Artificial Intelligence and Mathematics

ARTIFICIAL INTELLIGENCE
• Computers or intelligence system
with the ability to mimic or duplicate
the functions of the human brain.
OR

• Artificial intelligence is technology
and a branch of computer science that
studies and develops intelligent
machines and software

• John McCarthy was an American
computer scientist and cognitive
scientist.
• He coined the term "artificial
intelligence" (AI), developed the LISP
PROGRAMMING language family.

• Significantly influenced the design of
the ALGOL PROGRAMMING LANGUAGE,
popularized timesharing, and was very
influential in the early development of
AI.

• Alan Turing was a British scientist
known for his Computer , Algorithm
and the very famous TURING TEST.
• He had worked for the British army
during World War 2 in the code
ciphering section and had
successfully cracked many German
codes.

• Turing test
• The Turing test is a test of a machine's
ability to exhibit intelligent
behaviour equivalent to, or
indistinguishable from, that of a
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• A human judge engages in natural
language conversations with a human and
a machine designed to generate
performance indistinguishable from that
of a human being.
• All participants are separated from
one another. If the judge cannot reliably
tell the machine from the human, the
machine is said to have passed the test.
• The test does not check the ability to
give the correct answer to questions; it
checks how closely the answer
resembles typical human answers.
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• The conversation is limited to a
text-only channel such as a
computer keyboard and screen so
that the result is not dependent on
the machine's ability to render
words into audio.

• “Can machines think?”
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• 1943 - McCulloch and Pits -- modeling neurons
using on/off devices.
1950's - Claude Shannon and Alan Turing try to
write chess playing programs.
1956 - John McCarthy thinks of the name
"Artificial Intelligence".
1960's - Logic Theorist, GPS, microworlds, and
neural networks.
1971 - NP-Completeness theory (Cook and Karp)
casts doubt on general applicability of AI
methods.
1970's - Knowledge based systems and expert
systems.
1980's - AI techniques in widespread use, neural
networks rediscovered.
1990's - Deep Blue wins against world chess
champion. Image and Speech recognition becomes
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practical.

Perceptive system
A system that approximates the way
a human sees, hears, and feels
objects
Vision system
Capture, store, and manipulate
visual images and pictures
Robotics
Mechanical and computer devices
that perform tedious tasks with high
precision
Expert system
Stores knowledge and makes
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inferences

Learning system
Computer changes how it functions
or reacts to situations based on
feedback
Natural language processing
Computers understand and react to
statements and commands made in a
“natural” language, such as English
Neural network
Computer system that can act like
or simulate the functioning of the
human brain
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• Mathematics and articial
intelligence (AI) have had a
symbiotic relationship.
• It began when Allen Turing
dreamed of taking Hilbert's
tenth problem into the
realm of computation that
would blur the distinction
between human and machine
reasoning.

• Find an algorithm to determine
whether a given
polynomial Diophantine
equation{a Diophantine equation is

a polynomial equation that allows two or
more variables to take integer values only}

with integer coefficients has an
integer solution.
• Resolved. Result:
impossible, Matiyasevich's
theorem implies that there is no
such algorithm.
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• Boolean algebra {Propositional Logic} is the
subarea of algebra in which the values of

the variables are the truth values true and false,
usually denoted 1 and 0 respectively.

•

Instead of elementary algebra where the

values of the variables are numbers, and the

main operations are addition and multiplication,
the main operations of Boolean algebra are
the conjunction and, denoted ∧,

the disjunction or, denoted ∨, and

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•

Graph theory is the study of graphs, which are

mathematical structures used to model pairwise

relations between objects.
• Graphs are used to represent networks of
communication, data organization, computational
devices, the flow of computation.

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• Eigenvector is an advanced level of 3D
geometry and it is used in artificial intelligence
to detect motion and deduce expression .
• A square matrix is multiplied with the vector

or the axis and this results in a change and hence
can detect or simulate the same
• The eigenvalues are used to determine the

natural frequencies (or eigenfrequencies) of
vibration, and the eigenvectors determine the
shapes of these vibrational modes and hence can

determine motion

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 Statistics is the study of the collection,
organization, analysis, interpretation and
presentation of data.
 Created complex models such as nonlinear

models as well as the creation of new types,
such as generalized linear
models and multilevel models and uses the

most significant answer from the results to take
a decision .
 A large number of both general and special

purpose statistical software are now available.

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 OPTIMIZATION THEORY is the selection of the best
answer and can also be called a mix of
probability and statistics.

 An optimization problem consists of maximizing
or minimizing a real function by systematically
choosing input values from within an allowed set
and computing the value of the function.
 Optimization includes finding "best available"
values of some objective function given a
defined domain, including a variety of different
types of objective functions.
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ALGORITHMIC THEORY is a subfield
of information theory and computer
science that concerns itself with the
relationship between computation
and information.

Algorithmic information theory
principally studies complexity measures

on strings (or other data structures).

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LINEAR SYSTEM OF EQUATION is a collection of
linear equations involving the same set of variables.
 It helps in the location of the point {solution} and
can estimate the location graphically.
 it helps in computer
simulation.
 It can also determine the
Solution region.

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CONVEX OPTIMIZATION THEORY is used in the
adaptation of a robot. It takes a more
probability in learning approaches.
 It permits fast prototyping of learning
algorithms
without the need for designing an appropriate
training procedure explicitly.
minx f0(x) s.t. { fk(x)=0 ∀k = 1,...,nK

{ fl(x) ≤ 0 ∀l = nK + 1,...,nK +nL

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NEURAL NETWORK are

computational models inspired by
animal central nervous systems that are
capable of machine learning and pattern
recognition.
They are usually presented as systems of
interconnected neurons that can compute
values from inputs by feeding information

through the network.
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• Strong AI is hypothetical artificial
intelligence that matches or exceeds
human intelligence — the intelligence of
a machine that could successfully
perform any intellectual task that a
human being can.
• The skill to evolve itself is the most
astonishing and at the same time
dangerous skill which is used or shall
be used in strong AI.
• One proposal to deal with this is to
ensure that the first generally
intelligent AI is 'Friendly AI', and will
then be able to control subsequently
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developed AIs.

Artificial Intelligence and Mathematics

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