How can mathematicians grapple with abstruse concepts that are, for the majority of people, beyond comprehension? What mental processes enable a small proportion of people to produce mathematical work of remarkable creativity? In particular, is there a connection between mathematical creativity and autism? We revisit a book and a film that address these questions.

## Archive for August, 2022

### Space-Filling Curves, Part II: Computing the Limit Function

Published August 11, 2022 Occasional ClosedTags: Analysis

It is simple to define a mapping from the unit interval into the unit square . Georg Cantor found a one-to-one map from ** onto** , showing that the one-dimensional interval and the two-dimensional square have the same cardinality. Cantor’s map was not continuous, but Giuseppe Peano found a continuous surjection from onto , that is, a

*curve that fills the entire unit square.*Shortly afterwards, David Hilbert found an even simpler space-filling curve, which we discussed in Part I of this post.

Continue reading ‘Space-Filling Curves, Part II: Computing the Limit Function’

### Space-Filling Curves, Part I: “I see it, but I don’t believe it”

Published August 4, 2022 Occasional ClosedTags: Analysis

We are all familiar with the concept of dimension: a point is zero-dimensional, a line is one-dimensional, a plane is two-dimensional and the space around us is three-dimensional. A position on a line can be specified by a single number, such as the distance from a fixed origin. In the plane, a point can be located by giving its Cartesian coordinates , or its polar coordinates . In space, we may specify the location by giving three numbers .

Continue reading ‘Space-Filling Curves, Part I: “I see it, but I don’t believe it”’