In this article we discuss an approach to doing this which one can call mathematical data science. In this paradigm, one studies mathematical objects collectively rather than individually, by creating datasets and doing machine learning experiments and interpretations. Broadly speaking, the field of data science is concerned with assembling, curating and analyzing large datasets, and developing methods which enable its users to not just answer predetermined questions about the data but to explore it, make simple descriptions and pictures, and arrive at novel insights. This certainly sounds promising as a tool for mathematical discovery! Mathematical data science is not new and has historically led to very important results. A famous example is the work of Birch and Swinnerton-Dyer leading to their conjecture [BSD65], based on computer generation of elliptic curves and linear regression analysis of the resulting data. However, the field really started to take off with the deep learning revolution and with the easy access to ML models provided by platforms such as Py-Torch and TensorFlow, and built into computer algebra systems such as Mathematica, Magma and SageMath.

In this paper, we conduct a data-scientific investigation of Maass forms. We find that averaging the Fourier coefficients of Maass forms with the same Fricke sign reveals patterns analogous to the recently discovered "murmuration" phenomenon, and that these patterns become more pronounced when parity is incorporated as an additional feature. Approximately 43% of the forms in our dataset have an unknown Fricke sign. For the remaining forms, we employ Linear Discriminant Analysis (LDA) to machine learn their Fricke sign, achieving 96% (resp. 94%) accuracy for forms with even (resp. odd) parity. We apply the trained LDA model to forms with unknown Fricke signs to make predictions. The average values based on the predicted Fricke signs are computed and compared to those for forms with known signs to verify the reasonableness of the predictions. Additionally, a subset of these predictions is evaluated against heuristic guesses provided by Hejhal's algorithm, showing a match approximately 95% of the time. We also use neural networks to obtain results comparable to those from the LDA model.

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Eugene Schieffelin was the eccentric ornithologist who in 1890 shipped 60 starlings from London to New York City and set them free in Central Park. The next year he released 40 more, and today there are maybe 200 million starlings in the United States and Southern Canada. As immigrants go, starlings are shrewd flyers, clever mimics, and often unwelcome. The truth is they're no more than uptown blackbirds, stocky, three-ounce grifters with iridescent blue and green plumage, along with yellow beaks and a long history of displacing woodpeckers and flycatchers, and destroying entire crops of berries and cherries. Not to mention the havoc they cause at many airports.

Traffic jams are one of the biggest inconveniences of modern life and a new study suggests that tailgating could be causing them. Keeping an equal distance between the car in front and behind could help rid the world of'phantom' snarl ups brought on by bad driving habits. Experts suggest that adapting existing cruise control technology to look backwards as well as forwards could help commuters reach their destination twice as fast. Traffic jams are one of the biggest inconveniences of modern life and new research has found that tailgating could be causing them. Keeping an equal distance between the car in front and behind could help rid the world of'phantom' snarl ups brought on by bad driving habits The study team took inspiration from an unexpected source when looking at how best to resolve the issue of bunching on the roads. A starling murmuration is a group of thousands of birds which move and flow in perfect unison.

In an era of maturing artificial intelligence technology, what does the future of the corporation look like? Will the rise of robots help us do our jobs better, or harm them? This dynamic has become a mainstay of the dialogue around AI, with voices from technology visionaries such as Bill Gates and Stephen Hawking weighing in. But at Fortune's Most Powerful Women International Summit in Hong Kong on Tuesday, leaders at two of the world's most powerful tech giants pushed back on those concerns. AI is intended to help--not hinder--the human workforce, they said.

In an era of maturing artificial intelligence technology, what does the future of the corporation look like? Will the rise of robots help us do our jobs better, or harm them? This dynamic has become a mainstay of the dialogue around AI, with voices from technology visionaries such as Bill Gates and Stephen Hawking weighing in. But at Fortune's Most Powerful Women International Summit in Hong Kong on Tuesday, leaders at two of the world's most powerful tech giants pushed back on those concerns. AI is intended to help--not hinder--the human workforce, they said.

Called a murmuration, this defensive behavior is inspiring computer programming and other applications. Flocks of acrobatic starlings have long delighted observers, from Shakespeare to the present day. The birds--sometimes by the thousands--often seem to move as one, coursing through the air at breakneck speeds, turning on an instant. We recently published video of a beautiful starling swarm in the Netherlands. So many wings can be heard flapping in that video that it's easy to get why starling swarms are called murmurations.