Symbolic mathematics refers to manipulating mathematical expressions and objects using symbols on computers. It was the dominant paradigm in AI research from the 1950s to 1990s. One example is the STUDENT program from 1964 that could read and solve word problems by translating them into algebraic equations and solving for the unknown values in less than one second for most problems. While solving equations is more of an algebra exercise than true AI, STUDENT demonstrated symbol manipulation abilities and helped establish symbolic AI as an approach. However, symbolic AI faced technical limits and was later replaced by sub-symbolic neural network approaches that were inspired by the human brain.

1. PRESENTATION TOPICS:
• Student
• Solving Algebra Problems
Symbolic Mathematics:

2. SYMBOLIC MATHEMATICS:
❑What is meant by symbolic mathematics?
• In mathematics and computerscience it is a scientific area it
is refers to the study and development ofalgorithms and
softwaresfor manipulating mathematical expressions and
other mathematical objects.
• Symbolic calculations use symbols. Symbolic computation is
the sub-area of the mathematicsand computer science which
solve symbolic problems On symbolic objects representable
on computer.
• Examples of such objects are:
• Algebraic expressions
• Logical prepositions , and
• Programs themselves

3. SYMBOLIC MATHEMATICS:
❑What is symbolic mathematics in AI?
• In artificial intelligence, symbolic artificial intelligence is the term for
the collection of all methods in artificial intelligence research that are
based on high-level symbolic (human-readable) representations of
problems, logic and search.
• Symbolic ai was the dominant paradigm of ai research from the mid-
1950s until the middle 1990s.However, the symbolic approach would
eventually be abandoned in favor of sub symbolic approaches, largely
because of technical limits.
• One of the best-known symbolic mathematics software packages
is mathematica. Others include ALAM, ALGY, AMP, ashmedai, AXIOM*, C
AMAL, CAYLEY, ccalc, CLAM, cocoa(?), ESP, FLAP, FORM, MATHLAB,
etc…

4. WHAT IS SYMBOLIC AND NON-SYMBOLIC
AI?
▪ If one looks at the history of AI, the research
field is divided into two camps:
Symbolic AI Non-symbolic AI
• Symbolists firmly believed in
developing an intelligent
system based on rules and
knowledge and whose actions
were interpretable.
• Non-symbolic approach
strived to build a
computational system inspired
by the human brain.

5. Symbolic Mathematics Finally
Yields To Neural Networks
• By translating symbolic math into tree-like structures,
neural networks can finally begin to solve more abstract
problems.
• To allow a neural net to process the symbols like a mathematician,
charton and lample began by translating mathematical
expressions into more useful forms. They ended up reinterpreting
them as trees — a format similar in spirit to a diagrammed
sentence. Mathematical operators such as addition, subtraction,
multiplication and division became junctions on the tree.
• For almost all the problems, the program took less than 1 second
to generate correct solutions.

6. Symbolic Mathematics Finally Yields
To Neural Networks

7. STUDENT: SOLVING ALGEBRA PROBLEMS
❑ STUDENT:
• STUDENT was another early language understanding program,
written by daniel bobrow as his Ph.D. Research project in 1964.
• It was designed to read and solve the kind of word problems found
in high school algebra books.
• An example is:
• If the number of customers tom gets is twice the square of 20% of the
number of advertisements he runs, and the number of advertisements
is 45, then what is the number of customers tom gets?
• Student could correctly reply that the number of customers is 162.

8. STUDENT: SOLVING ALGEBRA
PROBLEMS
• To do this, STUDENT must be far more sophisticated than ELIZA;
it must process and “understand” a great deal of the input, rather
than just concentrate on a few key words.
• STUDENT program uses little more than the pattern-
matching techniques of ELIZA to translate the input into a
set of algebraic equations. From there, it must know
enough algebra to solve the equations, but that is not very
difficult.
• And it must compute a response, rather than just fill in
blanks.

9. SOLVING ALGEBRA PROBLEMS
• STUDENT Solving Algebraic Equations is more an exercise in
elementary algebra than in AI, but it is a good example of a symbol-
manipulation task, and thus an interesting programming problem.
• The STUDENT program mentioned the function solve-equations,
passing it one argument, a list of equations to be solved. solve-
equations prints the list of equations, attempts to solve them
using solve, and prints the result.
(defun solve-equations (equations)
"Print the equations and their solution"
(print-equations "The equations to be solved are:" equations)
(print-equations "The solution is:" (solve equations nil)))

10. SOLVING ALGEBRA PROBLEMS
• The real work is done by solve, which has the following
specification: (1) Find an equation with exactly one occurrence
of an unknown in it. (2) Transform that equation so that the
unknown is isolated on the left-hand side. This can be done if
we limit the operators to +, -, *,and /. (3) Evaluate the arithmetic
on the right-hand side, yielding a numeric value for the unknown.
(4) Substitute the numeric value for the unknown in all the other
equations, and remember the known value. Then try to solve the
resulting set of equations. (5) If step (1) fails—if there is no
equation with exactly one unknown—then just return the known
values and don’t try to solve anything else.