The best Mathematics History books: Reddit reviews

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Maybe in a very general way you could say that. But the history is quite complicated.

If you haven't read Playing at the World, I would highly recommend it. It is, hands down, the best academic study of the history of roleplaying games. Peterson did a mind-boggling amount of research, and mines obscure old gaming 'zines for some really interesting stuff.

One of the biggest revelations to me was that Arneson had been playing a kind of proto-RPG called a "Braunstein," invented by a college kid named David Wesely. These were games where people would take on the roles of average people in a medieval or Napoleonic town, like the Mayor or the Baker. They would run entire campaigns around these towns and the lives of the people in them and it heavily influenced Arneson's later work on D&D.

In fact, it was Arneson's Braunstein-style world called Blackmoor that would later evolve into a D&D campaign. (Monsters literally showed up in the castle dungeon...)

William Dunham has a great book,Journey through Genius: The Great Theorems of Mathematics, about this.

This is the work of Abraham Wald. If you're interested in survivorship bias, and thinking mathematically in general, please consider reading this book, which discusses this exact story, among others. I just read it last week, and I recommend it.

Hey, if you wanna understand 1+1 all you need to read is this little beauty:

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

I have not read it myself, because I am stupid, but I did read a comic book about how and why it was written: https://www.amazon.com/Logicomix-search-truth-Apostolos-Doxiadis/dp/1596914521

Logicomix is really cute if you're looking for something fun and human.

An advisor I worked with when studying formal methods recommended it to me. I got through it in about 20 minutes, but it reminded me to be considerate of things I normally would ignore in the domains of computation.

A fun read you might want to consider is Logicomix. Don’t let the graphic novel aspect deter you, the book goes pretty deep actually.

https://www.amazon.com/Logicomix-Search-Truth-Apostolos-Doxiadis/dp/1596914521/

Bill Gates posted a book on his blog awhile back, How Not to Be Wrong: The Power of Mathematical Thinking. I don't mean this in any sort of negative way, but you should check it out to get a handle on what the guy said. It is an interesting introduction into mathematical principles with a heavy focus on probability.

You may want to give "Playing at the World" by Jon Peterson (https://www.amazon.com/Playing-at-World-Jon-Peterson/dp/0615642047) a read. The emergence of RPGs as a k ow them required a few different things.

I recently started reading How Not To Be Wrong (The Power of Mathematical Thinking), by Jordan Ellenberg, and while the material is probably way too simple for most on this thread, it's very engaging and informative, relating real world examples to simple math concepts. It's especially good at pointing out how math is used and abused by people to come to inaccurate or sometimes completely false conclusions.

But I think math geniuses aside, everyone can get something out of this book. It's good.

This is a good book about the basic history of math. I had to read it for an undergraduate elective but ended up liking it very much because it gave me a new appreciation for all the amazing discoveries that you're asking about. The book is short and concise and reads like a popular science book rather than a textbook.

Some of the ancient mathematicians had genius brains that just work differently than common brains. And others spent a lot a lot a lot of time carefully drawing and measuring and calculating. Same as doing a long division problem these days on paper instead of using a calculator--more time-consuming but still doable.

Everyone should immediately buy Playing At The World and then spend six months reading it because it's 720 pages of extremely dense history. And it's amazing.

(I bought this just a few months ago and it seem to be out of stock now which sucks, but buy the ebook version or hit up your local library or whatever)

This is a great book. Godel Escher Bach... mind expanding is what I would call it.

https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567

> I don't believe anyone has a satisfying answer though.

The question may well be unanswerable. This leads to one of my favorite unanswerable questions: why is there something instead of nothing? (Favorite because anyone who says they've got an answer to this question is almost certainly either delusional or lying... so it's a good litmus test for 'woo'.)

I highly recommend Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid for a very readable exploration on why this is unanswerable.

This is not as much to learn math than to understand the beauty of it: Journey through Genius: The Great Theorems of Mathematics

1. Yes, it's possible, although it varies by person.
2. Yes - almost any process that can be done by hypnosis can, at least in theory, be done through self-hypnosis.
3. The mind is organic, complex, and unpredictable. This might even be structurally built into the study of cognition.

So... nothing is really engraved in a subconscious, because it's constantly changing and it's highly complex. There isn't a function. There's no deactivation switch, because there's no switch in the first place. The mind is not a machine and hypnotists aren't programmers.

Hypnotists are guides. They specialize in navigating some of this very poorly mapped territory. They're often quite good at it. In some cases - like smoking cessation or phobia reduction - they're reliably good at particular functions - so much so that it's published and statistically significant.

Don't let the reliability of some operations fool you, though. The mind isn't a series of mapped switches and mechanical functions, and IMO it never will be. As a result, the reliable answers in spaces like this will generally be frustratingly vague, just because no one can say "yup, I just slap that tear switch and call tech support if it doesn't work."

There is a popular book devoted to this topic entitled "Godel Escher Bach - The Eternal Golden Braid". It is not a particularly Christian book, it was written by a Buddhist mathematician in the 1970's, as he contemplated computers, math, artificial intelligence, and the like.

One of the central ideas of the book involves "Godel's Incompleteness Theorem", which says that you can never prove a "set" from only the data/information inside that set. For example, you cannot prove 2+2=4 unless there is something else, outside of the equation, that proves what a "2" or a "4" even are. Taken to the extreme -- we cannot even prove there is a universe (from inside the universe, as we are), unless there is something outside of the universe to give it some sort of context/meaning. When people say "you can't prove there's a god!", I always say "according to Godel's Theorem, you can't even prove there's a YOU".

In short - my argument would be... if there's a universe, then there "must" be "something" outside of the universe that gives the universe a context... is this "God"? Is it "Ultimate Truth"? This gives new insight into the meaning of the Hebrew name for God -- "I Am".

https://www.amazon.com/Gödel-Escher-Bach-Eternal-Golden/dp/0465026567

Two of my favorites:

• Gödel, Escher, Bach: An Eternal Golden Braid. Not precisely about math but it's very logic-driven and most of the arguments D. Hofstadter makes are math related. This book has given me a lot of insight.
• Flatland. Basically a kids book regarding geometry and how do we look at "space" and dimensions. It's simple, yet intriguing.

How to Solve it and The Art and Craft of Problem Solving are good books.

I really enjoyed this book when I was thinking of adding math as a double major with physics. It depends on your taste, of course, but this book was real "a ha!" moment for me

More elegant but not necessarily better

There is book by Courant, "What is mathematics?". I think you should check it out. You can get pdfs somewhere no need to buy.

Playing at the World: A History of Simulating Wars, People and Fantastic Adventures, from Chess to Role-Playing Games by Jon Peterson is not only a comprehensive study of the evolution of roleplaying games, which have been central to defining the modern perception of fantasy across all mediums, but also explores its literary influences which includes a thorough rundown of the history of fantasy literature.

I've been fascinated by consciousness and the mind/body problem since I was a teen. Never quite found the "answer" (spoiler: no one has), but some of my reading on how human consciousness works inadvertently left me with coping strategies for our mortality.

It's a long, dense read, but I would always recommend Gödel, Escher, Bach as my favorite among these types of books. The follow-up, I Am A Strange Loop is great as well.

What Is Mathematics? An Elementary Approach to Ideas and Methods by Courant and Robbins. “Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving.”

This story is also told in <em>How Not to Be Wrong</em>. They would have many people go to many different stores, if I remember correctly.

And to add to this, if you want even more history I would also recommend this book. While it can get a little complicated at times with the mathematics, the actual historical context is very clearly written and I think and excellent read if you are interested in how mathematics has developed and some of the most important results.

You should read Gödel, Escher, Bach if you are looking for the links between math, music, and language.

Okay thats fair.; Exact category is often debated.

The less debated fields don't have a replication crisis per se: They have a falsifiability crisis.

https://blogs.scientificamerican.com/cross-check/how-physics-lost-its-fizz/

Lost in Math: How Beauty Leads Physics Astray

The property of being able to understand Gödel's theorem. The reason I find this so mind boggling is that the theorem shows precisely that there must be something else than just computation. It is the ability to look at a system "from the outside" to understand its rules. I would say that all people have this even if most are unable to grasp Gödel's theorem. I find it unlikely that this property among people that cannot grasp that theorem would be somehow fundamentally different from this property in people that can. Hence, I would like to return to my initial argument and claim that this is strong evidence for that all human consciousness contains something inherently uncomputable. And probably dogs' consciousness, too.

The theorem is basically a short program (Gödel number) that within the system cannot be proven to neither follow nor break the rules. Its truth value in a sense is undecidable. But from outside of the system you can by understanding it also infer the truth value. The system is Turing complete, so within the system you can do everything that can be done with computation. If people were just Turing complete, they would not be able to understand it either. I am afraid I will not be able to simplify the message of that theorem into something that does it justice in a Reddit post. Sorry.

I actually used to think like you, but this theorem turned everything upside down. -Perhaps you would be willing to read one of my all time favourite books that covers this topic? https://www.amazon.com/Gödel-Escher-Bach-Eternal-Golden/dp/0465026567/

Probably Gödel, Escher, Bach: An Eternal Golden Braid. It's not directly related to cognitive science or game design (my education and job, respectively) but was a terrific foundation for both. Plus Hofstadter is an engaging writer and all-around good egg.