Trustworthiness matters: Building equitable and ethical science.

Trustworthy science requires research practices that center issues of ethics, equity, and inclusion. We announce the Leadership in the Equitable and Ethical Design (LEED) of Science, Technology, Mathematics, and Medicine (STEM) initiative to create best practices for integrating ethical expertise and fostering equitable collaboration.

What does Juneteenth mean in STEMM?

Juneteenth commemorates the freeing of the last large group of enslaved people in 1865 at the end of the American Civil War. We asked several Black scientists what Juneteenth means to them in the context of science, technology, engineering, mathematics, and medicine (STEMM)? Their answers run the emotional gamut.

STEM Pride: Perspectives from transgender, nonbinary, and genderqueer scientists.

In celebration of Pride Month, we asked transgender, genderqueer, and nonbinary scientists to tell us about what fascinates them, their ambitions and achievements, and how their gender identities have shaped their experiences in STEM. We owe a special thanks to 500 Queer Scientists (https://500queerscientists.com/), whose network and efforts at increasing LGBTQ+ scientists' visibility made this article possible.

Unrealized potential from smaller institutions: Four strategies for advancing STEM diversity.

Diversity within science, technology, engineering, and mathematics (STEM) remains disturbingly low. Relative to larger, highly funded universities, smaller schools harbor more diverse student demographics and more limited resources. Here, we propose four strategies leveraging the unique advantages of smaller institutions to advance underrepresented scholars along STEM pathways.

Active learning-based STEM education for in-person and online learning.

The COVID-19 global pandemic has forced the higher education sector to transition to an uncharted remote-learning format. This offers an opportunity to adopt active learning, which increases students' performance compared to lectures, narrows achievement gaps for underrepresented students, and promotes equity and inclusivity, as the basis of STEM education.

Patching the Leaks: Revitalizing and Reimagining the STEM Pipeline.

We identify problematic areas throughout the Science, Technology, Engineering and Mathematics (STEM) pipeline that perpetuate racial disparities in academia. Distinct ways to curtail these disparities include early exposure and access to resources, supportive mentoring networks and comprehensive training programs specifically for racially minoritized students and trainees at each career stage. These actions will revitalize the STEM pipeline.

Solving olympiad geometry without human demonstrations.

Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning1-4, owing to their reputed difficulty among the world's best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges1,5, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004.

Mass cytometry: blessed with the curse of dimensionality.

Immunologists are being compelled to develop new high-dimensional perspectives of cellular heterogeneity and to determine which applications best exploit the power of mass cytometry and associated multiplex approaches.

Building an allocentric travelling direction signal via vector computation.

Many behavioural tasks require the manipulation of mathematical vectors, but, outside of computational models1-7, it is not known how brains perform vector operations. Here we show how the Drosophila central complex, a region implicated in goal-directed navigation7-10, performs vector arithmetic. First, we describe a neural signal in the fan-shaped body that explicitly tracks the allocentric travelling angle of a fly, that is, the travelling angle in reference to external cues. Past work has identified neurons in Drosophila8,11-13 and mammals14 that track the heading angle of an animal referenced to external cues (for example, head direction cells), but this new signal illuminates how the sense of space is properly updated when travelling and heading angles differ (for example, when walking sideways). We then characterize a neuronal circuit that performs an egocentric-to-allocentric (that is, body-centred to world-centred) coordinate transformation and vector addition to compute the allocentric travelling direction. This circuit operates by mapping two-dimensional vectors onto sinusoidal patterns of activity across distinct neuronal populations, with the amplitude of the sinusoid representing the length of the vector and its phase representing the angle of the vector. The principles of this circuit may generalize to other brains and to domains beyond navigation where vector operations or reference-frame transformations are required.

Guiding STEM graduate students to better speaking skills.

Training to enhance the effectiveness of oral presentations is often neglected in science, technology, engineering, and mathematics (STEM) fields. In this article, we summarize our experience of teaching a semester-long class in speaking skills to STEM graduate students and advocate for the critical importance of these skills to professional success.

Overcoming gender bias in STEM.

Despite prevalent diversity and inclusion programs in STEM, gender biases and stereotypes persist across educational and professional settings. Recognizing this enduring bias is crucial for achieving transformative change on gender equity and can help orient policy toward more effective strategies to address ongoing disparities.

Developing a predictive science of the biosphere requires the integration of scientific cultures.

Increasing the speed of scientific progress is urgently needed to address the many challenges associated with the biosphere in the Anthropocene. Consequently, the critical question becomes: How can science most rapidly progress to address large, complex global problems? We suggest that the lag in the development of a more predictive science of the biosphere is not only because the biosphere is so much more complex, or because we do not have enough data, or are not doing enough experiments, but, in large part, because of unresolved tension between the three dominant scientific cultures that pervade the research community. We introduce and explain the concept of the three scientific cultures and present a novel analysis of their characteristics, supported by examples and a formal mathematical definition/representation of what this means and implies. The three cultures operate, to varying degrees, across all of science. However, within the biosciences, and in contrast to some of the other sciences, they remain relatively more separated, and their lack of integration has hindered their potential power and insight. Our solution to accelerating a broader, predictive science of the biosphere is to enhance integration of scientific cultures. The process of integration-Scientific Transculturalism-recognizes that the push for interdisciplinary research, in general, is just not enough. Unless these cultures of science are formally appreciated and their thinking iteratively integrated into scientific discovery and advancement, there will continue to be numerous significant challenges that will increasingly limit forecasting and prediction efforts.

Evaluating language models for mathematics through interactions.

There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs relies on static pairs of inputs and outputs; this is insufficient for making an informed decision about which LLMs are best to use in an interactive setting, and how that varies by setting. Static assessment therefore limits how we understand language model capabilities. We introduce CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We conduct a study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analyzing MathConverse, we derive a taxonomy of human query behaviors and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, among other findings. Further, we garner a more granular understanding of GPT-4 mathematical problem-solving through a series of case studies, contributed by experienced mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models that communicate uncertainty, respond well to user corrections, and can provide a concise rationale for their recommendations, may constitute better assistants. Humans should inspect LLM output carefully given their current shortcomings and potential for surprising fallibility.

Moms in Proteomics: building a supportive and unified community together.

There is a growing need to recognize, support, and promote diversity within scientific disciplines. Moms in Proteomics was founded to connect mothers in proteomics, a field exemplifying the constituent elements of science, technology, engineering, and math (STEM) from academia to industry, share stories of successes and challenges, and build a community of mothers in highly productive and influential careers.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age.

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

Array programming with NumPy.

Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

Emergent programmable behavior and chaos in dynamically driven active filaments.

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.

Evaluating the impact of short educational videos on the cortical networks for mathematics.

Many teaching websites, such as the Khan Academy, propose vivid videos illustrating a mathematical concept. Using functional magnetic resonance imaging, we asked whether watching such a video suffices to rapidly change the brain networks for mathematical knowledge. We capitalized on the finding that, when judging the truth of short spoken statements, distinct semantic regions activate depending on whether the statements bear on mathematical knowledge or on other domains of semantic knowledge. Here, participants answered such questions before and after watching a lively 5-min video, which taught them the rudiments of a new domain. During the video, a distinct math-responsive network, comprising anterior intraparietal and inferior temporal nodes, showed intersubject synchrony when viewing mathematics course rather than control courses in biology or law. However, this experience led to minimal subsequent changes in the activity of those domain-specific areas when answering questions on the same topics a few minutes later. All taught facts, whether mathematical or not, led to domain-general repetition enhancement, particularly prominent in the cuneus, posterior cingulate, and posterior parietal cortices. We conclude that short videos do not suffice to induce a meaningful lasting change in the brain's math-responsive network, but merely engage domain-general regions possibly involved in episodic short-term memory.

Understanding immunity in a tissue-centric context: Combining novel imaging methods and mathematics to extract new insights into function and dysfunction.

A central question in immunology is what features allow the immune system to respond in a timely manner to a variety of pathogens encountered at unanticipated times and diverse body sites. Two decades of advanced and static dynamic imaging methods have now revealed several major principles facilitating host defense. Suborgan spatial prepositioning of distinct cells promotes time-efficient interactions upon pathogen sensing. Such pre-organization also provides an effective barrier to movement of pathogens from parenchymal tissues into the blood circulation. Various molecular mechanisms maintain effective intercellular communication among otherwise rapidly moving cells. These and related discoveries have benefited from recent increases in the number of parameters that can be measured simultaneously in a single tissue section and the extension of such multiplex analyses to 3D tissue volumes. The application of new computational methods to such imaging data has provided a quantitative, in vivo context for cell trafficking and signaling pathways traditionally explored in vitro or with dissociated cell preparations. Here, we summarize our efforts to devise and employ diverse imaging tools to probe immune system organization and function, concluding with a commentary on future developments, which we believe will reveal even more about how the immune system operates in health and disease.

Developing cultural humility in immunology and STEMM mentoring.

Cultural humility allows a better understanding and appreciation of others, as well as fostering positive interactions with different kinds of individuals. Here, we discuss the difficulties faced by persons excluded because of their ethnicity or race (PEERs) in immunology and science, technology, engineering, mathematics, and medicine (STEMM), as well as the importance of cultural humility in research and academia.