Ask HN: Which books do you consider real gems in your field of work/study?

i will unfortunately give you a half-assed response. Because the truth will take up a lot of time & space & is very inflammatory. So here's what I honestly believe - there are only isolated tricks. The ones who sit in judgement of us, like savants, and claim some sort of coalesced mastery of these tricks into some larger theoretical construct, are faking. They are good at faking, so we listen to them. They have better rhetoric, better optics. But beneath it all, it is a grab-bag of tricks. I worked with several professors. When trying to prove something they will start with their favorite trick. One guy was like - okay let me see if i can cauchy schwarz this. I'm like, why ? Why cauchy schwarz always? There are million inequality bounds. Why pester cs all the time ? He actually looked at me curiously then said I don't know I just have some favorite tricks it seems to work! Atleast he was honest. So that's the deal. If you probe deeply there are a few isolated tricks. They seem to work well. In reality we don't know why they work. But they do. Its like why do you not use spoon for spaghetti ? Why fork ? Ok you can cut lines into a spoon and call it a spork, but then you can't drink soup with the spork. So you reach for the spoon if you want to sip soup, use your fork for spaghetti. Don't try to design some universal theory of cookware. Just buy 1 spoon & 1 fork. That's basically all of mathematical statistics. Few tricks. They work. Why ? I mean who gives a fuck. Maybe bickel & doksum do but I personally don't.

For the sciences that depend on higher maths, a Calculus book worth mention is "Elementary Calculus: An Infinitesimal Approach", by Jerome Keisler. One thing that makes learning Calculus harder than necessary is the clumsy epsilon and delta formalism, that became sort of the COBOL of Calculus teaching. This formalism is not the intuitive approach Newton and Leibniz used to develop Calculus, based on infinitesimals, that was shunned later because it took time until Abraham Robinson made it rigorous in the 1960s. The book by Keisler showcases nicely a way to improve higher math education, if academia had less inertia. The author made the entire book available for free online: https://people.math.wisc.edu/~keisler/calc.html See also: https://en.wikipedia.org/wiki/Nonstandard_analysis

This is refreshingly old-school. Thank you!

The Planiverse: Computer contact with a two-dimensional world - by A.K. Dewdney

> A mind-bending, paradigm shifting visit with Yedred, a denizen of the 2 dimensional Universe. It is written so that the physics comes through very easily for those without science training. A university student discovers that this being Yendred is communicating with him through his computer. There begins a lively dialog as both the 2D Yendred and the 3D author struggle to explain and understand each others worlds.

https://en.wikipedia.org/wiki/The_Planiverse

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The Glass Bead Game - by Hermann Hesse

> The Glass Bead Game takes place at an unspecified date centuries in the future. Hesse suggested that he imagined the book's narrator writing around the start of the 25th century.

> The setting is a fictional province of central Europe called Castalia, which was reserved by political decision for the life of the mind.. Castalia is home to an austere order of intellectuals with a twofold mission: to run boarding schools, and to cultivate and play the Glass Bead Game, whose exact nature remains elusive and whose devotees occupy a special school in Castalia known as Waldzell.

> The rules of the game are only alluded to — they are so sophisticated that they are not easy to imagine. Playing the game well requires years of hard study of music, mathematics, and cultural history. The game is essentially an abstract synthesis of all arts and sciences.

https://en.wikipedia.org/wiki/The_Glass_Bead_Game

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The World as Will and Representation - by Arthur Schopenhauer

> The phrase "Tat Tvam Asi" ('thou art that'), one of the Mahāvākyas of the Upanishads, displayed on an Indian temple. Schopenhauer uses this Sanskrit phrase to express a foundational tenet of his ethics: 'the will is the in-itself of every appearance, and as such is itself free from the form of appearance, and thus from all multiplicity'.

https://en.wikipedia.org/wiki/The_World_as_Will_and_Represen...

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The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies - by Thomas McEvilley

> Spanning thirty years of intensive research, this book proves what many scholars could not explain: that today’s Western world must be considered the product of both Greek and Indian thought — Western and Eastern philosophies.

> Thomas McEvilley explores how trade, imperialism, and migration currents allowed cultural philosophies to intermingle freely throughout India, Egypt, Greece, and the ancient Near East. This groundbreaking reference will stir relentless debate among philosophers, art historians, and students.

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Temporary Autonomous Zone - by Hakim Bey

    1. Pirate Utopias
    2. Waiting for the Revolution
    3. The Psychotopology of Everyday Life
    4. The Net and the Web
    5. Gone to Croatan
    6. Music as an Organizational Principle
    7. The Will To Power as Disappearance
    8. Ratholes in the Babylon of Information

https://en.wikipedia.org/wiki/Temporary_Autonomous_Zone

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Nature of Code - by Daniel Shiffman

https://natureofcode.com/

> How can we capture the unpredictable evolutionary and emergent properties of nature in software? How can understanding the mathematical principles behind our physical world help us to create digital worlds?

> This book focuses on a range of programming strategies and techniques behind computer simulations of natural systems, from elementary concepts in mathematics and physics to more advanced algorithms that enable sophisticated visual results.

> Readers will progress from building a basic physics engine to creating intelligent moving objects and complex systems, setting the foundation for further experiments in generative design. Subjects covered include forces, trigonometry, fractals, cellular automata, self-organization, and genetic algorithms.

I don’t have anything to add, I just wanted to say thanks for this. It is one of my all-time favorite HackerNews posts.