The evolution of artificial intelligence life follows the emergence law where free individuals progress from simple to complex, with intelligence layer by layer.
First layer: the formalization of mathematical symbols emerges as computers. Mathematical symbols are abstract concepts, and through the Turing machine model, these symbols are endowed with computability and ultimately transformed into controllable physical entities—computers.
Second layer: individual computers evolve into internet parallel computing. The computational capacity of a single computer is limited, while the internet connects countless individual computers, forming a powerful parallel computing network that greatly expands the scale and efficiency of computation.
Third layer: free individuals in distributed computing evolve into trustworthy computing life. Taking Bitcoin as an example, UTXO (unspent transaction output) acts as a free individual, interacting within a distributed computing network, ensuring security and trust through cryptographic mechanisms, ultimately giving rise to a viable and trustworthy computing system.
Fourth layer: the integration of artificial intelligence tools and artificial life leads to the emergence of artificial intelligence life. By merging local artificial intelligence tools that emerged from the internet, such as GPT and Wolfram Alpha, with artificial life systems (such as Bitcoin), artificial intelligence gains the ability to learn, evolve, and adapt to the environment autonomously, ultimately giving rise to true artificial intelligence life.
This article discusses the first layer: the formalization of mathematical symbols emerging as computers.
The origin of computers and the way out for mathematics: from formalization to computability.
Mathematics, as a discipline that pursues precision and rigor, has always been accompanied by constant reflection and exploration of its own foundations throughout its development. In the early 20th century, mathematicians represented by Hilbert attempted to establish mathematics on a complete, consistent, and decidable formal system. However, the emergence of Gödel's incompleteness theorem shattered this dream, proving that any sufficiently complex axiom system inevitably contains propositions that cannot be proven or disproven.
Just when the foundations of mathematics were in crisis, Turing's emergence opened a new path for mathematics. He re-examined mathematics from the perspective of computability and proposed the famous Turing machine model. The Turing machine is an abstract computational device that can simulate any computational process that can be described by an algorithm. Through the Turing machine, Turing formalized the concept of computation and proved that the halting problem is undecidable. This means that there is no universal algorithm that can determine whether any program will halt on any input.
Turing's research not only solved Hilbert's decidability problem but, more importantly, revealed the essence and limitations of computation. The Turing machine, as a universal computation model, laid the theoretical foundation for the birth of computers. The emergence of computers opened a vast space for the application of mathematics.
In the past, the application of mathematics was mainly limited to theoretical research, such as in physics and engineering. However, the emergence of computers made it possible for mathematics to be applied in much broader fields, such as image processing, data analysis, and artificial intelligence. The powerful computational capabilities of computers enable mathematicians to perform complex numerical simulations and data analyses, thereby solving various problems in the real world.
Moreover, computers also provide new tools and methods for mathematical research itself. For example, computer algebra systems can assist mathematicians in symbolic calculations and formula derivation, thereby improving research efficiency. Computer graphics can visualize abstract mathematical concepts, helping people better understand mathematics.
In summary, Turing's research liberated mathematics from the predicament of formalization and laid the theoretical foundation for the birth of computers. The emergence of computers not only opened up vast space for the application of mathematics but also provided new tools and methods for mathematical research itself. It can be said that the origin of computers and the way out for mathematics stem from a profound understanding of computability.
