In March, I wrote about the successful effort, after 64 years of computational striving, of finding integer solutions to the problem x³+y³+z³=33. This equation, along with x³+y³+z³=42, were the only two equations for which neither a solution nor a proof that no solution exists had been found for the right hand side being below 100. Finding that solution meant that only the 42 problem remained unsolved.

Now 42 problem too has been solved and in a nod to Douglas Adams, Andrew Sutherland (MIT) and Andrew Booker (Bristol), the finders of the solution, announced it on webpages titled Life, the Universe and Everything.

Every cube of a whole number is within one of a multiple of nine, which means that a sum of three cubes must be within three of a multiple of nine. So numbers of the form 9𝑘+49k+4 or 9𝑘+59k+5 cannot be written as the sum of three cubes.

In 1992, Roger Heath-Brown conjectured that every other whole number can be written as the sum of three cubes, in infinitely many different ways. Mathematicians on the whole seem to have been convinced by Heath-Brown’s argument that this ought to be true – but actually finding ways to write any particular number as a sum of three cubes remains a difficult problem.

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Researchers have made astonishing progress in developing a drug that combats Ebola that has been seen as disease that carried an immediate death sentence. What is amazing is that the drug was put through clinical trials under extremely difficult circumstances because the disease causes widespread panic since it is so highly contagious and lethal.

Two Ebola drugs have proven so effective in a clinical trial that researchers will make the treatments available to anyone infected with the virus in the Democratic Republic of the Congo (DRC), where Ebola has killed nearly 1,900 people over the past year.

The survival rate for people who received either drug shortly after infection, when levels of the virus in their blood were low, was 90%.

“It’s really good news,” says Sabue Mulangu, an infectious-disease researcher at the National Institute for Biomedical Research (INRB) in Kinshasa in the DRC, and an investigator on the trial. “Now we will be able to stress to people that more than 90% of people survive if they come into the [Ebola treatment unit] early and get this treatment.”
…

“I’m in awe about what seemed to be an impossible clinical trial to run,” says Sumathi Sivapalasingam, a senior director at Regeneron. “The team did this in such a complex emergency and still, the data quality is exceptional.”

The benefits of this drug are enormous, not least because it will also help to protect those health workers who run great risks in treating the infected.

Whenever I have bought a car, I tend to choose the color purely on the basis of how it looks and, of course, on my personality. Given the dullness of the latter, it should be no surprise that my choices in the past have been either steel gray or more recently dark gray. I had never considered the issue of how color relates to crash frequency. It appears that white cars are the least prone to accidents while black cars are the most.

Black cars are notably more dangerous to drive than white cars for reasons of visibility already. A study by Monash University Accident Research Centre in Australia, which studied crash data across the country from 1987 to 2004, found that compared to white cars as a baseline, crash risk was higher for just about every other common color, including red, blue, silver, green, gray, and, yes, black. Black performed the worst by every measure: In daylight, the chance of crash is 12% higher than that of white cars. At dawn and dusk, that jumps to 47%—though your relative risk of getting into an accident at that time is lower at those hours, the authors point out. Monash’s study was consistent with at least one other, from the University of Granada, which determined that yellow was a safe alternative to white.

I was surprised that black was worse even in daytime.

My dark grey car looks black at night which means that my choice was not good as far as accidents go. To be frank, I just do not like white or any of the other colors so I may just have to stomach the increased risk and hope that careful driving partially compensates.

According to a large-scale longitudinal study, people who are optimistic tended to live longer than those who are not, and it even increased the chances of ‘exceptional longevity’, the term used for people who live to be 85 or more.

The team split about 70,000 women into four equally sized groups, based on their scores for optimism. They then compared lifespan for the most optimistic with the least, taking into account factors including age, sex, race, education, depression and other health conditions present at the outset.

The results show the most optimistic group of women had a lifespan almost 15% longer than the least.

Similar results were seen in men, even though optimism was measured slightly differently. When the team compared the fifth of men boasting the highest optimism scores with the least optimistic, they found the most positive men had lifespans almost 11% longer.

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Recently it seems to have become fashionable among some scientists, mainly physicists, to harshly disparage philosophy in general and the philosophy and sociology of science in particular. This was not so in times gone by, especially during the time of ferment at the dawn of the twentieth century with the development of theories of relativity and quantum mechanics. While they were developing various successful computational techniques, people struggled to figure out what these theories meant because they seemed to defy our intuitions of how matter behaved at very small scales and when it was traveling very fast.
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Tom Scott explains what is known as the Two Generals problem in computer information theory, something that I had never heard of before, and how it can have real world implications, such as a recent case where the lack of awareness of the need to address this problem led to a food delivery company sending multiple orders to the same addresses.

All life on Earth is carbon-based which of course makes this molecule of considerable interest for scientists. A carbon atom has 6 electrons which means that it has four electrons in the valence shell and results in it being able to form different kinds of chains and combinations, such as buckminsterfullerenes (often shortened to just ‘fullerenes’, more popularly known as ‘buckyballs’) that consists of 60 carbon atoms in the shape of a geodesic sphere.
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