Kevin Hartnett, Quanta Magazine:

As a result of new work by Amir Ali Ahmadi and Anirudha Majumdar of Princeton University, a classical problem from pure mathematics is poised to provide iron-clad proof that drone aircraft and autonomous cars won’t crash into trees or veer into oncoming traffic.

The guarantee comes from an unlikely place — a mathematical problem known as “sum of squares.” The problem was posed in 1900 by the great mathematician David Hilbert. He asked whether certain types of equations could always be expressed as a sum of two separate terms, each raised to the power of 2.

Mathematicians settled Hilbert’s question within a few decades. Then, almost 90 years later, computer scientists and engineers discovered that this mathematical property — whether an equation can be expressed as a sum of squares — helps answer many real-world problems they’d like to solve.

Yet even as researchers realized that sum of squares could help answer many kinds of questions, they faced challenges to implementing the approach. The new work by Ahmadi and Majumdar clears away one of the biggest of those challenges — bringing an old math question squarely to bear on some of the most important technological questions of the day.

Feynman 100

The first principle is that you must not fool yourself — and you are the easiest person to fool.

You have no responsibility to live up to what other people think you ought to accomplish. I have no responsibility to be like they expect me to be. It’s their mistake, not my failing.

I would rather have questions that can’t be answered than answers that can’t be questioned.

Fall in love with some activity, and do it! Nobody ever figures out what life is all about, and it doesn’t matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough. Work as hard and as much as you want to on the things you like to do the best. Don’t think about what you want to be, but what you want to do. Keep up some kind of a minimum with other things so that society doesn’t stop you from doing anything at all.

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.

― Richard Feynman

From ScienceDaily website, source from Aalto University¹:

Perhaps the strangest prediction of quantum theory is entanglement, a phenomenon whereby two distant objects become intertwined in a manner that defies both classical physics and a “common-sense” understanding of reality. In 1935, Albert Einstein expressed his concern over this concept, referring to it as “spooky action at a distance.” […]

In work recently published in Nature, a team led by Prof. Mika Sillanpää at Aalto University in Finland has shown that entanglement of massive objects can be generated and detected.

The researchers managed to bring the motions of two individual vibrating drumheads – fabricated from metallic aluminium on a silicon chip – into an entangled quantum state. The objects in the experiment are truly massive and macroscopic compared to the atomic scale: the circular drumheads have a diametre similar to the width of a thin human hair. […]

‘The vibrating bodies are made to interact via a superconducting microwave circuit. The electromagnetic fields in the circuit are used to absorb all thermal disturbances and to leave behind only the quantum mechanical vibrations,’ says Mika Sillanpää, describing the experimental setup. […]

The results demonstrate that it is now possible to have control over large mechanical objects in which exotic quantum states can be generated and stabilized. Not only does this achievement open doors for new kinds of quantum technologies and sensors, it can also enable studies of fundamental physics in, for example, the poorly understood interplay of gravity and quantum mechanics.