Every four years, at the International Congress of Mathematicians, the Fields Medal is awarded to two, three, or four young mathematicians. To be eligible, the awardees must be under forty years of age. For the chosen few, who came from England, France, Korea and Ukraine, the award, often described as the Nobel Prize of Mathematics, … Continue reading Fields Medals presented at IMC 2022
Tag: Combinatorics
The Chromatic Number of the Plane
To introduce the problem in the title, we begin with a quotation from the Foreword, written by Branko Grünbaum, to the book by Alexander Soifer (2009): The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators: If each point of the plane is to be given a color, how many colors … Continue reading The Chromatic Number of the Plane
Derangements and Continued Fractions for e
We show in this post that an elegant continued fraction for $latex {e}&fg=000000$ can be found using derangement numbers. Recall from last week's post that we call any permutation of the elements of a set an arrangement. A derangement is an arrangement for which every element is moved from its original position. The number of … Continue reading Derangements and Continued Fractions for e
Arrangements and Derangements
Six students entering an examination hall place their cell-phones in a box. After the exam, they each grab a phone at random as they rush out. What is the likelihood that none of them gets their own phone? The surprising answer --- about 37% whatever the number of students --- emerges from the theory of … Continue reading Arrangements and Derangements
Order in the midst of Chaos
We open with a simple mathematical puzzle that is easily solved using only elementary reasoning. Imagine a party where some guests are friends while others are unacquainted. Then the following is always true: No matter how many guests there are at the party, there are always two guests with the same number of friends present. … Continue reading Order in the midst of Chaos
Folding Maps: A Simple but Unsolved Problem
Paper-folding is a recurring theme in mathematics. The art of origami is much-loved by many who also enjoy recreational maths. One particular folding problem is remarkably easy to state, but the solution remains elusive: Given a map with M × N panels, how many different ways can it be folded? Each panel is considered to … Continue reading Folding Maps: A Simple but Unsolved Problem
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