Books: Last Book You Read and Rate It

[Hippasus]

The Music of the Primes: searching to solve the greatest mystery in mathematics 300

Du Sautoy's text reads almost like a novel or work of fiction, but its subject matter is truly alluring and indeed mysterious. The first half or so was more exciting as it covers the major players when the mathematical landscape surrounding the famous Riemann Hypothesis was beginning to be formulated. The Riemann Hypothesis is a claim concerning the placement of the non-trivial zeros of the so-called critical line (real part=1/2) of the zeta function. The zeta function is an attempt to depict the distribution of the prime numbers in an aggregate sense. This book is like a who's who for the plethora of mathematicians who have been involved in some way with the Riemann Hypothesis. Unfortunately, this is where the book's value ends for me.

It was not particularly well written, in my view, as it is often hammy and forces metaphors at the expense of teaching and incisive exposition. The Riemann Hypothesis has involved number theory, mathematical analysis, computation, probability, as well as quantum physics, but the connections between these areas in regards to RH is rather tenuously described.

200: distasteful and pathetic
300: mediocre or subpar
400: average, but decent
500: very good
600: superb
700: transcendental

 

[MetalheadPenguinsFan]

8/10

 

[Hippasus]

Prime Obsession: Bernhard Riemann and the greatest unsolved problem in mathematics 500

This is the second book by John Derbyshire I have read. It is his earlier of two, the other being another popular math account, but on the history of algebra. I think this is the better of the two, although they are both good. This is also the second book on the famous Riemann Hypothesis I have read. That review is actually above on this page. This is just one of those unsolved problems that anyone would love to be able to solve, but has remained intractable after about 150 years. It is related to number theory, and more specifically, the distribution of the prime numbers.

Anyways, to the book itself. I was really craving something fun to read about math and analysis, but something that actually revealed legitimate mathematics at a slow pace. This book most certainly delivered on that front, but I still found myself "in the weeds" during a couple of the chapters. I'm not sure I learned all that much from it, but who knows, I might consult it in the future as a reference for a particular topic.

The structure of the book is pretty interesting: the odd-numbered chapters give basic mathematical exposition while the even-numbered chapters give the associated history. These actually blended together nicely.

 

[Indrid Cold]

If You Tell by Gregg Olsen: 9.0

Hard to believe this crap really happens.

 

[Babe Ruth]

If You Tell by Gress Olsen: 9.0

Hard to believe this crap really happens.

This was a wild book.. especially how Knotek incrementally tortured, then destroyed her (once) best friend. I think, Knotek may actually be out of prison now.. which seems unjust, but..

 

[Indrid Cold]

This was a wild book.. especially how Knotek incrementally tortured, then destroyed her (once) best friend. I think, Knotek may actually be out of prison now.. which seems unjust, but..

She was released in 2022. The book kept talking about how 'hot' she was, then I looked her up, and went Huh?

It makes me wonder, would I have let someone treat me the way she treated Shane when I was 17? I say HELL NO, but...

 

[Hippasus]

Number: the history of numbers and how they shape our lives 350

This is less a book about mathematics than it is a work of historical investigation. The origins of mathematical concepts are traced to practical problems in the context of myriad cultures through written history. For instance, calendars and accurate time-reckoning, navigation and exploration, commerce and accounting, scientific measurement, astronomy and an understanding of our place in the (physical) cosmos, and computers and automation. The connection between mathematics and religion is a recurring theme and is amply explored.

I found it to be quite imbued with a scientific and materialist reductionism concerning mathematics. It seems like a work of philosophy, but one that is unconsciously so, and poorly argued for to boot, perhaps by virtue of this lack of self-awareness.

The strength of this book is that it shows how disparate cultures separated by vast amounts of space and time are nevertheless connected and similar to one another. The Indian, Chinese, and Arab civilizations are held in particularly high repute by the author. Perhaps the most important of mathematical inventions was the notion of zero being able to be represented in a mathematical system. The Indians were the first to accomplish this, but the Chinese and Arabs did so as well, perhaps independently of one another. This is where mathematics gains a sort of maturity that enabled indefinite accuracy. It is this that gives the number concept a recursive structure. Zero enabled there to be an explicit signpost for the place-value numerical system. For us in North America, we use the decimal system (base-10). There is a wrapping-around in units of 10 as numbers can grow and be internally consistent. Thus, the potential for greater generality emerged.

Here is a quote from the chapter on the Mayans: "A sign for zero is needed to fill up any vacant places; this avoids confusing one place with another."

To know when different things are sufficiently similar, or even equivalent, was a quantum leap in our human development. The contrast with the so-called primitive cultures through history was very interesting and another boon of this book.

We are often taught from the Middle Ages through to contemporary times that the ancient Greeks and their focus on geometric proof was the coming of age of mathematics as we have come to know it. In school here in the United States, I would characterize it as a tacit affirmation of the philosophy of formalism. It is this orthodox point of view that the author argues against, and I dare say, he is largely successful in regard to this particular thesis.

The end of this book focuses particularly intensely on the invention of computers and automation. Of course, this innovation has utterly transformed our world, but from a mathematical standpoint, cannot be considered the end-all-and-be-all that the author seems to insinuate. He is quite optimistic about the prospects of sentient artificial intelligence.

Before giving an alternative account, not from the author, but from Kant as viewed from me, I would like to quote the author's stages of mathematical development through history, as a sort of summary of the present text under review:

"So far as mathematics is concerned, the ekumenai can be listed as follows:

1. Neolithic, pre-literate European and North American
2. Sumerian, Babylonian, Akkadian, Chaldean, Phoenician
3. Egyptian
4. Greek/Roman - first Pax Romana
5. Chinese, Japanese, Korean
6. Arab, Indian, Syrian - first Scientific Revolution
7. Roman Catholic, Mediaeval European - Second Pax Romana
8. Renaissance, Christian, European (especially Italian)
9. Western European (especially British, French and German) - second Scientific Revolution
10. Old European science and mathematics; world science"

---

In the age of the Enlightenment, mathematics has traditionally been considered as an exemplar and prime example of certainty for the rationalists. This was a legacy that passed through the Middle Ages and is often traced back to the ancient Greeks. That is, we have knowledge through clear and distinct intellectual perception. The senses, by contrast, are susceptible to spurious beliefs and distortion. Descriptions of nature are merely partial.

For the empiricist, on the other hand, ideas stem from the senses. It is through doubt that true progress can be made, and it is the distrust of age-old dogma that enabled the scientific revolution to occur and to so radically transform our world. For instance, through the experimental method, hypotheses may be falsified as edifices of knowledge may be built on each other through history.

Then came Kant, the philosopher for whom mathematics is a condition for the possibility of belief, like part of the lens that is necessary and through which we must look in order to perceive and make judgments concerning the world around us. He has been interpreted as a sort of synthesizer of this rationalist-empiricist antinomy concerning knowledge and metaphysics. One cannot judge about the true existence of abstract structures such as mathematics any more than a woman with poor vision can see without her glasses, or feel without her skin.