This page contains a list of all the books I have read since the year 2020. Each entry contains an interesting excerpt from the publication followed by a brief comment by me about the material.

## Fiction

(1 book)

### Nineteen Eighty-Four

By George Orwell (1949) · Reviewed on 10 Sep 2020

#### An Excerpt

They were the homes of the four Ministries between which the entire apparatus of government was divided. The Ministry of Truth, which concerned itself with news, entertainment, education, and the fine arts. The Ministry of Peace, which concerned itself with war. The Ministry of Love, which maintained law and order. And the Ministry of Plenty, which was responsible for economic affairs. Their names, in Newspeak: Minitrue, Minipax, Miniluv, and Miniplenty.

#### My Comment

This is a dystopian novel that popularised the term "Orwellian" as an adjective. The novel centres on the consequences of totalitarianism, mass surveillance, and repressive regimentation. The novel examines, quite vividly, how truth and facts are manipulated in a fictional dystopian society. One might even find some frightening similarities between the society in the book and the current society in the real world.

## Papers

(1 paper)

### On a Curious Property of 3435

By Daan van Berkel (2009) [PDF] · Reviewed on 13 Sep 2020

#### An Excerpt

Take for example the integer $$3435.$$ At first it does not seem that remarkable, until one stumbles upon the following identity. $3435 = 3^3 + 4^4 + 3^3 + 5^5$ This coincidence is even more remarkable when one discovers that there is only one other natural number which shares this property with $$3435,$$ namely $$1 = 1^1.$$

#### My Comment

This is a short five-page paper that coined the term Munchausen number to refer to a number in a given base that equals the sum of its digits raised to the power of itself. This paper proves that for every base $$b \in \mathbb{N}$$ such that $$b \ge 2,$$ there are only finitely many Muchausen numbers.

## Textbooks

(1 book)

### Introduction to Analytic Number Theory

By Tom M. Apostol (1976) · Reviewed on 01 Oct 2021

#### An Excerpt

Equation (24) becomes $np(n) = \sum_{k=1}^n \sigma(k) p(n - k).$ a remarkable relation connecting a function of multiplicative number theory with one of additive number theory.

#### My Comment

This is a fascinating textbook on analytic number theory. The book begins with simple properties of divisbility but it then soon introduces several new concepts like the Möbius function, Dirichlet product, the prime number theorem, etc. The book exposes various subtle nuances of the Riemann zeta function $$\zeta(s)$$ with great rigour and thoroughness. Results like $$\zeta(-1) = 1/12$$ that once felt mysterious look crystal clear and obvious after working through this book. I strongly recommend this book to anyone who wants to delve into the study of analytic number theory.

## Non-Fiction

(1 book)

### The Music of the Primes

By Marcus du Sautoy (2003) · Reviewed on 12 Sep 2020

#### An Excerpt

But for Grothendieck this was not abstraction for abstraction's sake. In his view this was a revolution that was necessitated by the questions that mathematics was trying to answer. He wrote volume after volume describing this new language. Grothendieck's vision was messianic, and he began to attract a following of faithful young disciples. His output was huge, covering some ten thousand pages. When a visitor complained at the poor state of the library at the Institut, he replied, 'We don't read books here, we write them.'

#### My Comment

This book explores the history of prime number theory. A large portion of the book focusses on the history of the Riemann hypothesis and its influence in the field of number theory. The book is full of many interesting anecdotes from the lives of great mathematicians.