Karen Uhlenbeck made history being the first woman recipient of the Abel Prize. She received the award for "her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics [which have] "led to some of the most dramatic advances in mathematics in the last 40 years." The news was covered in media worldwide, and was apt this Women's History Month. Read Tony Phillips' Take and Media Coverage of Math here.
(Photo: Andrea Kane/Institute for Advanced Study.)
"Collective memory is acknowledged to be a combination of two distinct processes: communicative memory, normally sustained by the oral transmission of information, and cultural memory, which is sustained by the physical recording of information." This observation is the basis for the discovery that "the attention received by cultural products decays following a universal biexponential function." The work is reported in "The universal decay of collective memory and attention" (Nature Human Behaviour 3, 8291, January, 2019). The authors, a team of five led by Cristan Candia and César Hildago (MIT) "use data on the citation of academic articles and patents, and on the online attention received by songs, movies and biographies, to describe the temporal decay of the attention received by cultural products."
The authors make some initial simplifying assumptions. "First, we assume that the current attention, $S(t)$, of a cultural product is the sum of the attention it garners from both communicative memory $u$ and cultural memory $v$. Hence, at any given time $S(t)=u(t)+v(t)$. Second, we assume that communicative and cultural memory decay, in relative terms, independently with decay rates $p+r$ for communicative memory and $q$ for cultural memory, and that information flows from communicative memory to cultural memory at a rate $r$. "
This model leads to a system of linear firstorder differential equations for $u(t)$ and $v(t)$ which, with initial conditions $u(0)=N$ and $v(0)=0$, gives $$u(t)=Ne^{(p+r)t}~~~~~v(t)=\frac{Nr}{p+rq}(e^{qt}e^{(p+r)t})$$ $$S(t)=\frac{Nr}{p+rq}[(pq)e^{(p+r)t} +re^{qt}].$$
The authors tested their model against various realworld "cultural products," e.g. American Physical Society papers (metric: citations received in the past six months), popular music (Spotify popularity and Last.fm play counts) and biographies of "highly performing athletes in tennis, basketball and the Olympics" (Wikipedia page views); they found that their model was "statistically better at explaining the empirically observed decay of attention than the [...] functions used in the previous literature." They add: "More importantly, in several of these empirical curves, the shoulder of the biexponential curve is clearly visible, allowing the model to help to unveil the point at which cultural memory takes over communicative memory."
The Washington Post's Morning Mix (February 26, 2019) spread the news: "Hello, hive mind: Bees can do basic arithmetic, a new study finds." Isaac StanleyBecker starts: "The ovalshaped brain of a honeybee is roughly the size of a single sesame seed. It contains fewer than 1 million neurons, while the human brain contains 100 billion. A team of entomologists is asking what all those extra nerve cells are good for after finding that bees can do the kind of fundamental mathematics once thought to distinguish humans and the primate animals they most closely resemble."
Quite a few animals can count but bees, as reported in Science Advances, are good at addition and subtraction, too. Researchers at the Royal Melbourne Institute of Technology trained 14 bees to associate blue with addition ($+1$) and yellow with subtraction ($1$). After some 100 trials, they were tested: At the entrance to a Ymaze was an image of $k$ (2 to 5) shapes (circles, squares, triangles or diamonds) in either yellow or blue on a black background. Inside the "decision chamber" they had to choose between two images of that color: in the blue mode, one had $k+1$ of the same shapes; in the yellow mode, one had $k1$ of them; in either case the other had a different number, same shape, same color.






StanleyBecker: "Each bee performed four tests, each consisting of 10 trips through the maze. In each test, conducted without punishments or rewards, the bees performed significantly better than chance. [...] The discovery casts doubt on the idea that numerical understanding is innate to humans, who are separated from honeybees by more than 400 million years of evolution, as the paper notes. The result suggests instead that bees, nonhuman animals and preverbal people may each be 'biologically tuned for complex numerical tasks,' a capacity honed through the struggle for survival in 'complex environments that have forced them to use numbers and quantify.'" The interior quotes are from Scarlett Howard, the lead author and a postdoctoral fellow at the CNRS, who added: "We're not the only sophisticated ones."
On March 19, 2019 the Norwegian Academy of Science and Letters announced that the Abel Prize for 2019 was awarded to to "Karen Keskulla Uhlenbeck of the University of Texas at Austin, USA" for "her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics." The Abel Prize is always a big deal; Uhlenbeck's being the first woman so honored made it especially newsworthy. Although some papers, like the Washington Post and The Guardian, just relayed the feed from the Associated Press, others went the extra mile.
[None of these reports mentions it, but work by Karen Uhlenbeck and Jonathan Sacks ("The Existence of Minimal Immersions of 2Spheres," Ann. Math. 113 124, 1981) provides an essential element of the recent proof of the Poincaré conjecture. See Terence Tao's blog on the topic. TP]
Tony Phillips
Stony Brook University
tony at math.sunysb.edu
Archive of Reviews: Books, plays and films about mathematics
Citations for reviews of books, plays, movies and television shows that are related to mathematics (but are not aimed solely at the professional mathematician). The alphabetical list includes links to the sources of reviews posted online, and covers reviews published in magazines, science journals and newspapers since 1996