Freezing liquids help to predict properties of prime numbers

May 3, 2012, Queen Mary, University of London

( -- The same freezing which is responsible for transforming liquids into glasses can help to predict some patterns observed in prime numbers, according to a team of scientists from Queen Mary, University of London and Bristol University.

At a low enough temperature, water freezes into ice by arranging its molecules into a very regular pattern called crystal. However many other freeze not into , but in much less regular structures called glasses - window glass being the most familiar example. Physicists have developed theories explaining the freezing phenomena, and built models for understanding the properties of glasses.

Now, a researcher from Queen Mary’s School of Mathematical Sciences, together with his colleagues from Bristol have found that frozen glasses may have something common with and the patterns behind them.

Dr Fyodorov explained: “The prime numbers are the elements, or building blocks, of arithmetic. Our work provides evidence for a surprising connection between the primes and freezing in certain complex materials in Physics.”

A prime number is a whole number greater than 1 which can only be divided by 1 or itself. Primes play fundamentally important role in pure mathematics and its applications; and many mathematicians have tried to predict the patterns observed in prime numbers. One theory, called the Riemann Zeta Function is believed to be the most successful in revealing and explaining properties of primes.

The Riemann Zeta Function detects patterns in prime numbers in the same way that you might spot harmonies in music. It can be thought of as a series of peaks and troughs – which may be legitimately called a ‘landscape’ - encoding the properties of primes.

Dr Fyodorov continues: “One of important questions about the Riemann Zeta function relates to determining how large the highest of the peaks in the landscape are. In our paper we have argued that, unexpectedly, answering that question is related to the problem of characterizing the nature of the freezing transition in certain complex materials in Physics, such as glasses.

The team hope that understanding freezing could help mathematicians make progress in attacking some of the grand challenges of number theory.

Dr Fyodorov concludes: “Looking for connections between the statistical mechanics of random energy landscapes, random matrix theory, and the theory of the Riemann zeta function appeared to be a fruitful and promising approach.”

Explore further: A zero sum game

Related Stories

A zero sum game

March 21, 2011

( -- New light has been shed on the 150-year-old math puzzle known as the Riemann hypothesis, say mathematical physicists at the University of Sydney.

New Pattern Found in Prime Numbers

May 8, 2009

( -- Prime numbers have intrigued curious thinkers for centuries. On one hand, prime numbers seem to be randomly distributed among the natural numbers with no other law than that of chance. But on the other hand, ...

The sum of digits of prime numbers is evenly distributed

May 12, 2010

( -- On average, there are as many prime numbers for which the sum of decimal digits is even as prime numbers for which it is odd. This hypothesis, first made in 1968, has recently been proven by French researchers ...

Through the looking glass: physicists solve age-old problem

October 17, 2011

( -- A problem plaguing physicists across the globe for centuries has finally made a leap towards resolution. The nature of glass has stumped scientists for years but now a researcher from Queen Mary, University ...

Exploring the sound of string theory

October 13, 2011

A new collaboration between physicists and sound artists at Queen Mary, University of London, has produced a sonification of string theory equations. The project is being unveiled at a concert on 5 and 6 November, 2011.

Recommended for you

After a reset, Сuriosity is operating normally

February 23, 2019

NASA's Curiosity rover is busy making new discoveries on Mars. The rover has been climbing Mount Sharp since 2014 and recently reached a clay region that may offer new clues about the ancient Martian environment's potential ...

Study: With Twitter, race of the messenger matters

February 23, 2019

When NFL player Colin Kaepernick took a knee during the national anthem to protest police brutality and racial injustice, the ensuing debate took traditional and social media by storm. University of Kansas researchers have ...

Solving the jet/cocoon riddle of a gravitational wave event

February 22, 2019

An international research team including astronomers from the Max Planck Institute for Radio Astronomy in Bonn, Germany, has combined radio telescopes from five continents to prove the existence of a narrow stream of material, ...


Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet May 03, 2012
1 / 5 (2) May 03, 2012
Ulam rose and the Rodin coil are prime generating sieves.
1.5 / 5 (10) May 05, 2012
Would someone at PLEASE hire a mathematically-literate person to do your math section???

The Riemann Zeta function is not a theory; it's a function. You may be referring to the Riemann Hypothesis, although the writing is so bad that it's hard to tell.

And where is the reference to this paper??? I want to read it, so now I have to google it.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.