Archivo: The New York Times

Alexander Grothendieck, who died on Nov. 13 at the age of 86, was a visionary who captivated the collective psyche of his peers like no one else. To say he was the No. 1 mathematician of the second half of the 20th century cannot begin to do justice to him or his body of work. Let’s resist the temptation to assign a number to a man of numbers. There are deeper lessons to be learned from this extraordinary human being and his extraordinary life.

Weapons that rely on artificial intelligence to decide what to target could become increasingly difficult to control, critics warn.

Research on the brain is surging. The United States and the European Union have launched new programs to better understand the brain. Scientists are mapping parts of mouse, fly and human brains at different levels of magnification. Technology for recording brain activity has been improving at a revolutionary pace.

Yet the growing body of data — maps, atlases and so-called connectomes that show linkages between cells and regions of the brain — represents a paradox of progress, with the advances also highlighting great gaps in understanding.

There is no “I” in team, we are told. It’s important for workers to share information and collaborate. So why would employees deliberately hide knowledge from their colleagues? And yet they do, all the time.

It has been nearly 20 years since a landmark education study found that by age 3, children from low-income families have heard 30 million fewer words than more affluent children, putting them at an educational disadvantage before they even began school. The findings led to increased calls for publicly funded prekindergarten programs and dozens of campaigns urging parents to get chatty with their children.

For the first time, and to the astonishment of many of their colleagues, researchers created what they call Alzheimer’s in a Dish — a petri dish with human brain cells that develop the telltale structures of Alzheimer’s disease. In doing so, they resolved a longstanding problem of how to study Alzheimer’s and search for drugs to treat it; the best they had until now were mice that developed an imperfect form of the disease.

Invasive species are both a fact of life and a scientific puzzle. Humans transport animals and plants thousands of miles from where they first evolved — sometimes accidentally, sometimes intentionally. Many of those species die off in their new homes. Some barely eke out an existence.

But some become ecological nightmares. In the Northeast, emerald ash borers are destroying ash trees, while Japanese barberry is blanketing forest floors, outcompeting native plants. Scientists aren’t certain why species like these are proving superior so far from home.

To giraffe researchers, the paradox of this keystone African herbivore goes beyond questions of its camouflaging coat. Giraffes may be popular, they said — a staple of zoos, corporate logos and the plush toy industry — but until recently almost nobody studied giraffes in the field.

In 1988, two determined psychology students sat in the office of an internationally renowned neuroscientist in Oslo and explained to him why they had to study with him.

Unfortunately, the researcher, Per Oskar Andersen, was hesitant, May-Britt Moser said as she and her husband, Edvard I. Moser, now themselves internationally recognized neuroscientists, recalled the conversation recently. He was researching physiology and they were interested in the intersection of behavior and physiology. But, she said, they wouldn’t take no for an answer

Statistics may not sound like the most heroic of pursuits. But if not for statisticians, a Long Island fisherman might have died in the Atlantic Ocean after falling off his boat early one morning last summer.