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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 
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 
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

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. 
The Straight Line
Euclid's definition of it is worthless, but his axioms remain basically sound. His successors in mathematics have extended his ideas to the curved line and a clearer concept of length 
Topology
A fascinating and important branch of modern mathematics is concerned with such matters as turning an inner tube inside out and bands and bottles that have only one side 
Geometry And Intuition
A classic description of how "common sense," once accepted as the basis of physics but now rejected, is also inadequate as a foundation for mathematics 
The Mathematician as an Explorer
The nature of mathematics is elucidated by one mathematician's account of how a memory word used by drummers in ancient India led him to the classic problem of the traveling salesman's route 
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