solution

mathematics

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July 14, 2026

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In mathematics, a solution refers to the answer to a problem or equation. For an algebraic equation, which is a statement of equality between two expressions involving variables and operations like addition and multiplication, a solution is a value or set of values for the variables that makes the equation true. This value is also called a root.12

Elementary algebra, a fundamental branch of mathematics, deals with the properties of numbers and their relationships. It uses symbols to represent numbers and operations, allowing for the manipulation of expressions and the formation of equations. The process of solving an equation involves finding the specific numbers that satisfy it. The set of all such values is known as the solution set.324

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mathematics
Differential equations
…that one should prove that solutions do indeed exist; it is not a priori obvious that every ordinary differential equation has solutions. The methods that Cauchy proposed for these problems fitted naturally into his program of providing rigorous foundations for all the calculus. The solution method he preferred, although the…
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…that one should prove that solutions do indeed exist; it is not a priori obvious that every ordinary differential equation has solutions. The methods that Cauchy proposed for these problems fitted naturally into his program of providing rigorous foundations for all the calculus. The solution method he preferred, although the…
Read More

number theory
Diophantus
These are equations whose solutions must be whole numbers. For example, Diophantus asked for two numbers, one a square and the other a cube, such that the sum of their squares is itself a square. In modern symbols, he sought integers x, y, and z such that (x²)² +…
Read More
These are equations whose solutions must be whole numbers. For example, Diophantus asked for two numbers, one a square and the other a cube, such that the sum of their squares is itself a square. In modern symbols, he sought integers x, y, and z such that (x²)² +…
Read More