Some believe that if you're main profession is pure math research, you don't need a scientific calculator. That's simply not true. Although I don't use one nearly as much as when I was an undergrad, I still need a calculator and the only one I'm willing to use is the Casio FX-991MS.

When it comes to the philosophy of science, not many publications are relevant to modern practice. Let's take math. The current literature still talks about platonism. Look harder and you might find the rise of non-Euclidean geometry or other breakthroughs like cardinality. In short, the bulk of mathematical philosophy still consists of math that's hundreds of years old. While these topics are still important, I find it much more interesting to look at the new philosophical issues present in *modern* mathematics and science.

That's why I was delighted to find *Lost in Math* by Sabine Hossenfelder, who is also the author of a popular physics blog called Backreaction.

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Today, public-key cryptography is everywhere, offering some measure of security for virtually all internet commerce transactions and secure shell connections. It's hard to imagine life without it, even though most people aren't aware of it.

Steven Levy's *Crypto* is a great book to explain it and how it all came about. In fact, I first read it almost twenty years ago when I was in high school, and just read it again the other day.

How did encryption in the digital age start out? How did public-key cryptography get invented? And how did public-key crypto get into the hands of pretty much everyone with a web browser all over the world despite the attempts of the U.S. government to control it? These questions are answered in Levy's book.

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I first heard of Edward Snowden when I was still a PhD student. He became world-famous for leaking huge numbers of NSA documents on their extensive surveillance and data collection program.

(N.B. To be clear, I do not condone what Snowden did, but even so this book makes for interesting reading.)

How this leak happened, and what the leak contained, is detailed in *No Place to Hide* by Glenn Greenwald. As Snowden entrusted Greenwald with the leaked documents, Greenwald is in a unique position to offer a detailed and accurate account of Snowden's leaked files.

The bulk of Snowden's documents describe the huge amounts of data are collected from pretty much anyone the NSA can get their hands on, regardless of who they are or where they live in the world. This data comes from various sources: intercepted internet transmissions, agreements with phone companies like AT&T, agreements with tech companies like Google, Facebook, and Microsoft, and other spy agencies. The data collected include the exact times and durations of phone calls, and the contents and metadata of emails. The data accumulated by the NSA is so huge that they have to build massive petabyte data centers to store it.

Greenwald's book is frightening, as he describes his first interactions with Snowden.

Many people, including journalists, denounced Greenwald and his associates for the leaks. A journalist for the New York Times lied in an article, and that was just one of many fabrications Greenwald endured to bring the leaked documents to the world. Greenwald and Snowden also had great support as well. As I said, all of this is frightening. Data-driven technology has only begun to mature and in the future we will see something that we've never seen before.

Greenwald wrote a very interesting book here, reporting on the Snowden leaks. Highly recommended.

By the way, if you're interested in this book, read Bruce Schneier's *Data and Goliath*. Schneier, an expert in computer security, worked with Greenwald on the Snowden files. *Data and Goliath* is more focused and detailed on the technical aspects of data collection and espionage, whereas Greenwald's book is more about the initial leak.

From Here to Infinity: A Guide to Today’s Mathematics

By Ian Stewart

1996 edition

"From Here to Infinity" is an enchanting read, which inspires both budding mathematicians, and curious outsiders alike. For mathematicians are mysterious beings to the general population; enshrouded in a cloak of cryptic symbols, they slip into another world, with an aura the ignorant classify as having a residue of chalky smoke, and mundane arithmetic.

Stewart bridges the gap between the uninformed individual and the world of mathematics with friendly, open approach. Several comprehensive chapters discuss intriguing topics, including chaos theory, knots, computer technology, algorithms, fractals, Fermat’s last theorem, and how to increase one’s odds of winning the lottery.

Never speaking down to the reader, Stewart provides many examples to illustrate a concept, which are punctuated with the occasional joke. For the reader with little exposure, the examples are fascinating, and show another side of thinking all together. However, as the examples develop, the level of math increases steeply. But, the initial feeling of frustration with a challenging idea gives way to a feeling of satisfied accomplishment with the completion of each chapter.

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Posting has slowed a little bit this month because of holidays, but in the last couple weeks during my visit home I decided to refresh some basic knowledge of valuation theory by going through thoroughly the book "Introduction to *p*-adic Numbers and Valuation Theory" by George Bachman. Naturally, I wrote this quick review.

Bachman's book is designed to be a leisurely introduction to valuation theory and *p*-adic numbers. It has only 152 pages and naturally cannot be comprehensive. It is, rather, an enjoyable read that does not require much advanced knowledge, though some experience with metric spaces is certainly required to fully appreciate the later chapters on the extension of valuations.

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