Researchers found mathematical structure that was thought not to exist

November 14, 2016

Researchers have found a mathematical structure that was thought not to exist. The best possible q-analogs of codes may be useful in more efficient data transmission.

In the 1970s, a group of mathematicians started developing a theory according to which codes could be presented at a level one step higher than the sequences formed by zeros and ones: mathematical subspaces named q-analogs.

For a long time, no applications were found – or were not even searched for – for the theory until ten years ago, when it was understood that they would be useful in the efficient data transmission required by modern data networks. The challenge was that, despite numerous attempts, the best possible codes described in the theory had not been found and it was therefore believed they did not even exist.

However, an international research group disagreed.

'We thought it could very well be possible,' says Professor Patric Östergård from Aalto University and smiles.

'The search was challenging because of the enormous size of the structures. Searching for them is a gigantic operation even if there is very high-level computational capacity available. Therefore, in addition to algebraic techniques and computers, we also had to use our experience and guess where to start looking, and that way limit the scope of the search.'

The perseverance was rewarded when the group consisting of five researchers found the largest possible structure described by the theory. The results were recently presented in the scientific publication Forum of Mathematics, Pi, which publishes only a dozen carefully selected articles per year.

Aalto University (Finland), Technion (Israel), University of Bayreuth (Germany), Darmstadt University of Applied Sciences (Germany), University of California San Diego (USA) and Nanyang Technological University (Singapore) participated in the study.

Green science

Although mathematical breakthroughs rarely become financial success stories immediately, many modern things we take for granted would not exist without them. For example, Boolean algebra, which has played a key role in the creation of computers, has been developed since the 19th century.

'As a matter of fact, information was green before anyone had even mentioned green alternatives,' says Östergård and laughs.

'Its basic idea is, actually, to try to take advantage of the power of the transmitter as effectively as possible, which in practice means attempting to transmit data using as little energy as possible. Our discovery will not become a product straight away, but it may gradually become part of the internet.'

Explore further: Even physicists are 'afraid' of mathematics

More information: MICHAEL BRAUN et al. EXISTENCE OF -ANALOGS OF STEINER SYSTEMS, Forum of Mathematics, Pi (2016). DOI: 10.1017/fmp.2016.5

Related Stories

Stepping beyond our 3-D world

January 18, 2016

Since the dawn of time, humans have endeavoured to unravel the laws governing the physical world around us. Over centuries we have tried to discover a Theory of Everything.

Recommended for you

Study into who is least afraid of death

March 24, 2017

A new study examines all robust, available data on how fearful we are of what happens once we shuffle off this mortal coil. They find that atheists are among those least afraid of dying... and, perhaps not surprisingly, ...

Scientists make new discovery about bird evolution

March 24, 2017

In a new paper published in National Science Review, a team of scientists from the Institute of Vertebrate Paleontology and Paleoanthropology, the Shandong Tianyu Museum of Nature, and the Nanjing Institute of Geology and ...

Mathematical framework explains diverse plant stem forms

March 23, 2017

It is well known that as plants grow, their stems and shoots respond to outside signals like light and gravity. But if plants all have similar stimuli, why are there so many different plant shapes? Why does a weeping willow ...

0 comments

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.