100 books like Shadows of the Mind

My first pick is the one most directly about Alan Turing himself. After 1950 his attention turned mainly to his new theory of mathematical biology, but his death in 1954 left most of this work unpublished.  His ideas were 20 or more years ahead of their time and few people could assess them. Jonathan Swinton is a leading expert in this field, and has been studying Turing’s manuscripts for 30 years. But his book has a much broader range: he adds so much on the culture of Manchester and its region, with a particular focus on women both as protagonists and observers. He has also illustrated his story with a wealth of pictures.

Ray Monk has, like me, been drawn to the idea of a linear biographical narrative fusing life and work together. My third pick is his biography of the American physicist Robert Oppenheimer. This is a fascinating story parallel to Turing’s. The Second World War brought both of them, hitherto pure researchers, to intense and crucial involvement in the world’s affairs. Nuclear weapons for Oppenheimer were what codebreaking was for Turing. Afterward, both were at odds with the governments they had empowered.

When in 1953 Turing wrote ‘I detest America’ he might well have been reacting to the McCarthy period in which Oppenheimer was attacked. But Ray Monk treats Oppenheimer’s pure scientific work as seriously as the political story. Oppenheimer’s 1939 paper on black holes was the background to Penrose’s 1965 paper cited in the Nobel physics prize of 2020. These dates illustrate the deep and decades-spanning connections that are involved… show more.

My fourth pick is another biography, of the economist John Maynard Keynes. Richard Davenport-Hines has divided up his account into ‘seven lives’. Yet by taking his personal life and sexual identity seriously, Davenport-Hines achieves an outstanding unification. Seriousness is not solemnity: readers will find here a delightful story about Keynes admiring Alan Turing’s fingernails at King’s College, Cambridge. There is much more to illustrate the extraordinary King’s College ambiance in which Turing found his home, and deeper connections: in late 1946, both were crossing the Atlantic, Keynes to rescue the British economy, Turing on his start-up of the computer industry. Keynesian economics are newly relevant now, but the liberal élite culture in which it was hatched may still surprise readers. When Turing started war work at Bletchley Park, he wrote to Keynes’s circle that Dillwyn Knox was ‘his boss’. Did he know, as Richard Davenport-Hines explains, that Knox had been… show more.

A primary reason to love math is because of its usefulness. This book shows two sides of math’s applicability, since it is so ubiquitously used in various algorithms.

On the one hand, such usage can be good, because statistical inferences can make our life easier and enrich it. On the other, when these are not properly designed or monitored, it can lead to catastrophic consequences. Mathematics is a powerful force, as powerful as wind or fire, and needs to be harnessed just as carefully.

Cathy O’Neil’s message in this book spoke deeply to me, reminding me that I need to be always vigilant about the subject I love not being deployed carelessly.  

There’s a lot of fear-mongering going around regarding the possibility of a superintelligent AI that could take over or even wipe out humanity. 

Larson gives a clear rationale for why this is not going to happen and further, why it is a big mistake to expect computer reasoning to be like human reasoning. He explains the ways computers think and how they differ from the ways we do. 

In short, we don’t have a clue how to give computers either consciousness or common sense. Without these, worrying about superhuman intelligence is worrying about the wrong thing. There is no way a computer using current AI methods could evolve into a general intelligence.  

Alan Turing’s 1936 paper “On Computable Numbers, with an Application to the Entscheidungsproblem” was foundational to the development of computer science. To this day, Turing machines, the theoretical computational devices imagined in Turing’s paper, are a research cornerstone as they embody the concept of “computable.” If a programming language can implement a Turing machine, then the language is deemed Turing complete and is, therefore, general-purpose enough to implement any algorithm.

Turing’s paper is readable, but Petzold’s book breaks it down in minute detail to explain the nomenclature and meaning behind Turing’s words. I believe all computer science students should study this paper, and you’ll be hard-pressed to find a more thorough review than the one presented in this book.

JL Borges is, in my view, the greatest literary mind of the 20th Century.

This is a book of stories, philosophical essays and parables, but even when he is writing fiction, his favoured form is that of the mock critical essay about a non-existent book or writer.

What I especially love about him is his wit, subtle and easily missed since it often takes the shape of philosophical rumination when he is actually debunking something held very highly. My natural mode of expression is irony, and Borges’s irony is inimitable.      

This is a short punchy book that provides a great introduction to the topic of codebreaking in England during the Great War, giving a sweeping overview and then some entertaining and tantalizing stories about the people involved. At just over a hundred pages, this is a quick read that serves as a fun introduction to the topic.

This is a book that is at once a biography, a testament to human genius in the face of imminent danger, and a story of human injustice. Alan Turing had an idea about a ‘universal machine’. A machine, when built at Bletchley Park, allowed the Allies in World War II to crack the German Enigma ciphers. This universal machine laid the foundations for modern computing and all the amazing advances we enjoy today. But at a price for Turing, he fought inner demons about his homosexuality and eventually paid the ultimate price.

I marveled at his genius, cheered his cryptographic successes with each cipher cracked, shouted against the tragedy of his arrest, cried at his untimely death. A death at his own hand at the age of 41. The world lost a genius due to a society’s labelling of homosexuality as a crime.

We still live in this world of… show more.

For me, this book got the closest to the nitty-gritty of why mathematicians like me, whose job is to prove theorems, find this activity so compelling.

It’s always been the long hunt, with all the frustration as well as the occasional success, that I’ve found so addictive. Doxiadis brought out the nuances of such pursuits brilliantly – the wily Uncle Petros tells the narrator to prove a mathematical statement despite knowing it is almost surely false.

Ah, these little tricks that we mathematicians enjoy playing on unsuspecting souls (I’ve been known to do this to my students a couple of times).