Archive for the ‘mathematics’ category: Page 22

Jun 28, 2023

Mathematicians Discover The Ninth Dedekind Number, After 32 Years of Searching

Posted by in categories: mathematics, supercomputing

Undeterred after three decades of looking, and with some assistance from a supercomputer, mathematicians have finally discovered a new example of a special integer called a Dedekind number.

Only the ninth of its kind, or D, it is calculated to equal 286 386 577 668 298 411 128 469 151 667 598 498 812 366, if you’re updating your own records. This 42 digit monster follows the 23-digit D discovered in 1991.

Grasping the concept of a Dedekind number is difficult for non-mathematicians, let alone working it out. In fact, the calculations involved are so complex and involve such huge numbers, it wasn’t certain that D would ever be discovered.

Jun 28, 2023

Supercomputer reveals ninth Dedekind number, solving decades-old maths problem

Posted by in categories: mathematics, supercomputing

The first eight Dedekind numbers have been known to us, but the ninth one has remained elusive — until now.

Mathematics is a fascinating subject with many unsolved mysteries, such as the Riemann hypothesis, Fermat’s last theorem, Goldbach’s conjecture, and Dedekind’s numbers. The Dedekind numbers were first discovered in the 19th century by Richard Dedekind and have interested mathematicians ever since.

The first eight Dedekind numbers have been known to us, but the ninth one has remained elusive until now. KU Leuven and Paderborn University scientists have solved a decades-old mathematics problem by computing the ninth Dedekind number.

Jun 27, 2023

Recruiting Editorial Board Members and Topical Advisory Panel Members for Section “Mathematical Modelling and Numerical Simulation of Combustion and Fire”

Posted by in categories: futurism, mathematics

We are currently recruiting Editorial Board Members (EBMs) and Topical Advisory Panel Members (TAPMs) for this Section. If you are an active researcher in this field and are passionate about publishing cutting-edge research, please contact us by email at [email protected].

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Continue reading “Recruiting Editorial Board Members and Topical Advisory Panel Members for Section ‘Mathematical Modelling and Numerical Simulation of Combustion and Fire’” »

Jun 27, 2023

Ninth Dedekind number discovered: Scientists solve long-known problem in mathematics

Posted by in categories: mathematics, supercomputing

Making history with 42 digits, scientists at Paderborn University and KU Leuven have unlocked a decades-old mystery of mathematics with the so-called ninth Dedekind number.

Experts worldwide have been searching for the value since 1991. The Paderborn scientists arrived at the exact sequence of numbers with the help of the Noctua supercomputer located there. The results will be presented in September at the International Workshop on Boolean Functions and their Applications (BFA) in Norway.

What started as a master’s thesis project by Lennart Van Hirtum, then a computer science student at KU Leuven and now a research associate at the University of Paderborn, has become a huge success. The scientists join an illustrious group with their work. Earlier numbers in the series were found by mathematician Richard Dedekind himself when he defined the problem in 1,897, and later by greats of early computer science such as Randolph Church and Morgan Ward. “For 32 years, the calculation of D was an open challenge, and it was questionable whether it would ever be possible to calculate this number at all,” Van Hirtum says.

Jun 27, 2023

Six Degrees of Connection: A Mathematical Take on Social Ties

Posted by in categories: biotech/medical, mathematics

Summary: Scientists used mathematics to explain the social phenomenon of six degrees of separation.

Their work suggests that the balance between the cost and benefit of maintaining social connections shapes the global human social network. According to their findings, individual efforts to optimize their social connections result in an average of six steps between any two people.

Continue reading “Six Degrees of Connection: A Mathematical Take on Social Ties” »

Jun 26, 2023

Mathematicians Discover New Way to Predict Structure in Graphs

Posted by in category: mathematics

In new work on graphs’ hidden structure, mathematicians probe the limits of randomness.

Jun 24, 2023

Alan Turing and the Limits of Computation

Posted by in categories: biological, mathematics, robotics/AI

Note: June 23 is Alan Turing’s birth anniversary.

Alan Turing wore many scientific hats in his lifetime: a code-breaker in World War II, a prophetic figure of artificial intelligence (AI), a pioneer of theoretical biology, and a founding figure of theoretical computer science. While the former of his roles continue to catch the fancy of popular culture, his fundamental contribution to the development of computing as a mathematical discipline is possibly where his significant scientific impact persists to date.

Jun 22, 2023

Chinese researchers used a quantum processor to simulate black hole-like conditions

Posted by in categories: cosmology, mathematics, quantum physics, supercomputing

They created a quantum system with properties analogous to black holes.

A collaborative effort from research teams across multiple organizations in China was successful in using quantum computing technology to test Hawking Radiation, the theory proposed by renowned physicist Stephen Hawking, the South China Morning Post.

Quantum computing is a complex field that involves using mathematics, computer science, and physics to solve complex problems. Interesting Engineering recently reported how a quantum computer recently beat a conventional supercomputer at complex math.

Jun 18, 2023

Smart drugs fall short as cognitive function enhancers

Posted by in categories: biotech/medical, information science, mathematics, neuroscience


Many everyday tasks can fall under the mathematical class of “hard” problems. Typically, these problems belong to the complexity class of nondeterministic polynomial (NP) hard. These tasks require systematic approaches (algorithms) for optimal outcomes. In the case of significant complex problems (e.g., the number of ways to fix a product or the number of stops to be made on a delivery trip), more computations are required, which rapidly outgrows cognitive capacities.

A recent Science Advances study investigated the effectiveness of three popular smart drugs, namely, modafinil (MOD), methylphenidate (MPH), and dextroamphetamine (DEX), against the difficulty of real-life daily tasks, i.e., the 0–1 knapsack optimization problem (“knapsack task”). A knapsack task is basically a combinatorial optimization task, the class of NP-time challenging problems.

Jun 16, 2023

Flow Proof Helps Mathematicians Find Stability in Chaos

Posted by in category: mathematics

A series of new papers describes how to fully characterize key dynamical systems with relatively little data.

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