## Pi Day 2020: A new crossword puzzle

Yes, it is that time of year — Pi Day (March 14, or 3/14 in North American month/day date notation) is here.

So in honor of the occasion, I have constructed a new crossword puzzle — see below. This puzzle honors several of the key persons through history who have made significant contributions to the theory and computation of Pi.

This puzzle conforms to the New York Times crossword conventions. As far as difficulty level, it would be comparable to the NYT Tuesday or Wednesday puzzles (the NYT puzzles are graded each week from Monday [easiest] to Saturday [most difficult]).

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## Universe or multiverse? The war rages on

Credit: Quanta Magazine

Introduction

A growing controversy over the multiverse and the anthropic principle has exposed a major fault line in modern physics and cosmology. Some researchers see the multiverse and the anthropic principle as inevitable, others see them as an abdication of empirical science. The controversy spans quantum mechanics, inflationary Big Bang cosmology, string theory, supersymmetry and, more generally, the proper roles of experimentation and mathematical theory in modern science.

The “many worlds interpretation” of quantum mechanics

Since the 1930s, when physicists first developed the mathematics behind quantum mechanics, researchers have found that this theory appears to

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## Do probability arguments refute evolution?

Introduction

In the past few decades, modern science has uncovered a world that is far vaster and more awe-inspiring than ever imagined before, and has uncovered a set of elegant natural laws that govern all the universe, deeply resonating with the notion of a cosmic lawgiver. It not just devout Judeo-Christian believers who find these results inspiring. For example, 46% of Americans (including 54% of atheists, 55% of agnostics and 43% of nones) say that they experience a “deep sense of wonder about the universe” on at least a weekly basis [Masci2016]. With regards to a harmony between science,

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Factorization and cryptography

Until a few decades ago, number theory, namely the study of prime numbers, factorization and other features of the integers, was widely regarded as the epitome of pure mathematics, completely divorced from considerations of practical utility. This sentiment was expressed most memorably by British mathematician G.H. Hardy (best known for mentoring Ramanujan and results on the Riemann Zeta function), who wrote in his book A Mathematician’s Apology (1941),

I have never done anything “useful”. No discovery of mine has made, or is likely to make, directly or indirectly, for good

## Jim Simons: The man who solved the market

Gregory Zuckerman, author of The Greatest Trade Ever, has published a new book highlighting the life and work of Jim Simons, who, at the age of 40, walked away from a very successful career as a research mathematician and cryptologist to try his hand at the financial markets, and ultimately revolutionized the field. Zuckerman’s new book is titled The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution.

Simons’ background hardly suggested that he would one day lead one of the most successful, if not the most successful, quantitative hedge fund operation in

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## The scientific debate is over: it is time to act on climate change

Credit: IPCC

The facts of climate change

At this point in time, the basic facts of climate change are not disputable in the least. Careful planet-wide observations by NASA and others have confirmed that 2018 was the fourth-warmest year in recorded history. The only warmer years were 2016, 2017 and 2015, respectively, and 18 of the 19 warmest years in history have occurred since 2001. Countless observational studies and supercomputer simulations have confirmed both the fact of warming and the conclusion that this warming is principally due to human activity. These studies and computations have been scrutinized in great

## Quantum supremacy has been achieved; or has it?

IBM’s “Q” quantum computer; courtesy IBM

For at least three decades, teams of researchers have been exploring quantum computers for real-world applications in scientific research, engineering and finance. Researchers have dreamed of the day when quantum computers would first achieve “supremacy” over classical computers, in the sense that a quantum computer solving a particular problem faster than any present-day or soon-to-be-produced classical computer system.

In a Nature article dated 23 October 2019, researchers at Google announced that they have achieved exactly this.

Google researchers employed a custom-designed quantum processor, named “Sycamore,” consisting of programmable quantum

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## Pi as the limit of n-sided circumscribed and inscribed polygons

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Credit: Ancient Origins

Introduction In a previous Math Scholar blog, we presented Archimedes’ ingenious scheme for approximating $\pi$, based on an analysis of regular circumscribed and inscribed polygons with $3 \cdot 2^k$ sides, using modern mathematical notation and techniques.

One motivation for both the previous blog and this blog is to respond to some recent writers who reject basic mathematical theory and the accepted value of $\pi$, claiming instead that they have found $\pi$ to be a different value. For example, one author asserts that $\pi = 17 – 8 \sqrt{3} = Continue reading Pi as the limit of n-sided circumscribed and inscribed polygons ## New paper proves 80-year-old approximation conjecture MathJax TeX Test PageMathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’\$’], [‘\$$‘,’\$$’]]}});

Log_10 of the error of a continued fraction approximation of Pi to k terms

Approximation of real numbers by rationals

The question of finding rational approximations to real numbers was first explored by the Greek scholar Diophantus of Alexandra (c. 201-285 BCE), and continues to fascinate mathematicians today, in a field known as Diophantine approximations.

It is easy to see that any real number can be approximated to any desired accuracy by simply taking the sequence of approximations given by the decimal digits out to some point, divided by the appropriate power

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## How many habitable exoplanets are there, really?

The TRAPPIST-1 system of exoplanets, approximately 40 light-years away

Exoplanets galore

As of the present date (August 2019), more than 4000 exoplanets have been discovered orbiting other stars, and by the time you read this even more will have been logged. Several hundred exoplanets were announced in a July 2019 paper (although these await independent confirmation). All of this is a remarkable advance, given that the first confirmed exoplanet discovery did not occur until 1992.

Most of the discoveries mentioned above are planets that are either too large or too close to their sun to possess liquid water, much

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