Book Review: On the Edge, The Art of Risking Everything

(Image: https://www.penguinrandomhouse.com/books/529280/on-the-edge-by-nate-silver/)

I just finished Nate Silver's latest book and asked Gemini to summarize the mathematical, sports gambling and poker elements of the book.

Nate Silver's On the Edge is a fascinating exploration of risk-taking, particularly through the lens of mathematics, sports gambling, and poker. Silver, renowned for his statistical analysis and predictive modeling, delves into the world of high-stakes decision-making, examining how individuals and institutions can gain an edge.

A significant portion of the book is dedicated to the world of poker, a game where skill and probability intersect. Silver dissects the intricacies of poker strategy, highlighting the importance of understanding pot odds, implied odds, and the concept of expected value. He also explores the psychological factors that influence decision-making under pressure, drawing parallels to other high-stakes endeavors.

While the book touches on various aspects of risk-taking, its focus on mathematics and probability provides a rigorous framework for understanding uncertainty. Silver's ability to translate complex statistical concepts into accessible language makes the book engaging for both seasoned data enthusiasts and casual readers.

Ultimately, On the Edge is a thought-provoking exploration of the human capacity for risk and reward. By examining the strategies and mindsets of successful risk-takers, Silver offers valuable insights for anyone seeking to make better decisions in a world full of uncertainty.

In summary, I recommend the book. As I read it, I thought that readers not familiar with poker or sports gambling might get lost in some of the analogies that Silver outlines. However, he included an expansive glossary in the book to explain the terms he uses throughout the book.

Timeline of Systematic Data and the Development of Computable Knowledge

WolframAlpha has a nice visual summary of mathematics over the past 20,000 years: https://www.wolframalpha.com/docs/timeline.

It includes topics included in this blog, such as:

The Ishango bone, a tally stick from central Africa, dates from about 20,000 years ago. See: https://jamesmacmath.blogspot.com/2023/12/the-ishango-bone-one-of-earliest.html.

The On-Line Encyclopedia of Integer Sequences (OEIS):

https://jamesmacmath.blogspot.com/2020/10/what-is-next-number-in-sequence.html

A New Kind of Science:

https://jamesmacmath.blogspot.com/2023/08/book-review-new-kind-of-science-online.html

MacMahon and Ramanujan

(Image: Public Domain, https://commons.wikimedia.org/w/index.php?curid=6707227)

(Image: Passport photograph of Ramanujan created in 1913)

As a proud McMahon, I claim relationship to all McMahons and MacMahons (good and bad). In this post, I outline a connection to the great mathematician Srinivasa Ramanujan.

Percy Alexander MacMahon and Srinivasa Ramanujan, though separated by continents and generations, shared a profound connection through their groundbreaking work in combinatorics and number theory. Their lives and contributions intersected in unexpected ways, leaving an indelible mark on the mathematical landscape.

MacMahon, a British mathematician, was a pioneer in the field of combinatorics, the study of counting and arranging objects. His work on partitions of integers, permutations, and symmetric functions laid a solid foundation for future generations of mathematicians. He was known for his meticulous and systematic approach to problem-solving.

Ramanujan, a self-taught Indian mathematician, burst onto the mathematical scene with his extraordinary intuition and ability to produce complex formulas and identities seemingly out of thin air. His work on number theory, infinite series, and elliptic functions was revolutionary, often defying conventional mathematical thinking.

Though their paths never crossed in person, MacMahon and Ramanujan were indirectly connected through their shared interest in combinatorics. Ramanujan's work on partitions of integers, for example, was closely related to MacMahon's research. In fact, Ramanujan's formulas for the number of partitions of integers were later proved and refined by MacMahon and other mathematicians.

Ramanujan's unconventional style and unorthodox methods sometimes clashed with the more traditional approach of mathematicians like MacMahon. However, MacMahon recognized Ramanujan's extraordinary talent and supported his work. He helped to bring Ramanujan to England and provided him with the resources and intellectual stimulation he needed to thrive.

The relationship between MacMahon and Ramanujan is a testament to the power of mathematical collaboration and the importance of recognizing and nurturing exceptional talent. Their work continues to inspire and influence mathematicians today, and their legacies will endure for generations to come.

The Power of Learning, Part 2

(Image: https://www.iconfinder.com/pillowleaf)

A year ago, I posted about the power of learning. Inspired by the story behind this post, I set out a goal to write Mathematica code to produce a sequence in the On-Line Encyclopedia of Integer Sequences (OEIS: https://oeis.org/), everyday for an entire year. Today, I accomplished this mission and can confirm that committing to do something everyday for a year is a good way to learn a new skill. I'm far from being an expert in Mathematica, but I am now at a much higher level than I was year ago. My Mathematica contributions to the OEIS, as well as my integer sequences, are https://oeis.org/search?q=james+mcmahon&language=english&go=Search.

New Record-Breaking Prime Number Discovered, 2^136,279,841-1

 

New Record-Breaking Prime Number Discovered

Mathematicians have discovered a new record-breaking prime number, the largest known prime to date. The number, 2^136,279,841-1, is a Mersenne prime, a type of prime number that is one less than a power of two.

The discovery was made by the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project that uses volunteers' computers to search for Mersenne primes. The new prime was found by a volunteer in the United States.

The previous record for the largest known prime number was held by 2^77,232,917-1, which was discovered in 2018. The new prime is more than twice as large as the previous record holder.

The discovery of new prime numbers is important for several reasons. First, they are used in cryptography, which is the science of secure communication. Second, they are used in number theory, a branch of mathematics that studies the properties of numbers. Third, they are simply interesting in their own right.

The discovery of the new prime number is a major milestone for the GIMPS project. It is also a testament to the power of distributed computing. By harnessing the power of thousands of volunteers' computers, GIMPS has been able to make significant contributions to the field of mathematics.

What is a Mersenne Prime?

A Mersenne prime is a prime number that is one less than a power of two. In other words, it is a number of the form 2^n - 1, where n is a positive integer.

Mersenne primes are named after Marin Mersenne, a French monk who lived from 1588 to 1648. Mersenne studied these numbers and made a list of all the Mersenne primes up to 2^257 - 1. However, his list was not entirely correct.

Since Mersenne's time, many more Mersenne primes have been discovered. The largest known Mersenne prime is 2136,279,841-1.

Why are Mersenne Primes Important?

Mersenne primes are important for several reasons. First, they are used in cryptography. The RSA cryptosystem, which is one of the most widely used public-key cryptosystems, uses large prime numbers, including Mersenne primes.

Second, Mersenne primes are used in number theory. Number theorists study the properties of Mersenne primes and other types of prime numbers.

Third, Mersenne primes are simply interesting in their own right. They are a fascinating example of a mathematical pattern that has been studied for centuries.

Great Internet Mersenne Prime Search (GIMPS)

The Great Internet Mersenne Prime Search (GIMPS) is a distributed computing project that uses volunteers' computers to search for Mersenne primes. The project was founded in 1996 by George Woltman.

GIMPS has discovered several Mersenne primes, including the largest known Mersenne prime, 2136,279,841-1. The project is a great way for people to contribute to mathematics and science.

If you are interested in learning more about Mersenne primes or the GIMPS project, I encourage you to visit the GIMPS website at https://www.mersenne.org/.

News about this recently discovered prime: 

https://www.livescience.com/physics-mathematics/mathematics/largest-known-prime-number-spanning-41-million-digits-discovered-by-amateur-mathematician-using-free-software

https://www.newscientist.com/article/2452686-amateur-sleuth-finds-largest-known-prime-number-with-41-million-digits/

Numberphile video: https://www.numberphile.com/videos/man-who-found-the-worlds-biggest-prime