The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities -- which correspond to our intuition and habitual behaviors -- but still lacks something important regarding system 2 abilities -- which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.

AlphaTensor was designed to perform matrix multiplications, but the same approach could be used to tackle other mathematical challenges.Credit: DeepMind An artificial intelligence (AI) developed by machine-learning company DeepMind in London has tackled a type of calculation called matrix multiplication. The system -- called AlphaTensor -- leverages the skills that DeepMind's game-playing AIs use to beat human players at games such as Go and chess. Matrix multiplication is a widely used mathematical technique that involves multiplying numbers arranged in grids, or matrices, that might represent sets of pixels in images, air conditions in a weather model or the internal workings of an artificial neural network. AlphaTensor broke ground by finding shortcuts to solve these problems with fewer steps (A. The same general approach could have applications in other kinds of mathematical operation, its developers say, such as decomposing complex waves or other mathematical objects into simpler ones.

An unprecedented number of first-time investigators have secured viewing time on NASA's Hubble Space Telescope in the years since the agency overhauled the application process to reduce systemic biases. In 2018, NASA changed the way it evaluates requests for observing time on Hubble by introducing a'double-blind' system, in which neither the applicants nor the reviewers assessing their proposals know each other's identities. All the agency's other telescopes followed suit the next year. The move was intended to cut discrimination on the basis of gender and other factors, including bias against scientists who are at small research institutions, or who haven't received NASA grants before. Data from the Space Telescope Science Institute (STScI) in Baltimore, Maryland, which manages Hubble, show that since the change was introduced, more first-time principal investigators have been securing viewing time on Hubble. How do mathematicians come up with new theories?

Machines are getting better at maths – artificial intelligence has learned to solve university-level calculus problems in seconds. François Charton and Guillaume Lample at Facebook AI Research trained an AI on tens of millions of calculus problems randomly generated by a computer. The problems were mathematical expressions that involved integration, a common technique in calculus for finding the area under a curve. To find solutions, the AI used natural language processing (NLP), a computational tool commonly used to analyse language. This works because the mathematics in each problem can be thought of as a sentence, with variables, normally denoted x, playing the role of nouns and operations, such as finding the square root, playing the role of verbs.