A Severe Misalignment of AI in Mathematics
A Severe Misalignment of AI in Mathematics is a declaration about artificial intelligence and mathematical research, published on September 11, 2026 at mathandai.org with 25 initial signatories
Mathematics
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Showing 1-60 of 82 articles
AI Co-Mathematician
AI Co-Mathematician is an interactive, agentic research system built by Google DeepMind to help professional mathematicians work on open-ended research problems.
AIME (American Invitational Mathematics Examination)
The American Invitational Mathematics Examination (AIME) is a 15-question, 3-hour mathematics competition for high school students in the United States and Canada
Ada Lovelace
Augusta Ada King, Countess of Lovelace (born Augusta Ada Byron; 10 December 1815 to 27 November 1852), usually called Ada Lovelace
AlphaGeometry 2
AlphaGeometry 2 (often abbreviated AG2) is a neuro-symbolic artificial intelligence system built by Google DeepMind that solves Olympiad-level Euclidean geometry problems by pairing a Gemini-based language…
AlphaProof Nexus
AlphaProof Nexus is a formal proof search system from Google DeepMind that pairs a general-purpose language model with the Lean proof assistant in an agentic loop, submitting each candidate proof step to the…
AlphaTensor
AlphaTensor is an artificial-intelligence system from DeepMind that uses deep reinforcement learning to discover faster algorithms for matrix multiplication.
Automatic Differentiation
Automatic differentiation (abbreviated AD, also called algorithmic differentiation, autodiff, or autograd) is a family of techniques for computing exact derivatives of a function specified by a computer program
AxiomProver
AxiomProver is an automated theorem-proving system developed by Axiom Math. The company describes it as an autonomous multi-agent system for Lean 4 that translates mathematical tasks into formal statements and…
Bayes' theorem
Bayes' theorem (also called Bayes' rule or Bayes' law) is a fundamental theorem of probability theory that describes how to update the probability of a hypothesis given new evidence.
Bayesian statistics
Bayesian statistics is a statistical paradigm in which probability expresses a degree of belief that is updated as evidence arrives, using Bayes' theorem.
Bellman Equation
The Bellman equation is a recursive formula stating that the value of a state equals the immediate reward received there plus the discounted value of the next state
Bias (Math) or Bias Term
The bias term is a learnable additive constant b added to the weighted sum of a neuron's inputs before an activation function is applied, computed as $$z = w \cdot x + b$$.
Broadcasting
Broadcasting is the set of rules that lets element-wise operations (addition, subtraction, multiplication, division) act on arrays or tensors of different but compatible shapes by virtually stretching the…
Control theory
Control theory is the mathematical and engineering discipline concerned with designing and analysing systems that achieve desired behaviour through measurement and feedback.
Convergence
Convergence in machine learning is the point at which an iterative optimization algorithm reaches a stable solution, meaning the loss function stops decreasing meaningfully and further parameter updates yield…
Convex Function
A convex function is a real-valued function whose graph curves upward into a bowl or cup shape, so that the line segment (chord) connecting any two points on the graph lies on or above the graph itself.
Convex Optimization
Convex optimization is the branch of mathematical optimization that minimizes a convex function over a convex set, a problem class with one defining advantage: every local minimum is also a global minimum.
Convex Set
A convex set is a set of points in which the line segment connecting any two points of the set lies entirely within the set .
Convolution
Convolution is a mathematical operation that combines two functions to produce a third function, expressing how the shape of one is modified by the other.
Cross-Entropy
Cross-entropy is a measure from information theory of how many bits (or nats) are needed to encode data drawn from a true probability distribution P when using a code optimized for a different
Curse of Dimensionality
The curse of dimensionality is the set of problems that arise when data has a large number of features (dimensions): as dimensions increase, the volume of the space grows exponentially, the available data…
Distributionally Robust Optimization
Distributionally robust optimization (DRO) is a framework for making decisions when the probability distribution of uncertain inputs is not known exactly.
Earth Mover's Distance
Earth Mover's Distance (EMD), also known as the Wasserstein-1 distance, Kantorovich-Rubinstein metric, or Mallows's distance
Entropy
Entropy is a quantitative measure of the uncertainty, randomness, or average information content in a probability distribution: for a discrete random variable it equals the average number of yes/no questions…
Formalization of Fermat's Last Theorem (Anthropic, 2026)
The formalization of Fermat's Last Theorem is a complete, machine-checked proof of Fermat's Last Theorem (FLT) in the Lean 4 proof assistant that Anthropic published on September 4, 2026.
FrontierMath
FrontierMath is an advanced mathematical reasoning benchmark created by Epoch AI in collaboration with over 60 expert mathematicians, including Fields Medalists Terence Tao, Timothy Gowers, and Richard…
FunSearch
FunSearch is a method from Google DeepMind that pairs a large language model with an automated evaluator to discover new solutions to hard problems in mathematics and computer science.
Geometric Deep Learning
Geometric deep learning (GDL) is an area of deep learning that designs neural networks around the structure and symmetries of their data.
Gradient
In machine learning, the gradient is the vector of partial derivatives of a loss function with respect to every model parameter, and it points in the direction in which the loss increases most steeply.
Hyperplane
A hyperplane is a flat, affine subspace of dimension n-1 embedded in an n-dimensional space, defined by the linear equation $$w \cdot x + b = 0$$, where w is a normal vector and b is a scalar offset .
Independently and Identically Distributed (i.i.d.)
Independently and identically distributed (abbreviated i.i.d., iid, or IID) data is a collection of random variables in which each variable has the same probability distribution as the others and all variables…
Inductive bias
Inductive bias (also called learning bias) is the set of assumptions that a learning algorithm uses to predict outputs for previously unseen inputs.
Information Gain
Information Gain (IG) is a measure from information theory that quantifies the reduction in entropy (uncertainty) achieved by partitioning a dataset on a particular feature: it equals the entropy of the parent…
Information theory
Information theory is the mathematical study of the quantification, storage, and communication of information, founded by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication." Shannon…
KL Divergence (Kullback-Leibler Divergence)
Kullback-Leibler divergence, often abbreviated KL divergence and written $$D_{\mathrm{KL}}(P \parallel Q)$$
Lambda
Lambda (the Greek letter λ) is a symbol used across machine learning, statistics, and computer science to denote several distinct quantities
Lambda Calculus
Lambda calculus (often written λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.
Latent semantic analysis (LSA)
Latent semantic analysis (LSA), called latent semantic indexing (LSI) in information retrieval contexts, is an unsupervised technique that maps both terms and documents into a shared low-dimensional vector…
Lean (Theorem Prover)
Lean is an open source interactive theorem prover and dependently typed functional programming language created by Leonardo de Moura, first launched at Microsoft Research Redmond in 2013.
Leiden Declaration on Artificial Intelligence and Mathematics
The Leiden Declaration on Artificial Intelligence and Mathematics is a statement on the use of artificial intelligence in mathematical research, published on 2 June 2026 at leidendeclaration.ai and deposited…
Linear
In machine learning and mathematics, linear describes a function or relationship in which the output is built from the inputs only through addition and multiplication by constants.
Log Loss
Log loss is the negative log-likelihood of the predicted probabilities and the standard loss function for probabilistic classification: for binary labels it is computed as…
Log-Odds
Log-odds, also known as the logit, is a mathematical transformation that converts a probability value between 0 and 1 into a real number spanning from negative infinity to positive infinity.
MATH-500
MATH-500 is a 500-problem benchmark for evaluating the mathematical reasoning of large language models, formed by holding out 500 problems from the test split of the MATH benchmark of Dan Hendrycks et al.
Manifold Hypothesis
The manifold hypothesis is the conjecture that real-world high-dimensional data, such as natural images, speech, and text representations, concentrates on or near a manifold of much lower dimension embedded…
Markov Decision Process (MDP)
A Markov Decision Process (MDP) is a mathematical framework for modeling sequential decision-making in stochastic environments, formally defined by the 5-tuple $$(S, A, P, R, \gamma)$$: a set of states, a set…
Markov chain
A Markov chain is a stochastic process in which the probability of the next state depends only on the current state and not on the sequence of states that came before it.
Mathematical reasoning in AI
Mathematical reasoning in AI is the ability of computer systems to solve mathematical problems: carrying out multi-step calculations, proving theorems, and answering competition or research questions that…
Mathlib
Mathlib (formally mathlib4, the active Lean 4 incarnation) is the community-maintained, open-source unified library of formalized mathematics for the lean theorem prover, and it is the largest single library…
Matrix factorization
Matrix factorization is a family of mathematical techniques that decompose a matrix into a product of two or more smaller matrices.
Matrix multiplication
Matrix multiplication combines an M by K matrix A with a K by N matrix B to produce an M by N matrix C
Minerva (language model)
Minerva is a large language model developed by Google Research that specializes in quantitative reasoning, meaning it answers mathematics, science, and engineering questions by writing out step-by-step…
Minimax Loss
Minimax loss is a loss function rooted in game theory and decision theory that measures the worst-case performance of a strategy, algorithm, or model.
Nash equilibrium
A Nash equilibrium is a combination of strategies, one for each player in a game, such that no player can raise their own payoff by changing strategy alone while everyone else keeps theirs unchanged.
Nonlinear
Nonlinear describes any function, model, or relationship that does not satisfy the property of linearity.
Normal distribution
The normal distribution, also called the Gaussian distribution, is a continuous probability distribution defined by two parameters, a mean $$\mu$$ and a variance $$\sigma^2$$
NumPy
NumPy (short for Numerical Python) is the foundational open-source library for numerical and scientific computing in Python, providing an n-dimensional array object called ndarray along with a large collection…
NuminaMath
NuminaMath is a family of openly licensed competition-mathematics resources developed by the non-profit Project Numina, spanning the largest public dataset of competition math problems and solutions, a set of…
OpenAI Navier-Stokes Proposed Solution
OpenAI Navier-Stokes Proposed Solution is a proposed resolution of the Navier-Stokes existence and smoothness Millennium Prize Problem announced by OpenAI on September 8, 2026.