Chapter 485: Chapter 156: How Could I Forget?

Across the ocean, in most places, it is already late at night or even early morning.

Yet discussions triggered by today’s sudden update of Ann.Math are still ongoing.

Alright, it can no longer be called a discussion; it’s more like an academic earthquake.

Researchers in mathematics might not subscribe to other journals, but they cannot not subscribe to the four top journals. They are, of course, familiar with the publication patterns of these top journals.

Ann.Math, being a bimonthly journal, has almost never published within the first three days of the month, which makes this seem rather impatient.

Of course, this has made many people start to pay attention to the papers in this issue immediately.

Especially among a group of scholars studying algebraic geometry and number theory, the impact of Qiao Yu’s cover paper is said to be at a nuclear explosion level.

The reason is that the Generalized Modal Axiomatic System proposed by Qiao Yu actually belongs to a programmatic mathematical idea, and it is a highly creative and avant-garde mathematical thought.

However, unlike the Langlands program, Qiao Yu is not proposing a series of conjectures, but directly begins to prove these propositions, reflecting a very direct operational mindset.

Qiao Yu not only provides a theoretical framework but also actively dedicates himself to proving related propositions.

Similar to a path combining theoretical research and verification, it seamlessly connects from the proposal of the concept to the theoremization process.

Honestly, extending the boundaries of classical mathematical thinking through a new axiomatic system is something every mathematician hopes to do.

For example, when talking about calculus, people think of Newton and Leibniz; their status in the field of mathematics is undoubtedly indisputable.

Similarly, if Qiao Yu can perfect his Generalized Modal Axiomatic System, this set of research methods might become a compulsory course for future mathematics students, just like calculus.

The reason is simply that it is useful.

If one does not consider its abstract nature, if Qiao Yu can enrich this axiomatic system, it would undoubtedly make many currently tricky problems appear simpler.

The key to this is the expansion of the toolkit.

Many people do not quite understand the meaning of tools in mathematical operations, but to put it bluntly, it is the construction of theorems using rigorous logic by mathematicians in papers.

For example, calculus, Fourier Transform, Laplace Transform, complex analysis, variational method, sieve method, group theory, differential geometry, symplectic geometry, Markov chain, and so on…

The current situation in mathematics development is that these mathematical tools can only function in specific fields.

But mathematicians believe there are deeper connections between these branches of mathematics, though nobody has discovered what form these connections take.

This led to algebraic geometry, which essentially connects algebraic equations and geometric curves.

And then, in mathematical physics, symplectic geometry is used to study Hamiltonian dynamics, its structure also arising from symmetry and geometric transformation in mathematics.

Even the Langlands program, the fundamental purpose of which is to unify algebra, number theory, and representation theory, creates deeper connections by establishing a more profound mathematical tool framework.

Its most successful part is providing a macro perspective, allowing mathematicians to analyze the common patterns behind these mathematical tools.

This also leads many to believe and judge that the perspectives of different mathematical tools may be abstracted into a more generalized axiomatic system in the future.

Simply put, Qiao Yu is currently doing such work, which can be seen as a new attempt to unify mathematical logic tools.

Of course, one attempt may not create much of a ripple. There are countless attempts by mathematicians. Only a handful truly make an impact.

But there are no secrets in the mathematics community, and the lavish lineup of reviewers for these two papers had already been spread around.

After all, for these big names, reviewing such a paper they collectively considered logically rigorous is not something that requires confidentiality.

What usually goes unexposed is when, knowing a paper is utterly worthless, due to personal relations, they grudgingly approved it when someone asked for a favor.

So the phrase crafted by Dugan Lott, helped by Pierre Derini, also spread around.

“This will be the greatest milestone work of this century, possibly second to none!”

After the paper’s publication, even friends privately messaged Pierre Derini to ask if this evaluation was real, and Pierre Derini admitted it without hesitation.

He even said Andrew Wiles thought he wasn’t wrong…

Yes, Pierre Derini now feels that Lott Dugan is his perfect spokesperson.

Well, if it weren’t for Qiao Yu’s paper presented at the Huaxia Mathematics Society today, he might have jokingly pushed Lott Dugan out.

But now there’s no need for that.

Although Qiao Yu only delivered the report at the mathematics society early this morning, Pierre Derini had already read this paper on the prime number problem several days ago.

He’s even still studying it today.

After Tao Xuanzhi accepted the Huaxia Mathematics Society’s invitation to co-review this paper, he also conducted some in-depth discussions with Pierre Derini.

Their joint conclusion was that transforming the distribution of prime numbers into a modal problem on geometric paths is a very bold attempt.

What they both admired most was how Qiao Yu’s paper borrowed the idea from the Prime Number Theorem in constructing the modal density function.