AI Solves 100-Year-Old Math Mystery? The 'Secret' in Our Daily Coffee

A visualization of AI analyzing the complex swirling movements of a fluid
AI Summary

AI has found a clue to solving a fluid dynamics challenge that has troubled humanity for over a century. We explore the core of this discovery, which promises to revolutionize weather prediction and aircraft performance.

Imagine dropping a single drop of white milk into your warm Americano this morning. Think of the beautiful, irregular brown swirls that appear. Or the ever-changing movements of clouds outside an airplane window, or the terrifying vortex of a typhoon that sweeps everything away in summer.

All these phenomena represent the movement of “fluids” (substances with the property of flowing), such as air or water. They are everywhere around us and very familiar, yet surprisingly, humanity has not yet conquered the formula that perfectly explains this movement. However, recently, researchers from Google DeepMind and New York University (NYU) used a powerful tool called Artificial Intelligence (AI) to find a crucial clue to solving this 100-year-old mystery. Discovering newsolutions to century-old problems in fluid…

Why is this important for our lives?

Fluid dynamics (the study of how liquids and gases move) is not just a complex mental battle for mathematicians. This field is connected to almost every convenience and safety in the world we encounter every day.

  1. Accurate weather forecasts that save your vacation plans: To predict which path a typhoon will take or whether it will really rain during tomorrow’s commute, the massive flow of air must be calculated perfectly down to the decimal point. If AI conquers this equation, “erroneous” weather forecasts will become a thing of the past. Google DeepMind AI Cracks Century-Old Fluid Mysteries… - Decrypt
  2. Eco-friendly planes and cars that save fuel costs: Reducing air resistance by just 0.1% can save an airplane thousands of tons of fuel. Perfectly understanding fluid flow allows for the design of “dream models” that minimize air resistance, leading directly to reduced carbon emissions to save the planet. Google DeepMind AI Cracks Century-Old Fluid Mysteries… - Decrypt
  3. The final puzzle of intellectual history, a mathematical Holy Grail: This problem is considered one of the “Millennium Prize Problems” (the seven greatest challenges in mathematics). Whoever solves it will receive a $1 million prize and the honor of establishing a breakthrough milestone in the history of human intelligence. Discovering new options to century-old issues in fluid dynamics…

Easy Understanding: Navier-Stokes Equations and “Singularity”

Mathematicians use a very complex set of equations called the “Navier-Stokes equations” to describe the movement of fluids. Discovering newsolutions to century-old problems in fluid… These equations are like a “nature’s rulebook” that shows how the velocity, pressure, and density of a fluid change over time. Finding New Solutions for older problems of the… - Dataforcee Digital

However, there is one fatal problem: this rulebook sometimes causes an “error.” Mathematicians call this a “Singularity.” To use an analogy, it’s like an “Error” message appearing on a calculator because the numbers have become too large. As a vortex gets smaller and smaller, energy gathers at a single point, and at some moment, the speed becomes “infinite,” making mathematical calculation impossible. Discovering new options to century-old issues in fluid dynamics… Since speed never becomes infinite in actual nature, a major task for the mathematics community has been to determine whether these errors appear because our mathematical formulas are incomplete. Fluid Dynamics Solutions: AI Tackles Century-Old Problems

AI Reporter’s Analogy: “Balancing a Pencil on its Sharp Tip”

Pushmeet Kohli of Google DeepMind, who participated in this research, explained the solutions found by AI with a very interesting analogy. “It’s like trying to balance a pencil on its very sharp tip.” Google DeepMind discovers newsolutions to century-old problems… - LinkedIn

Laying a pencil flat on its side is easy and stable, but balancing it on its tip requires such precise balance that it is almost impossible. Even the slightest shake will cause it to fall. In mathematics, this is called “Instability.” Such “unstable but very special states” exist within fluid flows, but they were so hard to find that they were almost never discovered using conventional methods. However, AI has succeeded in finding these seemingly impossible balance points remarkably well. Google DeepMind discovers newsolutions to century-old problems… - LinkedIn

How did AI Persuade the 100-Year-Old Stubborn Problem?

Researchers combined advanced technologies: “Machine Learning” (where computers learn on their own through data) and a “High-precision Gauss-Newton optimizer.” [Google DeepMind’s New AI Approach to the Millennium Prize… HyperAI](https://hyper.ai/en/news/44427) Simply put, they made AI study the laws of physics and then undergo hundreds of millions of trials and errors at incredible speeds.
  1. Learning: Teach the AI the physical laws of fluid dynamics. This is called “Physics-informed neural networks,” a process that makes AI calculate with “physical common sense” rather than just guessing numbers. Google DeepMind discovers newsolutions to century-old problems… - LinkedIn
  2. Search: AI scans through hundreds of millions of possibilities—more than a human mathematician could see in a lifetime—and catches “suspicious points” where calculations might get tangled or a singularity might occur.
  3. Verification: It precisely verifies whether the point found by AI is indeed a perfect solution that follows mathematical rules.
As a result, the researchers successfully and systematically discovered families of new “unstable solutions” in three different fluid equations. Discovering new options to century-old issues in fluid dynamics… This is a feat that would have been unimaginable back when humanity struggled with just formulas and paper. [Google DeepMind’s New AI Approach to the Millennium Prize… HyperAI](https://hyper.ai/en/news/44427)

The Future We Can Expect

This discovery isn’t a magic wand that will predict tomorrow’s weather with 100% accuracy right away. However, it is an event equivalent to rebuilding the foundations of the building called science very solidly.

AI’s Perspective: A Word from MindTickleBytes AI Reporter

In summarizing this news, I was strongly impressed that “AI has finally begun to deeply understand mathematics, the language of science.” While AI has mostly been a “performer” that draws pretty pictures or writes smooth text, it is now evolving into a “scholar” that digs into the fundamental operating principles of the universe. Will the day come when AI’s name is written on the final answer sheet for the $1 million “Millennium Prize Problems”? Perhaps that day will arrive much sooner than we imagine.


References

  1. Discovering newsolutions to century-old problems in fluid…
  2. Google DeepMind AI Cracks Century-Old Fluid Mysteries… - Decrypt
  3. Discovering new options to century-old issues in fluid dynamics…
  4. Discovering newsolutions to century-old problems in fluid…
  5. [Google DeepMind’s New AI Approach to the Millennium Prize… HyperAI](https://hyper.ai/en/news/44427)
  6. Fluid Dynamics Solutions: AI Tackles Century-Old Problems
  7. Google DeepMind discovers newsolutions to century-old problems… - LinkedIn
  8. Discovering newsolutions to century-old problems in fluid…
  9. Fluiddynamicsfeels natural once you start with quantum… - YouTube
  10. Google DeepMind AI Cracks Century-Old Fluid Mysteries… - Decrypt
  11. Finding New Solutions for older problems of the… - Dataforcee Digital
Test Your Understanding
Q1. What is the name of the equation that explains the movement of fluids, for which AI sought solutions in this study?
  • Pythagorean Theorem
  • Navier-Stokes Equations
  • Theory of Relativity
The Navier-Stokes equations are key equations that describe the flow of fluids like air or water.
Q2. What did Pushmeet Kohli of Google DeepMind compare the specific solutions found by the researchers to?
  • Passing through a needle's eye
  • Balancing a pencil on its tip
  • Finding a needle in a haystack
Pushmeet Kohli explained that these solutions are so precise and unstable that they are as difficult to find as 'balancing a pencil on its tip.'
Q3. The problem of singularities in the Navier-Stokes equations is included in which prize competition?
  • Nobel Prize in Mathematics
  • Fields Medal Problem
  • Millennium Prize Problems
Proving the existence of singularities in the Navier-Stokes equations is one of the seven 'Millennium Prize Problems,' known as the greatest unsolved mysteries in mathematics.
AI Solves 100-Year-Old Math...
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