If reading that sentence generates a small knot in the pit of my stomach, I have to wonder, what does it feel like to say it? That's exactly what I read in a recent article (AI maths whiz creates tough new problems for humans to solve, Nature, 3 February 2021). It is a quote from Doron Zeilberger, a professor of mathematics at Rutgers University. Whatever: what prompted it is something known as the Ramanujan Machine (ramanujanmachine.com). Named, as you can imagine, for the great mathematician Srinivasa Ramanujan, the Machine will, its authors tell us, "harness your computer power to make new [mathematical] discoveries."

In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse probability distributions, that can be used to represent sparse features or data, may or not reduce the dimensionality of the item space. However, the embeddings do provide a different and often more meaningful representation of the items for a particular task at hand. Also, we give upper bounds and more precise guidelines for choosing the embedding dimension.

Thanks to its role underpinning many of the recent advances in artificial intelligence, machine learning has become of mainstream interest to many technologists and developers. Here we'll explain what it is, how you can get started plus the best tools and languages you need to develop machine learning technology. Machine learning is a subset of artificial intelligence defined by US computing pioneer Arthur Samuel in 1959 as a'field of study that gives computers the ability to learn without being explicitly programmed'. Instead, computers are'trained' to spot patterns or identify trends by feeding them large amounts of data. You may have also heard of'deep learning' or'neural networks', another subset within machine learning.

The story of self-taught mathematical wizard Srinavasa Ramanujan -- who in 1913 traveled from colonial India to the halls of Cambridge in Britain, shattering stereotypes with his theoretical ingenuity before dying tragically young at 32 -- has already inspired a number of books, plays and films. The latest cinematic treatment, writer-director Matthew Brown's "The Man Who Knew Infinity," is a reverent portrait starring ever-earnest Dev Patel as Ramanujan and Jeremy Irons as his supportive professor, G.H. Hardy. But the movie, a real-life "Good Will Hunting" of sorts, suffers from being nothing like the cultural outlier Ramanujan was: It's one more respectable British biopic following a formula. Early scenes in Madras show the twentysomething wunderkind as a shipping clerk with a young wife (Devika Bhise), filling books and writing equations in chalk on temple floors but with nobody to impress. When Trinity College shows interest, Ramanujan makes the journey, only to be met with skepticism and institutional prejudice outside the deep bond formed with the admiring, disciplined Hardy, who pushes for proofs that will show his inspirations to be merit worthy.