Finding the elixir of life has always been an important quest of humanity. The topic of longevity, hence answering the question about the maximal age attainable (now and in the future) of humans has fascinated civilizations throughout the ages. Starting from the example of the oldest person on record, Jeanne Calmant, we introduce basic statistical techniques from survival (also reliability) analysis in order to study the process of aging from a statistical point of view. Recent findings on the topic are applied to the question of whether there is a plateauing of the hazard rate at high age. We then turn to the important problem of risk communication in the case of hurricanes. In particular, we compare and contrast the two hurricanes Katrina (2005) and Ida (2016) that hit the coast of Florida around New Orleans. Especially in the case of Ida, we comment upon the communication around the risk due to the ensuing flash floods over the northeast coast of the United States. New architectural and city planning initiatives, such as sponge cities, deserve our attention.

During the night of January 31 to February 1, 1953, the southwest coast of the Netherlands experienced a ferocious storm, killing over 1800 people, causing untold suffering and a major economic loss. As a consequence, the Dutch government initiated the Delta Project, which, through a combination of engineering works, should make the country safe for years to come. As part of this project, risk measures were introduced, like the so-called Dutch standard of a 1 in 10 000 years safety measure. Their statistical estimation was worked out and embedded in major engineering projects. These resulted in the construction of numerous new dikes along the coast. Through this example, we highlight several aspects of hazard protection. First, mathematics has an important role to play. Second, interdisciplinarity is key. Third, with such major and costly projects, spanning several generations, a clear communication to politicians as well as the public is both demanding as well as necessary.

It is January 28, 1986. While the world was watching, just 73 seconds after take-off, the Challenger Space Shuttle exploded, killing all seven astronauts on board. The crew included the teacher Christa McAuliffe who would have lectured schoolchildren from space. An important factor that contributed to the disaster was the extremely low temperature at launch. “Extreme” here means “well below temperatures experienced at previous launches”. In this chapter, we give a short overview of the errors that contributed to the explosion. These errors range from purely managerial errors to technical as well as statistical errors. Our discussion includes a statistical analysis of the malfunctioning of so-called rubber O-rings as a function of temperature at launch. As a prime example of efficient risk communication we also recall the press conference at which the physics Nobel Prize winner, Richard Feynman, made his famous “piece-of-rubber-in-ice-water” presentation. This exposed the cause of the accident in all clarity.

Our book was written during the COVID pandemic. As a result, it was natural to include a chapter on this topic. In line with the overall theme of our book, we highlight aspects close to the understanding and communication of risk. Topics included in more detail are the inherent danger of exponential growth and the need for adhering to the precautionary principle when faced with a new, possibly catastrophic and hence not yet widely understood, type of risk. The precautionary principle enables decision-makers to adopt measures when scientific evidence about an environmental or human health hazard is uncertain and the stakes are high. A question we address to some extent is whether this pandemic happened totally unexpectedly; was it a so-called Black Swan? We present evidence that it most certainly was not. We give examples of early warnings from scientific publications, highly visible presentations in the public domain as well as regulatory measures in force to absorb the consequences of a possible pandemic. In discussions around risk, numbers, especially large ones, and also units of measurement play an important role; we offer some guidance here.

Time for a break! Chapter 7 takes you for a guided walk through a tiny part of mathematical wonderland. We will encounter several mathematical personalities. An important one is Andrew Wiles, who solved Fermat’s Last Theorem. The story about how he finally obtained a proof is a must-read. We learn about the Fields Medal, the equivalent of a (non-existing) Nobel Prize in mathematics. We also tell you about the four-yearly International Congresses of Mathematicians and their influence on the field. There will be a first step on the ladder towards a theory of randomness; key names here are Jacob Bernoulli and Andrei Nikolajewitsch Kolmogorov. Randomness also comes to us through the famous discussion between Niels Bohr and Albert Einstein on “God throwing dice”. Of course, we include Leonhard Euler and his most beautiful formula of mathematics.

We single out the 2006 L’Aquila earthquake in Italy as it yields a dramatic perspective on the problem of evidence-based communication. In the aftermath of this earthquake, several scientists were sentenced to jail for insufficiently clear communication related to an imminent earthquake. Though the sentences were later overturned, we can all learn from this example. It is interesting that this court case took place in the country that also tried Galileo Galilei in the seventeenth century for his defense of heliocentrism. A wonderful example in this context is provided by Galileo’s Dialogo published in 1632. In this publication, Galileo communicates his findings to a wider public through a series of dialogues between two philosophers and a layman. We present several parallels to present-day discussions on risk and science communication.

One of the most counterintuitive examples involving randomness is the birthday problem. From 23 persons onwards, the probability of finding at least two people in a group with the same birthday is above 50%. Leonhard Euler’s solution of the Koenigsberg bridge problem heralded the start of the fascinating field of graphs and networks with applications to numerous applied problems across many disciplines. In 1929 the Hungarian writer Frigyes Karinthy highlighted the world’s smallness through his wonderful story “Chains” where he introduced the by now well-known “separation by six” idiom. Starting from these examples, we discuss some risks due to network effects present on the World Wide Web and social media. We present the reader with a glimpse of the fascinating world of coincidences. For instance, the law of truly large numbers states that, with a large enough sample, any outrageous thing is likely to happen. Real-life examples highlight the meaning of this law.

This books reveals aspects of risk on a combined walk/hike/stroll through the landscape of risk. In the walk, we meet several cautionary tales and present historical events from a variety of areas including floods, technological disasters, earthquakes, tsunamis, finance as well as pandemics. From this walk we transition, via a chapter on stories from the realm of mathematics, into a more technically demanding hike. After an introduction of some of the main techniques from probability and statistics, needed to revisit and better understand the cautionary tales, we finish with a stroll discussing several examples where these techniques are applied. A better understanding is achieved by introducting many pedagogical and historical examples. Throughout the book, we stress the need for evidence-based communication. An overall common thread of the book is “From if to what if”. The "what if" thinking links up with the modeling of extreme events and the necessity of stress testing. Throughout, obtaining and analyzing data are key. A special feature of the book is the inclusion of several cartoons by Enrico Chavez. They typically bring arguments made in the text to their key essentials.