Why did I write this book? Certainly there are quite a few mathematicians who could write a better book on bounded gaps. I thought that the series of wonderful breakthroughs deserved to be celebrated with several accounts of the mathematical content of the breakthroughs, so why not! In addition, the style adopted for Equivalents of […]
Read MoreThe original post can be found at www.principia.blog Everyone knows that The Principia was based on the inspiration that struck Newton when the apple struck his head, as you can see from the cartoon above. The thought that passed through his head was as follows: “Clearly the earth attracts the apple in the same way that it attracts […]
Read MoreIn modern times we experience regular public exchanges of opinion, whether about COVID-19 policies, humanity’s influence on climate, or whether or not the local jail needs replacing. When arguing in the public sphere, opposing sides each frame their take on a subject and present supporting arguments and facts. Unfortunately, this is often where the discussion […]
Read MoreJust a few years ago, who would have thought that algorithms would be regularly making important decisions once made by humans, and they would be so complex that we would not be able to fully understand how they made their decisions (even though we rely on their decisions in life-threatening situations). And further, that algorithms […]
Read MoreAs cities, counties and states begin to relax social distancing guidelines, it is important for local and state public health organizations to conduct rigorous disease surveillance looking for indications of COVID-19 resurgence. Recognizing that there will continue to be some level of disease incidence in the population, the question is whether relaxing social distancing guidelines […]
Read MoreAlgorithms are sometimes compared to cathedrals, in that they share the same ambition, and the same folly. Some algorithms, such as telephone operating systems, data management systems, or search engines, are huge objects involving the contributions of thousands of people. With algorithms, Homo sapiens has finally created a tool equal to its aspirations. Why do […]
Read MoreUnderstanding turbulence is an important and challenging problem with a million dollar prize money on it. We illustrate the complexity of a turbulent flow using an example. Consider coffee being mixed vigorously, say by stirring (Figure 1(a)). The kinetic energy fed at the large-scales cascades to intermediate scales and then to small scales, as shown […]
Read MoreIn the century preceding the French Revolution advanced mathematics began to play a role in ordinary affairs. If you wanted to find the position of a ship at sea, design fortifications or price annuities, then you needed mathematics. In a process accelerated by the Revolution, first the French and then the German states set up […]
Read More