Ramanujan’s 100-year-old pi formula is still revealing the Universe

 

Most people first encounter the irrational number π (pi) -- commonly approximated as 3.14 and extending infinitely without repeating -- during school lessons about circles. In recent decades, advances in computing have pushed this familiar constant far beyond the classroom, with powerful supercomputers now calculating pi to trillions of decimal places.

Researchers have now uncovered an unexpected twist. Physicists at the Centre for High Energy Physics (CHEP), Indian Institute of Science (IISc) report that mathematical formulas developed a century ago to compute pi are closely linked to some of today's most important ideas in fundamental physics. These connections appear in theoretical descriptions of percolation, fluid turbulence, and even certain features of black holes.

Ramanujan's Remarkable Pi Formulae

In 1914, shortly before leaving Madras for Cambridge, renowned Indian mathematician Srinivasa Ramanujan published a paper presenting 17 different formulas for calculating pi. These expressions were strikingly efficient, allowing pi to be computed much faster than existing techniques of the time. Despite containing only a small number of mathematical terms, the formulas produced an impressive number of accurate digits.

Their impact has endured. Ramanujan's methods became foundational to modern mathematical and computational approaches for calculating pi, including those used by today's most advanced machines. "Scientists have computed pi up to 200 trillion digits using an algorithm called the Chudnovsky algorithm," says Aninda Sinha, Professor at CHEP and senior author of the study. "These algorithms are actually based on Ramanujan's work."

A Deeper Question Behind the Mathematics

For Sinha and Faizan Bhat, the study's first author and a former IISc PhD student, the mystery went beyond computational efficiency. They asked why such powerful formulas should exist in the first place. Rather than treating them as purely abstract results, the team searched for an explanation rooted in physics.

"We wanted to see whether the starting point of his formulae fit naturally into some physics," says Sinha. "In other words, is there a physical world where Ramanujan's mathematics appears on its own?"

Where Pi Meets Scale Invariance and Physics Extremes

Their investigation led them to a broad family of theories known as conformal field theories, and more specifically to logarithmic conformal field theories. These theories describe systems that exhibit scale invariance symmetry -- meaning they look the same regardless of how closely they are examined, similar to fractals.

A familiar physical example appears at the critical point of water, defined by a precise temperature and pressure at which liquid water and water vapor become indistinguishable. At this point, water displays scale invariance symmetry, and its behavior can be captured using conformal field theory. Similar critical behavior arises in percolation (how substances spread through a material), during the onset of turbulence in fluids, and in certain theoretical treatments of black holes. These phenomena fall within the domain of logarithmic conformal field theories.

Using Ramanujan's Structure to Solve Physics Problems

The researchers discovered that the mathematical framework at the heart of Ramanujan's pi formulas also appears in the equations underlying these logarithmic conformal field theories. By exploiting this shared structure, they were able to compute key quantities within the theories more efficiently. Such calculations could ultimately improve scientists' understanding of complex processes like turbulence and percolation.

The approach mirrors Ramanujan's own method of starting from a compact mathematical expression and rapidly arriving at precise results for pi. "[In] any piece of beautiful mathematics, you almost always find that there is a physical system which actually mirrors the mathematics," says Bhat. "Ramanujan's motivation might have been very mathematical, but without his knowledge, he was also studying black holes, turbulence, percolation, all sorts of things."

A Century-Old Insight With Modern Impact

The findings reveal that Ramanujan's formulas, developed more than 100 years ago, offer a previously hidden advantage for making modern high-energy physics calculations faster and more manageable. Beyond their practical value, the researchers say the work highlights the extraordinary reach of Ramanujan's ideas.

"We were simply fascinated by the way a genius working in early 20th century India, with almost no contact with modern physics, anticipated structures that are now central to our understanding of the universe," says Sinha.

Journal Reference:

1. Faizan Bhat, Aninda Sinha. Ramanujan’s 1/π Series and Conformal Field Theories. Physical Review Letters, 2025; 135 (23) DOI: 10.1103/c38g-fd2v 

Courtesy: Indian Institute of Science (IISc). "Ramanujan’s 100-year-old pi formula is still revealing the Universe." ScienceDaily. ScienceDaily, 16 December 2025. <www.sciencedaily.com/releases/2025/12/251216081949.htm>. 

 

 

 

A flesh-eating fly once eradicated is moving back toward the U.S.

When the New World screwworm last spread across the United States, it caused widespread damage to livestock and took decades to eliminate. That history is now driving a new effort by researchers at the University of California Riverside, who are working to stop the parasitic fly before it can reestablish itself.

Despite its name, the New World screwworm is not a worm. It is the larval, or maggot, stage of a metallic-looking blowfly known as Cochliomyia hominivorax. Most blowflies are harmless and play an important role by breaking down dead animals. This species is different because it feeds on living tissue.

"Not all blowflies are this species. We don't have to be afraid of all flies," said Amy Murillo, UCR assistant professor of entomology and principal investigator of the project. "But this particular species isn't one we want here."

Monitoring California for Early Warning Signs

Backed by $507,000 from the California Department of Food and Agriculture, UCR entomologists are launching a statewide monitoring program to detect any early signs of the fly's return. The screwworm lays its eggs in open wounds on warm-blooded animals, including humans. Once the eggs hatch, the maggots burrow into flesh in a corkscrew motion, which is how the insect got its name.

The New World screwworm was once common across California and much of the southern United States. About 60 years ago, it was successfully wiped out using a large-scale program that released millions of sterile male flies. Because female screwworms mate only once, the strategy caused the population to collapse. That effort pushed the species south to Panama, where the U.S. Department of Agriculture has maintained a protective barrier ever since.

A Growing Threat to the North

In recent years, the screwworm has started appearing again in parts of Central America and southern Mexico. Experts believe the resurgence is linked to the movement of infested animals, often transported by people who unknowingly help the pest spread.

"It hasn't been found in California yet, but it's within 70 miles of the Texas border," Murillo said. "We need to be prepared."

Traps, Lures, and Early Detection

Murillo is working with Alec Gerry, a UCR veterinary entomology professor and CE Specialist, to deploy traps across California. These traps use a lure developed by the USDA that mimics the smell of rotting flesh. While many blowfly species are attracted to it, the lure is also effective at drawing in the New World screwworm. Researchers will regularly check the traps for any sign that the invasive fly has crossed into the state.

The project also includes an outreach effort aimed at veterinarians, livestock handlers, and entomologists. These groups are the most likely to encounter screwworm infestations early, and catching an outbreak quickly is key to stopping it from spreading.

Why Livestock Face the Greatest Risk

Screwworms pose a serious threat to farm animals, especially those with common injuries from barbed wire, birthing, or procedures such as dehorning. Without treatment, infestations can quickly worsen as flies lay more eggs, enlarging wounds and sometimes leading to death.

California's dairy and cattle industries are particularly vulnerable. "Most people think of citrus or avocados as being our top exports, but it's actually dairy that leads our agricultural economy," Murillo said.

Public Awareness as a Line of Defense

Even though the fly has not been detected in California, researchers say public awareness is an important part of prevention. "Not all blowflies are harmful, and many are beneficial," Murillo said. "But if you notice something unusual on your pet or livestock, reach out to a vet. Don't ignore it."

If an outbreak were to happen again, Murillo said the same sterile insect technique used in the past would still be the most effective tool for stopping it.

Rare but Possible Human Infections

Although screwworms primarily target animals, humans can also be affected under certain conditions, particularly when open wounds go untreated. Infections have been documented in people who traveled to regions where the fly is active. Even so, livestock remain the primary concern.

"They need an opening in the flesh, and it doesn't have to be large. They don't make wounds, but they do exploit them," Murillo said.

Staying Alert Without Panic

Murillo emphasized that the goal is preparedness, not fear.

"You don't have to worry that they're going to start eating your flesh," Murillo said. "But we do hope that this project will help people to be more vigilant in recognizing and preventing screwworm infestations in animals should they return to California."

Story Source:

Materials provided by University of California - Riverside. Note: Content may be edited for style and length.

 

Courtesy:

University of California - Riverside. "A flesh-eating fly once eradicated is moving back toward the U.S.." ScienceDaily. ScienceDaily, 18 December 2025. <www.sciencedaily.com/releases/2025/12/251217082501.htm>.