Metamathematics: Foundations & Physicalization

Wolfram's best work to date! An exceptionally straightforward and elegant approach to what is "really going on" behind logic, math, and by extension computer science. Wolfram condenses concepts that would be explained over hundreds of pages in traditional academia (with all of its ornate baggage) into just a few pages - and the insights are much clearer this way. Just a brilliant work that is obviously the result of a genius spending decades thinking about a particular topic (and developing the underlying tools himself with Mathematica). Wolfram is a bit of an iconoclast and tends to be lazy about citing academia - but don't let that deter you. In fact, these tendencies give this book a unique and self-coherent style that is unmatched by any other author on the topic. In a similar vein as GEB (Hofstader's masterpiece), this book ranks as one of the most brilliant and unique collections of accessible mathematical insight in decades, and is sure to go under-appreciated by mainstream academia due to the unfortunate rancor that has built up between it and Wolfram. Hopefully with time, we can all come around to agreeing on the significance of the underlying framework Wolfram describes. That's all for now - go read the book!

This is the second publication of Stephen Wolfram that I have read and I am very pleased with both! I am an enthusiast of reading science, math and physics...etc. I find Mr. Wolframs writing to be highly knowledgeable (almost scary knowledgeable), thought provoking, however approachable. From reading his works, you know that if you ever had an audience with him for 5 minutes or more - your life would be changed, Mr. Wolfram is brilliant and it shines through in his books. His thinking is on a different plain than most, but again, he allows you to come in and understand his mastery of complicated subject matter.

complete 2 effectivity

Wolfram's genius is somewhere between pure math and applied computer science, something that often rankles the more academic-inclined but every once and awhile produces a work of profound and lasting profundity. This is one such work, largely because it contains the means of modelling not just individual mathematical theorems, but the structure behind mathematics itself.Even if others have discussed such topics, no one has brought together the illustrative structure in such great form and with such significant implications for mathematics and other fields, such as physics. The implication, which is cannot be overstated, is that mathematics can be thought of not merely as individual theorems that are discovered one at a time, but large, possibly overlapping, syntactical structures which coincide and create realities. This is the additionally the foundation of other key Wolfram inspired concepts such as the ruliad, multicomputation, and his work on fundamental physics.

a triumph for graph fans

Stephen’s body of work is extensive and can be difficult to wrap your head around. Reading New Kind of Science and WPP (project to find a fundamental theory of physics) left me with many questions about the crux of his approach to science (and technology).In his books “Metamathematics” Stephen employs his “make no presumptions about what the cokputer can do” approach, connecting key ideas in WPP and NKS like observer theory and branchial space and enumerating all possible outcomes. For me, it’s connecting this approach across NKS and WPP that rounds out and polishes the impact of Stephen’s approach, and the application possibilities of his theoretical framework (the construction of new technologies, products and services).I don’t think you have to be a pure mathematician to enjoy this work (I’m an engineering type who always shied away from purely theoretical mathematics). For me, being primed for the ideas via NKS and Wolfram Physics Project was the only way I could sustain attention for some of these challenging topics.

Just received the printed version and the content is printed in the opposite direction than the cover…That happened in 2023.. in a mathematics book..unbelievable ..