About Jonathan Shock

I'm a lecturer at the University of Cape Town in the department of Mathematics and Applied Mathematics. I teach mathematics both at undergraduate and at honours levels and my research interests lie in the intersection of applied mathematics and many other areas of science, from biology and neuroscience to fundamental particle physics and psychology.

Datascience for Neuroimaging: An Introduction, by Ariel Rokem and Tal Yarkoni – A review

NB. I was sent this book as a review copy.

From Princeton University Press

I initially presumed that this book would begin with a relatively advanced level of coding knowledge before delving into neuroimaging. However, its broader scope makes it a far better and more thorough resource. In fact, coding discussions start only after the first 50 pages. The initial 50 pages provide a superb introduction to the prerequisites for Python coding. Two particularly notable areas, unusual for books of this type, are the in-depth introductions to version control (Git) and computational environments and containers (Conda and Docker). Such topics are often omitted from introductory coding books, leading to significant challenges for students with some coding experience. For example, many students end up reinstalling Linux due to not setting up a virtual environment, indicative of the widespread lack of awareness among those with intermediate coding knowledge. Moreover, in-depth discussion of version control is rare in books focusing on specific applied data science topics.…

By | March 3rd, 2024|Book reviews, Reviews|0 Comments

When Animals Dream: The Hidden World of Animal Consciousness, by David M. Peña-Guzmán – A review

NB. I was sent this book as a review copy.

From Princeton University Press

The links between dreams, consciousness and memory are absolutely fascinating. I had imagined that the insight that we could get into animal dreaming was limited to dogs running in their sleep and waking themselves up by banging, violently into a wall. However, there is so much more research on this topic than I was aware of. The signals that octopuses can provide to us as to their thoughts through their colouration, shape and texture is incredibly rich, and an entire narrative can seemingly be read off from these visual clues while they sleep. David clearly has some serious frustration with researchers who don’t want to make the leap to the conclusion that this is really dreaming in the way that we know it, but could simply be the animal running through stereotyped behaviour simulations, in an unconscious way.…

By | December 13th, 2023|Book reviews, Reviews, Uncategorized|1 Comment

Free Agents: How Evolution Gave Us Free Will, by Kevin Mitchell – a review

NB. I was sent this book as a review copy.

From Princeton University Press

There is much to like about this book. Kevin’s discussions on evolution and neuroscience are detailed, clear, and insightful. His writing in general flows nicely and much of the book is definitely a useful text. However, for me, this does not include the sections which actually talk about free will.

The problems start early on in the book, on page 21 where he says (bold font mine throughout):

Meaning became the driving force behind the choice of action by the organism. That choice is real: the fundamental indeterminacy in the universe means the future is not written. The low-level forces of physics by themselves do not determine the next state of a complex system. In most instances, even the details of the patterns of neural activity do not actually matter and are filtered out in transmission.

By | November 16th, 2023|Book reviews, Reviews|4 Comments

“You are not expected to understand this”: How 26 lines of code changed the world, edited by Tori Bosch – a review.

NB. I was sent this book as a review copy.


From Princeton University Press

What a wonderful book! This book, made up of 26 chapters, is a look into the world of computer code, but more than that, about the interrelationship between people and code, from the good, the bad, and the ugly.

Each chapter is written by a different author, or pair of authors, and covers a massively wide range of subjects, from the first coders and programs, to the errors in code which have caused disaster, to the short lines of code which have had massive effects on society.

One thing to note is that people who are so often marginalised in modern computer science are given their voice and their rightful place. This includes the characters who are covered (including Jean Sammet, who I knew nothing about but who developed one of the most important and widely used programming languages to this day) to the LGBTQ+ community in Iran and how they used Telegram to get around the Revolutionary Guards.…

By | May 1st, 2023|Book reviews, Reviews|2 Comments

The Self-Assembling Brain, by Peter Hiesinger – a review

NB. I was sent this book as a review copy.


From Princeton University Press

Science so often lives in silos, or perhaps more accurately silos of Babel. We sit in our offices, ignoring a great deal of what is happening down the corridor from us, let alone in the building next door or the one on the other side of the campus.  A lot of this is down to inertia, and the academic culture of mistrust. But a great deal of the problem is down to the technical languages that, over the years, we become fluent in, and as we do so we shut out those other scientists who may actually be talking about something very similar, just in a complementary language.

The self-assembling brain is a book unlike any other that I’ve read, in that it is very explicitly trying to deal with this problem. The topic is that of the creation of the physical structures in the brain during, particularly, development.…

By | April 9th, 2023|Book reviews, Reviews|2 Comments

Patterns, Predictions and Actions: Foundations of Machine Learning, by Hardt and Recht – a review

NB. I was sent this book as a review copy.


From Princeton University Press

I’ve just taught a course on mathematics for data science. Sadly it was only ten hours long, so there was only so much that I could cover. However, I feel that was taught was sufficient to get my students to the point that they would feel both comfortable with, and highly motivated to read Patterns, Predictions and Actions.

The balance between theory, application and narrative in the book is, I think, just right, making it a genuinely pleasurable book to read cover to cover, or to dip into a given topic to find the mathematical details (or at least what you need to get started). As with any foundational book, each topic could be covered in massively more detail, but that would simply make it a book, different from the authors’ intentions. The jump between the ideas and mathematical principle of Support Vector Machines, as given on one page, the optimisation methods of linear programming, and the practical aspect of coding up of such an algorithm are missing, but given the aims of the book, this doesn’t feel like a loss.…

By | January 29th, 2023|Book reviews, Reviews|1 Comment

The Story of Proof: Logic and the History of Mathematics, by John Stillwell – a review

NB. I was sent this book as a review copy.

The last book of Stillwell’s that I reviewed was Reverse Mathematics which was utterly fascinating, and truly mind-bending. I was very much looking forward to another of his books, and this one did not disappoint. It is a much less alternative perspective on mathematics than the previous, but no less beautifully written or compelling.

I teach pure mathematics to first year undergraduates (amongst others), and so often find that the very concept of a mathematical proof is something that is so hard to grasp. What is sufficient to concretely prove something? What can be assumed? What sort of proof is appropriate within a given context? High school maths generally sets students up very badly in this realm.

Stillwell’s book on the Story of Proof is perhaps a little beyond what could be grasped easily by most first year students, though very keen ones, with patience could certainly make their way through it, and would benefit enormously from doing so.…

By | January 29th, 2023|Book reviews, Reviews|1 Comment

THE BIG BANG OF NUMBERS. How to build the universe using only maths, by Manil Suri (Bloomsbury, 2022) – a review by Henri Laurie

Goodreads link.

Oh no. Not another overview of mathematics, for “everyone”. Set theory, numbers from natural to complex, geometry, algebra. Axiomatics. Gödel. Infinity. Applications. Philosophy??

Isn’t this all a big yawn? Hasn’t this been done again and again? For example by Lancelot Hogben, Eric Temple Bell, Reuben Hersch (and that’s just off the top of my head)?

Not at all, as it turns out. Suri has a marvellous new angle, one that allows him to bypass almost everything those authors wrote about. There is nary a formula or a figure or a proof (except for the endnotes), nor much about big names or history or the various  fields of mathematics.

Instead, there is an emphasis on *ideas* and on pursuing them wherever they may lead. Indeed, Suri gives us mathematics as the passionate pursuit of meaning, as engrossing as physics or music.

The conceit he uses is that one can design a universe very like ours starting from nothing – that is, from the empty set.…

By | November 7th, 2022|Book reviews, Reviews|0 Comments

The best writing on Mathematics, 2021, Edited by Mircea Pitici – a review

NB. I was sent this book as a review copy.

I’ve been reading this series every year now for the last five years or so, and it never disappoints. Mircea does an amazing job each time at collecting such a diverse ideas, voices, and areas of mathematics, that I usually find the vast majority of them to be exceptional. This year is no different.

The book came out during Covid, and rather aptly starts off talking about the effects on mathematicians of involuntary confinement of one form or another. In fact the very first chapter talks of the work of Poncelet, who was involved in Napoleon’s failed campaign, and subsequently imprisoned in Russia, and of his teacher’s Monge, who studied aspects of projective geometry. It just so happened that the diagram of Monge’s published in the essay was precisely what I had needed for a particular problem that I was working on (though in higher dimensions).…

By | October 6th, 2022|Book reviews, Reviews|0 Comments

On useful study habits

I’ve been teaching MAM1000W for around 9 years now, and I am learning all the time. I learn both about new ways to think about old subjects (and how to try and best explain them), and I learn about the way students study, about what works and what doesn’t, and what are some of the habits of students who succeed. Not all of these ideas will be perfect for everyone, but I hope that they will help.

Passive versus active learning

Trying to teach as clearly as possible is a double-edged sword. Of course I want students to come away feeling like they have understood the subject, but if they come away with too much confidence, then they won’t do the one thing which they have to do to actually understand it…and that is practice, but practice of a very particular kind. There is a balance that we should all be thinking about when trying to improve on something (be it sports, music, languages, or maths), and that is finding the right questions to practice on which are hard enough to make us have to sweat a little, but not so hard so as to make us give up completely.…

By | May 13th, 2022|Courses, First year, MAM1000, Undergraduate|2 Comments