated into modern science in the 18th century. Several important mathematician's contributions to early computers are also outlined, such as Pascal's calculating machine and Babbage's Analytical Engine. The document ends by discussing ongoing research into modeling the human brain mathematically.

1. By – Shreet Mishra (XI)
Roll no. – 47

2. In 21st century mathematics is used
In robotics
In space research
In sports
In Biological calculation
In field of information technology etc.

3. Development of mathematics as a
part of science
 In 18th century mathematics was already
become a part of modern science.
Mathematics begins to develop very fast
because of it’s introduction to schools.
 Therefore everyone have a chance to learn
the basic fundamentals of mathematics

4. Development of mathematics
as a part of science
 Thanks to that, large number of new
mathematicians appear on stage
 There are many new ideas, solutions to old
mathematical problems,researches which
lead to creating new fields of mathematics.
 Old fields of mathematics are also
expanding.

5. Contribution of mathematicians
in field of computer technology -
In 1642 AD, Blaise Pascal , a French
mathematician invented a calculating machine
named as Adding Machine.
This machine was capable of doing Addition and
Subtraction. This device is known as the First
Calculator of the world.
In 1671 AD, Gotfried Leibnitz, a German
Mathematician improved the Adding machine
and made a new machine capable of performing
multiplication and division also.

6. Contribution of mathematicians
in field of computer technology -
 Charles Babbage was a British mathematician.
In 1822, he designed a machine called
Difference Engine. It aimed at calculating
mathematical tables.
 In 1833, Charles Babbage designed a machine
called Analytical Engine. It had almost all the
parts of a modern computer.
 Hollerith, a Mathematician, invented a fast
counting machine named Tabulating
Machine in 1880.

7. LEONHARD EULER
Euler worked in almost mathematics, graph theory and
number theory, as well as , lunar theory, optics and other
areas of physics ad thus developed a famous formula of
mathematics which gave a new turn to modern science.

8. Descartes’ vision
 On November 10, 1619
when Descartes was 23, he
had a vision in which it was
“revealed” to him that the
universe is mathematical
and logical.
 Since Descartes, science
was gripped with the idea
of a universe that can be
described mathematically.

9. Mathematics as a language of
physics
 Mathematics is a
language which seems
to be well suited for
describing the physical
universe.
 Defining characteristic
is precision.
 It shares some
similarities with music.

10. Google and Linear Algebra
 Google set itself apart
from other search
engines by its ability to
quantify
“relevance”with the
help of mathematics.

11. Mathematics in the Life Sciences
 Mathematical neuroscience tries to model neuronal
activity. Main problem of neuroscience is how does the
nervous system process information? Main problem of
Population genetics: how genetic mutations and
selection are propagated in a population. Main
problem of Epidemiology: dynamics of diseases?
Mathematics is playing an important role in solution
of these problems.

12. The Language of Life
 Biological calculation
seems to be more
“horizontal”.
 This “horizontal” nature
of biological calculation
eliminates the problem of
compounding errors.
 The language of the
nervous system seems to
have less “arithmetical
depth” than we are used to
in mathematics.

13. The Nature of Mathematical Calculation
 In numerical calculations that involve approximations
or “errors”, repeated calculations can compound the
“errors” to the point of rendering the calculation
meaningless.
 “Arithmetical” or “logical” depth refers to the number
of serial arithmetic operations that have to be
performed in a calculation.

14. The Language of Life
 The nervous system seems
to use a radically different
method of notation which
is stochastic: not the
positional system.
 Meaning is conveyed by
statistical properties of the
message.
 Meaning is also conveyed
by statistical properties of
different messages
transmitted
simultaneously.

15. Mathematics and the human brain
 DARPA recently asked for proposals to build a
mathematical model of the human brain.
 That effort will radically alter the way we construct
digital computers.
 It may also radically alter our views of intelligence and
consciousness and our humanity.

16. the
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