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The Federal Support of Mathematics
Between the late 1960's and the start of this decade it declined by about a third, and without new Federal initiatives the future health of mathematics is at risk. A plan for renewal is presented 
Mathematics
Pure mathematicians have become more rigorous and applied mathematicians less inhibited. The interaction of mathematics and physics continues to enrich both 
A Museum to Illustrate the Development of Mathematics

The Teaching of Elementary Mathematics
Continuing a survey, begun last month, of the current ferment in science education. The outlook in mathematics: The next few years will bring substantial changes in highschool curricula 
Innovation in Mathematics
The first of four articles on innovation in four central fields. The mathematician seeks a new logical relationship, a new proof of an old relationship, or a new synthesis of many relationships 
The Mathematics of ThreeDimensional Manifolds
Topological study of these higherdimensional analogues of a surface suggests the universe may be as convoluted as a tangled loop of string. It now appears most of the manifolds can be analyzed geometrically 
The Mathematics of Communication
An important new theory is based on the statistical character of language. In it the concept of entropy is closely linked with the concept of information 
Books
On the nature of mathematics and of mathematicians: two new semipopularizations of the subject for intelligent laymen 
Computer Software in Science and Mathematics
Computation offers a new means of describing and investigating scientific and mathematical systems. Simulation by computer may be the only way to predict how certain complicated systems evolve 
The Limits of Reason
Ideas on complexity and randomness originally suggested by Gottfried W. Leibniz in 1686, combined with modern information theory, imply that there can never be a "theory of everything" for all of mathematics 
Books
A new description of the history of mathematics 
Worlds of Four Dimensions
A Field of Mathematics Equally Interesting to Student and Layman 
Beyond Understanding?
Computers are changing the spirit of mathematics 
Step Right Up! It’s the Carnival of Mathematics!
The Carnival of Mathematics is a monthly blogging roundup of fun mathrelated blog posts organized by the friendly folks of the Aperiodical. 
By Solving the Mysteries of ShapeShifting Spaces, Mathematician Wins $3Million Prize
The second annual Breakthrough Prize in Mathematics goes to topologist Ian Agol of the University of California, Berkeley

Is there an Infinity?
The great German mathematician Georg Cantor proved that, so far as mathematics is concerned, there is. Presenting a celebrated account of his ideas and their consequences 
The Rhind Papyrus
In 1700 B. C. an Egyptian scribe named A'hmosè set down his"knowledge of existing things all," a document which is now the principal source of what we know of Egyptian mathematics 
Fiber Bundles and Quantum Theory
A branch of mathematics that extends the notion of curvature to topological analogues ofa Mobius strip can help to explain prevailing theories of the interactions of elementary particles 
Leonhard Euler and the Koenigsberg Bridges
In a problem that entertained the strollers of an East Prussian city the great mathematician saw an important principle of the branch of mathematics called topology 
Georg Cantor and the Origins of Transfinite Set Theory
How large is an infinite set? Cantor demonstrated that there is a hierarchy of infinities, each one "Larger" than the preceding one. His set theory is one of the cornerstones of mathematics