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Description
A Modern Introduction to Classical Number TheoryNatural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to
Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to give him a full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.
One feature of the book is the supplementary material after each section, there by broadening the reader's knowledge and imagination. These contents either discuss the rudiments of some aspects or introduce new problems or conjectures and their extensions, such as perfect number problem, Egyptian fraction problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Hilbert Waring problem, Euler's conjecture, Fermat's Last Theorem, Laudau's problem and etc.
This book is written for anyone who loves natural numbers, and it can also be read by mathematics majors, graduate students, and researchers. The book contains many illustrations and tables. Readers can appreciate the author's sensitivity of history, broad range of knowledge, and elegant writing style, while benefiting from the classical works and great achievements of masters in number theory.
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4.7 ★★★★★
Based on 21 reviews
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★★★★★ 5
Spoiler-free Review - The Martian Dialed Up To 11
Format: Kindle
If you loved the Martian in either book or movie form, Project Hail Mary will likely delight you.
The main character (who I'll leave nameless to avoid spoilers) is nearly identical to The Martian's lead, Mark Watney. They have similar personalities, the same fundamental mission of surviving in a hostile environment, and both use real-world biology, chemistry, and physics to solve their problems from start to finish. The book provides an early test for whether or not you'll enjoy it: on page five, when our protagonist is being quizzed by an annoyingly paternalistic computer that is demanding to know the cube root of eight, our hero replies with the smart aleck answer: "two times e to the two-i-pi". If you find this interaction amusing, all good; if it's off-putting, turn back now.
In fairness, Project Hail Mary shares The Martian's flaws as well. The protagonist's character is a bit better developed - but only slightly. The conflict is entirely man-vs-environment. And though the protagonist is often in situations that might cause one to ponder the essential truths of the human condition, he never does. His personality and behavior as a sarcastic problem-solving scientist / engineer are pitch-perfect but the book rarely goes any deeper. He has an established motivation and a flaw to be overcome - but these are really just superficial grace-notes (see what I did there?). This is not Crime and Punishment. Instead, it's a page-turning action-hero book - where instead of firing shots, the action hero saves the day by doing science really well. Books that celebrate real science are rare, so if that's what you came for, you're going to love what Project Hail Mary delivers.
Although largely similar, there are four main ways in which Project Hail Mary differs on the Martian so I'll touch on those now:
1. The stakes are higher - much higher! In The Martian, Mark Watney is already a bit of a super hero - he's an astronaut after all - and all he really needs to do is stay alive. In Project Hail Mary, our hero is much more of an every-man and his job is nothing less than to save the human race.
2. The Martian is told in chronological order. In Project Hail Mary, our hero awakens with a serious case of amnesia and can't even remember his own name. He starts his adventures at essentially the most dull part of his recent life. As time passes he both tackles dramatic new challenges and remembers the wild adventures that brought him here. Andy Weir does a fantastic job of interweaving the past and the present and the result is a very effective narrative framework that lands on a "Wow!" moment at the end of nearly every chapter.
3. Project Hail Mary is a buddy story. In The Martian, Mark Watney is alone in his battle against the elements of Mars for nearly the entire book. By contrast, Project Hail Mary, once it really gets going, is absolutely a tale of buddy-bonding. This surprised and, ultimately, delighted me. It helps give the protagonist a bit more of a human side. And the team problem-solving scenes are, again, pitch-perfect.
4. Project Hail Mary puts the 'fiction' back in Science Fiction. In The Martian, leaving aside the opening wind storm and the closing chapter of wish-fulfillment heroics, we are essentially in a very tightly written NASA simulation. I found this incredibly enjoyable - but one could reasonably ask, where are the big ideas? Where are the bold 'what ifs'? The answer is, they're in Project Hail Mary! The science is still real and omni-present, but the fiction is big, bold, and awesome. If you're main draw for the Martian was the NASA lore and you wished Weir would write an even tighter sequel detailing the Apollo 13 events, you may be a bit disappointed - but everyone else is going to love this change of pace!
So that's it in a nutshell: Project Hail Mary is a fantastic next book to read after The Martian. It's a clear spiritual successor but brings new ideas and structure to the game. Enjoy!
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Reviewed in the United States on February 16, 2025
★★★★★ 4
Excellent Hard Sci-Fi… Until the Politics Pull You Out
Format: Kindle
I was really excited to dive into Project Hail Mary. As a longtime Isaac Asimov fan, I’ve been craving fresh, modern hard science fiction that actually respects the science. This book delivered — at least for a while.
The author injects real science into the story in a way that’s both fun and fantastic. You don’t need to be an engineer to follow it; a solid high-school education is plenty. The concepts stretch your imagination without ever feeling impossible, and for the first chunk of the book I was hooked. I genuinely thought I’d found a new favorite author.
Then the jarring interruptions started.
Out of nowhere you get yanked out of the immersive sci-fi world by modern political pandering that feels completely unnecessary. A random parenthetical about Columbus “discovering an already inhabited world” when comparing something to the New World. Casual pronoun lectures. Characters selected or described by race and identity in ways that scream “check the boxes.” These moments don’t serve the story — they feel injected. Once you notice the author’s leanings, it becomes hard to unsee.
Each time it happens, the fantasy evaporates. It takes several chapters to sink back into the story… only for the next micro-lecture to pull you right back out.
Overall, I loved the writing, the hard science, and the imagination. It’s some of the best sci-fi I’ve read in years. I just wish the author had trusted the story instead of sneaking in real-world politics. It’s like eating the best meal of your life… and then finding a hair or two in it.
Strongly recommended for the sci-fi, with the above caveat.
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Reviewed in the United States on May 17, 2026
★★★★★ 5
Engrossing and Thought-Provoking
Format: Hardcover
This is an absolutely engrossing read in the first half of the book, especially--so much so that I actually canceled a social plan so that I could keep reading.
The author shifts effortlessly across scenes and time--the play of past and present is very much part of the book's plot and insight--and I developed a fast curiosity and unsettling investment in understanding our anti-heroine/heroine Natalie. This surprised me, because had a friend not recommended the novel I never would have signed on to spend time in the head of a "tradwife." For me the novel was an imagined and imaginative provocation on American womanhood (and masculinity) in the 21st century, where no options or "performances" seem entirely satisfying or even real. I found it simultaneously disturbing and darkly humorous, especially in its depiction of young women's collegiate lives.
However, readers should have some tolerance for caricature throughout. While I howled at the depictions of the miserable lives of aspiring "modern" women in the dorms and figuratively pounded my fists at the hypocrisy of the tradwife, I was also conscious of hyperbole and exaggeration--no, their lives aren't that bad; nor, I would guess, are the "tradwives" as bad as Natalie, who is a profoundly unlikable character.
I did find that the novel bogged down in its middle and late-middle chapters--the mystery of what's happening to Natalie remains but the momentum seems to stall out into repetition. I also felt that the ending seemed too rushed and too tidy, given the nuance we see earlier in the novel. It ends with what feels like a reductive endorsement of modern (or post-modern) life for women when, earlier in the novel, we get to contemplate the flaws in ALL of the scripts and performances that women--and the hapless Caleb-- are asked to live by, or choose... Indeed, the characters that I would have loved to hear more from are the two who seemed more grounded and, ultimately, perhaps happier than the others: Natalie's sister and even her mother... The concluding exposition felt rushed, as did the analysis, in other words...Some of the religious scenes seemed tone-deaf to me... I'm not an evangelical, but Natalie's relationship to God strained credulity.
**Highly recommend** this to anyone looking for a provocative and engrossing read on women's lives and constraints in the age of social media that engages in a fascinating thought experiment along the way...
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Reviewed in the United States on May 26, 2026
★★★★★ 4
An unexpected reading experience!
Format: Hardcover
Very unexpected novel! I went into it without any knowledge or prior information of what it was going to be about. Main character is not a person you would want to be friends. So when calamities happen to her it was hard for me to muster up much sympathy or compassion. It was more of “you had this coming, you deserve every miserable minute”. And boy, there were many! Some harder to believe than others. As I was reading, I first thought- I don’t want to keep this book, it’s not worth saving. But it developed to be definitely the type of story that sticks in your mind, you find yourself revisiting parts and characters and wondering why that happened and why did that person react a certain way. And to me that’s a book worth reading and keeping on my limited bookshelf. So I changed my opinion as I read to the end of the novel. It is certainly a book worthy of a neighborhood book group discussion. I am recommending and sharing my copy to family members and reading friends.
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Reviewed in the United States on May 20, 2026
★★★★★ 5
Beneath the perfect surface
Format: Kindle
Yesteryear completely caught me off guard in the best possible way. What begins as a fascinating look into social media influence, curated perfection, and historical living slowly unfolds into something far deeper and far more emotional than I expected.
The storytelling was incredibly well done, especially the way the author balanced the polished modern influencer world against the harsh realities of 1800s frontier life. The transitions between timelines and perspectives were seamless, and by the end, every piece fit together in a way that completely redefined the story.
What made this especially compelling for me was how layered Natalie’s character felt. Her upbringing, family expectations, faith, public image, and the pressure to maintain perfection all shaped the choices she made throughout the story. Rather than feeling one-dimensional, she felt like someone slowly buckling under the weight of everything she believed she was supposed to be.
The emotional impact of this book surprised me. Beneath the historical elements and social media commentary is a story about identity, appearances, family, and the toll that constant performance can take on a person and those around them.
This is one of those books where the less you know going in, the better the experience will be. I expected an entertaining premise, but I ended up with a story that lingered long after I finished the final page.
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Reviewed in the United States on May 28, 2026
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