What should a genius look like?!
If this question were posed to anyone at the Xilin Institute of Mathematics other than Qiao Ze, they would likely point upward in unison.
This is especially true for the newly joined assistant researchers at the Mathematics Research Institute.
The first thing this group does upon entering the Mathematics Research Institute is surprisingly similar to the Qiao Class: learning.
As Dou Dou's recruitnt notice stated, their work involves fundantal and applied research targeted at special algebraic systems like Qiao's Algebraic Geotry and its corresponding Qiao Space. While refining the academic discipline, they simultaneously aim to make it applicable to more fields.
For example: fundantal physics, aerospace, engineering construction, software design, and so on...
Much like Taylor's Theorem, it's not just mathematicians who need to study it.
In civil engineering, Taylor's Theorem can be used for structural analysis, particularly for evaluating a structure's response under different loads.
In electronics and chanical engineering, designing control systems often utilizes Taylor's Theorem to approximate a system's dynamic behavior. For instance, when designing an airplane's autopilot system or any chanism requiring precise dynamic responses, Taylor's Theorem helps engineers understand and predict how the system reacts under varied inputs.
Beyond that, fields like thermodynamics and fluid chanics, electronic circuit analysis, chanical engineering and dynamics, acoustics, and vibration analysis—as well as nearly all nurical simulations and optimizations needed in engineering—frequently involve the use of Taylor's Theorem.
Likewise, since Qiao's Algebraic Geotry can replace Taylor's Theorem to provide more precise expansions, the series of theorems and formulas it contains naturally can play a significant role in these engineering applications, such as drastically reducing computational power for the sa calculations.
Due to the inherent abstraction and complexity of Qiao's Algebraic Geotry, it's difficult for most people to understand, but it can be directly implented into software and used in computers. The new researchers will mainly focus on these tasks in the future.
Those with a talent for theoretical research can pursue pure mathematics to further expand the entire Qiao's Algebraic Geotry system. For those whose talent isn't as outstanding, they can focus on applied research. Of course, Qiao Ze could accomplish all this himself, but it would take a very long ti.
If it were any other mathematician, completing the supplentation of Qiao's Algebraic Geotry in a lifeti would already be a source of great pride. But clearly, Qiao Ze is not like that.
The reason is simple: after extensive contemplation, he has already determined that Qiao's Algebraic Geotry is insufficient to solve the Grand Unified Theory.
While Qiao's Algebraic Geotry possesses multi-dinsional data structures, making it superior to all existing mathematical tools in addressing the Grand Unified Theory by handling the behavior of the four fundantal forces across different scales and energy levels,
Qiao Ze even predicted the existence of the containnt graviton through theorems in Qiao's Algebraic Geotry, which has already been proven.
However, Qiao's Algebraic Geotry remains inadequate in describing many problems on the microscopic level, particularly those phenona exceeding the Standard Model in dealing with nonlinear dynamical systems.
For instance, Qiao Ze encountered difficulties using this tool to handle the non-locality in Superstring Theory, which proposes that strings are not zero-dinsional points but rather one-dinsional objects with finite length. This leads to physical phenona at the microscopic scale exhibiting non-locality, which Qiao's Algebraic Geotry tools cannot precisely address.
Additionally, based on the data Dou Dou obtained, CERN's high-energy particle collision experints revealed nonlinear dynamical behaviors of particles under extre conditions. These behaviors are challenging to fully describe within the frawork of Qiao's Algebraic Geotry, especially when considering the creation of new particles and unknown interactions.
Fortunately, Su's wedding dress fitting provided Qiao Ze with inspiration: superposition and interaction.
Superposition is actually easy to understand, as the principle of superposition is one of the core features of quantum chanics. Schrödinger's cat in the closed box exists in a superposition state—multiple possible states—before the box is opened.
Translated into mathematics, this is a new structure. The goal of this result is to simultaneously resolve solutions from multiple different theories and explore their superposition effects.
As for interaction, Qiao Ze defines it mathematically as "interweaving."
Its definition establishes a profound form of connection and interaction between different mathematical models, theories, or systems of equations. This allows the attributes and behaviors of distinct models to interact, transform, and rge within a unified frawork.
This interaction includes not only operational-level interactions in mathematics, such as the union or transformation of equations but also theoretical-level interactions—how to describe and understand the fundantal structure and interactions of the physical world through a brand-new mathematical language.
Compared to Qiao's Algebraic Geotry, the greatest feature of these two new tools might be their enhanced complexity and abstraction.
Purely in terms of abstraction and complexity, if Qiao Ze's mathematical intertwining principle becos part of the future mandatory university curriculum, concepts like the interaction between objects and morphisms in category theory or the continuous mapping of elents across different topological spaces might have to be taught at the junior high level.
As for Qiao's Algebraic Geotry, at best, it's equivalent to high school mathematics knowledge.
Yes, all foundational.
Such is the imagination of a genius.
At the very least, Qiao Ze has paved the way from simplicity to sophistication.
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