Mathematics in the Modern World
Presenting an issue on mathematics in both its pure and applied aspects. Although the two are sometimes separated, a line cannot be drawn between them, and they traditionally fructify each other...
Features
Number
With geometry it is one of the two pillars at the base of mathematics. The concept of number is enlarged by building up number systems and by seeking to break them down into their most primitive elements...
Geometry
For 2,000 years geometry meant Euclidean geometry. Then it was found not only that other geometries described physical space equally well but also that geometry was properly the study of all possible spaces...
Algebra
Elementary algebra deals exclusively with the general properties of numbers. Higher algebra can deal effectively with anything and on occasion is pursued without reference to anything in particular...
Probability
The real world confronts the mathematician with events that are not strictly predictable. The methods he has developed to deal with such events have opened new domains of pure mathematics...
The Foundations of Mathematics
When a new mathematical idea is found to be useful, a superstructure of mathematics rises from it. Later the original idea may prove to be shaky, but it must be repaired without destroying the superstructure...
Mathematics in the Physical Sciences
The outstanding examples of the power of mathematics to relate the facts of nature can be found in physics. The latest example is the use of group theory to relate the fundamental particles...
Mathematics in the Biological Sciences
Biologists use mathematics, but the complex systems they study resist mathematical description. The kind of description that might someday be helpful is suggested by the abstract analysis of self-reproduction...
Mathematics in the Social Sciences
Certain social sciences such as economics deal with facts that are usually represented by numbers. New techniques for relating these numbers point toward the mathematical analysis of entire societies...
Control Theory
In technology the most advanced applications of mathematics are in the design of machines that control themselves. The same methods are relevant to the control mechanisms of living organisms and societies...
Computers
These machines that do arithmetic at high speed have evolved in response to the need to apply mathematics. Now they also promise to play a role in the progress of mathematics itself
Departments
50 and 100 Years Ago: September 1964
Science and the Citizen: September 1964
- Letters
Letters to the Editors, September 1964
- Recommended
Books
- Mathematical Recreation
Mathematical Games
- Amateur Scientist
The Amateur Scientist
- Departments
The Authors
Bibliography
