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Scientists from the Universities of Paderborn and Leuven solve long-known problem in mathematics.

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.

As Nvidia’s recent surge in market capitalization clearly demonstrates, the AI industry is in desperate need of new hardware to train large language models (LLMs) and other AI-based algorithms. While server and HPC GPUs may be worthless for gaming, they serve as the foundation for data centers and supercomputers that perform highly parallelized computations necessary for these systems.

When it comes to AI training, Nvidia’s GPUs have been the most desirable to date. In recent weeks, the company briefly achieved an unprecedented $1 trillion market capitalization due to this very reason. However, MosaicML now emphasizes that Nvidia is just one choice in a multifaceted hardware market, suggesting companies investing in AI should not blindly spend a fortune on Team Green’s highly sought-after chips.

The AI startup tested AMD MI250 and Nvidia A100 cards, both of which are one generation behind each company’s current flagship HPC GPUs. They used their own software tools, along with the Meta-backed open-source software PyTorch and AMD’s proprietary software, for testing.

In a significant leap for the field of quantum computing, Google has reportedly engineered a quantum computer that can execute calculations in mere moments that would take the world’s most advanced supercomputers nearly half a century to process.

The news, reported by the Daily Telegraph, could signify a landmark moment in the evolution of this emerging technology.

Quantum computing, a science that takes advantage of the oddities of quantum physics, remains a fast-moving and somewhat contentious field.

Google claims to have proved its supremacy over conventional machines with new quantum computer.

Google has developed a quantum computer that instantly makes calculations that would take the best existing supercomputers 47 years, in a breakthrough meant to establish beyond doubt that the experimental machines can outperform conventional rivals.

A paper from researchers at Google published online claims that the company’s latest technology is “beyond the capabilities of existing classical supercomputers”.

The concept of a computational consciousness and the potential impact it may have on humanity is a topic of ongoing debate and speculation. While Artificial Intelligence (AI) has made significant advancements in recent years, we have not yet achieved a true computational consciousness that can replicate the complexities of the human mind.

It is true that AI technologies are becoming more sophisticated and capable of performing tasks that were previously exclusive to human intelligence. However, there are fundamental differences between Artificial Intelligence and human consciousness. Human consciousness is not solely based on computation; it encompasses emotions, subjective experiences, self-awareness, and other aspects that are not yet fully understood or replicated in machines.

The arrival of advanced AI systems could certainly have transformative effects on society and our understanding of humanity. It may reshape various aspects of our lives, from how we work and communicate to how we approach healthcare and scientific discoveries. AI can enhance our capabilities and provide valuable tools for solving complex problems.

However, it is important to consider the ethical implications and potential risks associated with the development of AI. Ensuring that AI systems are developed and deployed responsibly, with a focus on fairness, transparency, and accountability, is crucial.

Continue reading “AI and Humanity's Future” »

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.

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.

Quantum computing could revolutionize our world. For specific and crucial tasks, it promises to be exponentially faster than the zero-or-one binary technology that underlies today’s machines, from supercomputers in laboratories to smartphones in our pockets. But developing quantum computers hinges on building a stable network of qubits—or quantum bits—to store information, access it and perform computations.

Yet the qubit platforms unveiled to date have a common problem: They tend to be delicate and vulnerable to outside disturbances. Even a stray photon can cause trouble. Developing fault-tolerant qubits—which would be immune to external perturbations—could be the ultimate solution to this challenge.

A team led by scientists and engineers at the University of Washington has announced a significant advancement in this quest. In a pair of papers published June 14 in Nature and June 22 in Science, the researchers report that in experiments with flakes of semiconductor materials—each only a single layer of atoms thick—they detected signatures of “fractional quantum anomalous Hall” (FQAH) states.

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.