Isaac Newton developed calculus, expecting to apply it to dynamics. Mathematics is therefore dedicated to dynamics,
and because dynamics is the basis of engineering, mathematics contributes to manufacturing technology.
Modern society cannot get along without electricity, where vector analysis, a kind of mathematics,
is used in electromagnetism. Mathematical disciplines such as Fourier analysis
handling periodic functions and differential equations are also important.
Life sciences such as medicine deal with extremely complicated living bodies.
Probability and statistics are applied thereto because exact prediction of the future is not possible, as it might be with physics.
We reason that "This patient will be cured with medical treatment with a probability of 70%, and no serious side effect is anticipated even if in case of incomplete recovery.
Therefore this medical treatment should be conducted."
Today’s world economy has been experiencing extremely rapid changes.
The most important issue is the prediction of economic fluctuation, which is a business of economics.
Mathematics, such as vectors, matrices, and calculus,
is employed extensively in modern economics.
Computers also share a close relation with mathematics.
Because computers are literally supposed to compute, naturally they are closely related to mathematics.
The foundation of mathematics??those studies at the root of mathematics??is almost identical to fundamental computer theory.
Two major discoveries in the 20th century are the theory of relativity and quantum mechanics.
The theory of relativity, which considers gravity as "curved space", employs "Riemannian geometry", the theory of a curved space.
The idea of probability is crucial for quantum mechanics because the solution of its fundamental equation provides the "probability that matter exists."
Additionally, its fundamental equation is given as a differential equation in a space of infinite dimensions.
Consequently, advanced mathematics is of practical use everywhere.
The latest applications include algebra for safe communications and probability theory for finance theory, which is a theory of investment.