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We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and theoretical physics in 2017, we summarize how this emerging field has grown over the past years, and show how various machine-learning algorithms can help with pattern detection across disciplines in the mathematical sciences. At the heart is the question how does AI help with theoretical discovery, and the implications for the future of mathematics.

Information about millions of people is collected for behavioural targeting, a type of marketing that involves tracking people's online behaviour for targeted advertising. It is hotly debated whether data protection law applies to behavioural targeting. Many behavioural targeting companies say that, as long as they do not tie names to data they hold about individuals, they do not process any personal data, and that, therefore, data protection law does not apply to them. European Data Protection Authorities, however, take the view that a company processes personal data if it uses data to single out a person, even if it cannot tie a name to these data. This paper argues that data protection law should indeed apply to behavioural targeting. Companies can often tie a name to nameless data about individuals. Furthermore, behavioural targeting relies on collecting information about individuals, singling out individuals, and targeting ads to individuals. Many privacy risks remain, regardless of whether companies tie a name to the information they hold about a person. A name is merely one of the identifiers that can be tied to data about a person, and it is not even the most practical iden

This is a slightly edited translation of a paper in Dutch which appeared in Nieuw Archief voor Wiskunde (5) 25 (2024), No.2, 87-90 on the occasion of I.G. Macdonald's death in 2023, and aimed at a very broad mathematical audience. First we review some of Macdonald's most important older results. Then we focus on the period 1985-1995 when Macdonald often visited the Netherlands and there was much interaction between his work, notably the Macdonald polynomials, and the work by the authors. We end with some glimpses about Macdonald as a person.

A camel can carry one banana at a time on its back. It is on a diet and therefore can only have one banana at a time in its stomach. As soon as it has eaten a banana it walks a mile and then it needs a new banana (in order to be able to continue its itinerary). Let there be a stock of N bananas at the border of the desert. How far can the camel penetrate into the desert, starting at this point? (Of course it can form new stocks with transported bananas.)

We present a novel physical-world attack on autonomous vehicle (AV) lane detection systems that leverages negative shadows -- bright, lane-like patterns projected by passively redirecting sunlight through occluders. These patterns exploit intensity-based heuristics in modern lane detection (LD) algorithms, causing AVs to misclassify them as genuine lane markings. Unlike prior attacks, our method is entirely passive, power-free, and inconspicuous to human observers, enabling legal and stealthy deployment in public environments. Through simulation, physical testbed, and controlled field evaluations, we demonstrate that negative shadows can cause up to 100% off-road deviation or collision rates in specific scenarios; for example, a 20-meter shadow leads to complete off-road exits at speeds above 10 mph, while 30-meter shadows trigger consistent lane confusion and collisions. A user study confirms the attack's stealthiness, with 83.6% of participants failing to detect it during driving tasks. To mitigate this threat, we propose Luminosity Filter Pre-processing, a lightweight defense that reduces attack success by 87% through brightness normalization and selective filtering. Our finding

Due to their ease of use and high accuracy, Word2Vec (W2V) word embeddings enjoy great success in the semantic representation of words, sentences, and whole documents as well as for semantic similarity estimation. However, they have the shortcoming that they are directly extracted from a surface representation, which does not adequately represent human thought processes and also performs poorly for highly ambiguous words. Therefore, we propose Semantic Concept Embeddings (CE) based on the MultiNet Semantic Network (SN) formalism, which addresses both shortcomings. The evaluation on a marketing target group distribution task showed that the accuracy of predicted target groups can be increased by combining traditional word embeddings with semantic CEs.

On 13-01-2024 the annual wintersymposium of the Koninlijk Wiskundig Genootschap (KWG) was held in the academiegebouw in Utrecht. The symposium had the theme ``inzichtelijk abstract''. Thomas Rot gave a lecture on his favourite theorem from topology. This article is a written account of this lecture. Audience comprised mostly of high school teachers and that is also the target audience of this article. The slides (in Dutch), which contain more pictures, are available~[8].

A brief history of planar aperiodic tile sets is presented, starting from the Domino Problem proposed by Hao Wang in 1961. We provide highlights that led to the discovery of the Taylor--Socolar aperiodic monotile in 2010 and the Hat and Spectre aperiodic monotiles in 2023. The Spectre tile is an amazingly simple monotile; a single tile whose translated and rotated copies tile the plane but only in a way that lacks any translational periodicity. We showcase this breakthrough discovery through the 60$+$ years that aperiodic tile sets have been considered.

Any rational number can be written as the sum of distinct unit fractions. In this survey paper we review some of the many interesting questions concerning such 'Egyptian fraction' decompositions, and recent progress concerning them.

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et al., l.c.).

The VEDLIoT project targets the development of energy-efficient Deep Learning for distributed AIoT applications. A holistic approach is used to optimize algorithms while also dealing with safety and security challenges. The approach is based on a modular and scalable cognitive IoT hardware platform. Using modular microserver technology enables the user to configure the hardware to satisfy a wide range of applications. VEDLIoT offers a complete design flow for Next-Generation IoT devices required for collaboratively solving complex Deep Learning applications across distributed systems. The methods are tested on various use-cases ranging from Smart Home to Automotive and Industrial IoT appliances. VEDLIoT is an H2020 EU project which started in November 2020. It is currently in an intermediate stage with the first results available.

This paper is an exposition, written for the Nieuw Archief voor Wiskunde, about the two recent breakthrough results in the theory of sphere packings. It includes an interview with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Maryna Viazovska.

NASA's Perseverance rover has reached an impressive new milestone on Mars, completing the equivalent of a full marathon by driving 26。2 miles (42。195 kilometers) across the Red Planet

K2-18b is one of the most promising worlds for the search for extraterrestrial life, so astronomers conducted an unusually powerful radio survey using both the VLA and MeerKAT telescopes。 Advanced software analyzed millions of signals, filtering out Earth-based interference and other false positives。 No convincing artificial radio transmissions wer

Water’s odd behavior becomes even more dramatic when it is supercooled, but scientists have struggled to compare the many different ways of describing its microscopic structure。 Researchers at the University of Osaka used an AI model trained on computer simulations to evaluate 16 different structural descriptors。 The system identified the most effe

A decades-old puzzle about water has finally been unraveled。 Researchers found that water trapped in tiny nanoscale spaces is not inherently more reactive。 Instead, the intense pressures created inside these microscopic gaps explain most of the effect, while the surrounding material can further enhance water's chemistry if it interacts with the rea

A centimeter-sized crystal has revealed clear signs of quantum entanglement, showing that large, everyday objects can display surprisingly deep quantum behavior。 The discovery could help solve the mystery of strange metals while opening new possibilities for ultra-precise quantum sensors and other advanced technologies

Scientists have rewritten the story of gallium after discovering that its unusual atomic bonds re-form at high temperatures, contradicting decades of accepted theory。 The finding changes how researchers explain why the metal melts so easily and behaves unlike almost any other metal。 Beyond solving a long-standing scientific mystery, the work could

A newly developed material can control and "program" heat, allowing it to direct thermal radiation, switch modes, and remember its settings without continuous power。 The innovation could lead to smarter infrared sensors, better energy technologies, and memory devices that use light and heat instead of electrical charges