by Douglas R. Hofstadter (1979)

2022 reads, 19/20:

“This is axiom”

The above quote is not from this book, but instead, the final lyric in the final song off Bon Iver’s 2011 album, Bon Iver, Bon Iver. These three words encapsulate everything that Justin Vernon was trying to say not only in that whole song, but the whole album: we are here, and in this place, we are self-evident. In math, an axiom is the strongest statement you can make, something that cannot be proved because of its self-evidence (for example the first equality axiom, which states $x = x$, i.e. a number equals itself). And much like I am comparing this foundational mathematical term to music, Hofstadter does the same in his book Gödel, Escher, and Bach: An Eternal Golden Braid.

Hofstadter masterfully weaves Gödel’s Incompleteness Theorem, Bach’s fugues, and Escher’s drawings together to create a map between the neurological structure of the brain and the rise of artificial intelligence. His starting point is defining a ‘strange loop,’ a type of self-reference which leads you back to the original statement, and works from there. If you hold on for the whole ride, his final chapters provide an interesting and original take on minds and machines. In between these chapters lie dialogues between a slew of characters such as the tortoise and Achilles, which are not just entertaining, but also excellent at priming you for the ideas about to be introduced in the next chapter. Some did not enjoy the dialogues, but I thought they were some of the best parts of the book.

At times, this does read like a textbook, but it’s not dry or boring at all; Hofstadter is inviting us to try to get to the point before he gets there, which makes reading GEB almost conversational. I started to lose a bit of interest in the latter half of the Part II, solely because I am not super interested in genetics; to me, Hofstadter is at his best when he is writing about logic, paradoxes, and writing dialogues with hidden meanings. Others would disagree, however, as some really enjoy the neurological aspects, and don’t see the point of the math. And as I mentioned, you don’t really get to the crux of what Hofstadter wants to convey in this book until the final three chapters, which could turn off some people.

Anyone who has an interest in math, puzzles, computer science, neurology, genetics, or even art would at least moderately be interested in what Hofstadter is saying. By no means is a formal background in math required, you just need interest. The reason it took me so long to finish this was not because it was boring, in fact the opposite – his ideas need time to marinate before you go on. In this book, the journey was much better than the destination.

#readingyear2022 #math #science #physicallyowned

by Stuart Rojstaczer (2014)

2022 reads, book 2/20:

I wish Goodreads let you do half stars. I was really interested in the concept of this book going in. The main character, Sasha, is not only dealing with the loss of his mother, but also the fact that she could have solved one of the greatest problems in mathematics (worth one million dollars), but rumor has it she spitefully took the proof to her grave. So, other mathematicians who knew her come to sit Shiva, and try and see if she has the solution anywhere hidden in the house.

However, when actually reading the book, this plot seemed to take a backseat to the more memoir-eqsue style of the main character’s narration, consistently going back and forth between present and past, both in his life and his mother’s. I didn’t really mind this style of writing, but I was just expecting more of a comedy or mystery, so it seemed to drag at points. However, I enjoyed the characters a lot, and their interactions with one another were entertaining. Lastly, the book ended well by satisfyingly tying everything together.

#readingyear2022 #math

by Simon Singh (1998)

“The Last Theorem is at the heart of an intriguing saga of courage, skulduggery, cunning, and tragedy, involving all the greatest heroes of mathematics.”

This books chronicles the history of Fermat’s Last Theorem, beginning with the teachings of Pythagoras in 6th century BC, leading into Fermat’s claim that he had the proof figured out in the 17th century, all the way to the final proof of the theorem in the mid-1990s. Mathematicians throughout history tried to prove this particular problem, and as more and more failed the more it essentially became a race. I mean, imagine being able to say you proved what past mathematicians such as Euler, Cauchy, and Gauss could not.

From the viewpoint of someone who works more with applied math, this book made me appreciate those who work in pure math, specifically number theorists. This is math most people, including myself, will never use, as they work on the types of problems that takes years to understand. It's also probably why Fermat’s Last Theorem has been a topic in popular culture, since the problem was at least easy to understand.

One of the best parts of this book is the heartbreaking section on Goro Shimura and Yutaka Taniyama, who together posited the Taniyama–Shimura conjecture in the mid-1950s and acted as a major missing link to prove the theorem. Unfortunately, Taniyama committed suicide and was unable to see his conjecture and the Last Theorem proved in the 1990s. I appreciated how section of the book highlighted their contributions and wished that they had more recognition for their work.

#readingyear2021 #math