If you were accused of a crime, who would you rather decide your sentence—a mathematically consistent algorithm incapable of empathy or a compassionate human judge prone to bias and error? What if you want to buy a driverless car and must choose between one programmed to save as many lives as possible and another that prioritizes the lives of its own passengers? And would you agree to share your family’s full medical history if you were told that it would help researchers find a cure for cancer?
These are just some of the dilemmas that we are beginning to face as we approach the age of the algorithm, when it feels as if the machines reign supreme. Already, these lines of code are telling us what to watch, where to go, whom to date, and even whom to send to jail. But as we rely on algorithms to automate big, important decisions—in crime, justice, healthcare, transportation, and money—they raise questions about what we want our world to look like. What matters most: Helping doctors with diagnosis or preserving privacy? Protecting victims of crime or preventing innocent people being falsely accused?
Hello World takes us on a tour through the good, the bad, and the downright ugly of the algorithms that surround us on a daily basis. Mathematician Hannah Fry reveals their inner workings, showing us how algorithms are written and implemented, and demonstrates the ways in which human bias can literally be written into the code. By weaving in relatable, real world stories with accessible explanations of the underlying mathematics that power algorithms, Hello World helps us to determine their power, expose their limitations, and examine whether they really are improvement on the human systems they replace.
The contributions in the volume provide a window into a variety of subjects related to reductive groups: real and complex analysis on homogeneous spaces, arithmetic aspects of moment geometry, geometry of flag varieties, restriction theory of representations, modern aspects of special functions, multiple Dirichlet series, and unfolding identities in the theory of automorphic forms.
Throughout the work, great emphasis was placed on making the articles accessible to interested newcomers to these fields and graduate students. Representation Theory, Complex Analysis, and Integral Geometry aims to stimulate future research in these areas.
Contributors: J. Bernstein, G. Chinta, D. Ciubotaru, J. Faraut, S. Gindikin, J. Jorgenson, J. Kramer, B. Krötz, Y.A. Neretin, K. Nishiyama, O. Offen, H. Schlichtkrull, M.J. Slupinski, R.J. Stanton, B. Speh, P.E. Trapa, T.N.Venkataramana
Sprinkling his discussion of numbers and probabilities with quirky stories and anecdotes, Paulos ranges freely over many aspects of modern life, from contested elections to sports stats, from stock scams and newspaper psychics to diet and medical claims, sex discrimination, insurance, lotteries, and drug testing. Readers of Innumeracy will be rewarded with scores of astonishing facts, a fistful of powerful ideas, and, most important, a clearer, more quantitative way of looking at their world.
In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without . As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone-from those who fumble over fractions to those who solve complex equations in their heads-winds up marveling at what numbers can do.
Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach it to them.