In August 2023, Scott Aaronson and I reported the results of testing GPT4 with the Wolfram Alpha and Code Interpreter plug-ins over a collection of 105 original high-school level and college-level science and math problems (Davis and Aaronson, 2023). In September 2024, I tested the recently released model GPT-4o1-preview on the same collection. Overall I found that performance had significantly improved, but was still considerably short of perfect. In particular, problems that involve spatial reasoning are often stumbling blocks. On September 12, OpenAI (2024) released two preliminary versions, "ChatGPT-o1-preview" and "ChatGPT-o1-mini" of a forthcoming product "ChatGPT-o1".

Our test sets were too small and too haphazard to support statistically valid conclusions, but they were suggestive of a number of conclusions. We summarize these here, and discuss them at greater length in section 7. Over the kinds of problems tested, GPT-4 with either plug-in is significantly stronger than GPT-4 by itself, or, almost certainly, than any AI that existed a year ago. However it is still far from reliable; it often outputs a wrong answer or fails to output any answer. In terms of overall score, we would judge that these systems performs on the level of a middling undergraduate student. However, their capacities and weaknesses do not align with a human student; the systems solve some problems that even capable students would find challenging, whereas they fail on some problems that even middling high school students would find easy.

More than one hundred benchmarks have been developed to test the commonsense knowledge and commonsense reasoning abilities of artificial intelligence (AI) systems. However, these benchmarks are often flawed and many aspects of common sense remain untested. Consequently, we do not currently have any reliable way of measuring to what extent existing AI systems have achieved these abilities. This paper surveys the development and uses of AI commonsense benchmarks. We discuss the nature of common sense; the role of common sense in AI; the goals served by constructing commonsense benchmarks; and desirable features of commonsense benchmarks. We analyze the common flaws in benchmarks, and we argue that it is worthwhile to invest the work needed ensure that benchmark examples are consistently high quality. We survey the various methods of constructing commonsense benchmarks. We enumerate 139 commonsense benchmarks that have been developed: 102 text-based, 18 image-based, 12 video based, and 7 simulated physical environments. We discuss the gaps in the existing benchmarks and aspects of commonsense reasoning that are not addressed in any existing benchmark. We conclude with a number of recommendations for future development of commonsense AI benchmarks.

The paper discusses the capacities and limitations of current artificial intelligence (AI) technology to solve word problems that combine elementary knowledge with commonsense reasoning. No existing AI systems can solve these reliably. We review three approaches that have been developed, using AI natural language technology: outputting the answer directly, outputting a computer program that solves the problem, and outputting a formalized representation that can be input to an automated theorem verifier. We review some benchmarks that have been developed to evaluate these systems and some experimental studies. We discuss the limitations of the existing technology at solving these kinds of problems. We argue that it is not clear whether these kinds of limitations will be important in developing AI technology for pure mathematical research, but that they will be important in applications of mathematics, and may well be important in developing programs capable of reading and understanding mathematical content written by humans.

The Winograd Schema Challenge - a set of twin sentences involving pronoun reference disambiguation that seem to require the use of commonsense knowledge - was proposed by Hector Levesque in 2011. By 2019, a number of AI systems, based on large pre-trained transformer-based language models and fine-tuned on these kinds of problems, achieved better than 90% accuracy. In this paper, we review the history of the Winograd Schema Challenge and discuss the lasting contributions of the flurry of research that has taken place on the WSC in the last decade. We discuss the significance of various datasets developed for WSC, and the research community's deeper understanding of the role of surrogate tasks in assessing the intelligence of an AI system.

Most work on physical reasoning, both in artificial intelligence and in cognitive science, has focused on closed-world reasoning, in which it is assumed that the problem specification specifies all relevant objects and substance, all their relations in an initial situation, and all exogenous events. However, in many situations, it is important to do open-world reasoning; that is, making valid conclusions from very incomplete information. We have implemented in Prolog an open-world reasoner for a toy microworld of containers that can be loaded, unloaded, sealed, unsealed, carried, and dumped.

Arabshahi, Singh, and Anandkumar (2018) propose a method for creating a dataset of symbolic mathematical equations for the tasks of symbolic equation verification and equation completion. Unfortunately, a dataset constructed using the method they propose will suffer from two serious flaws. First, the class of true equations that the procedure can generate will be very limited. Second, because true and false equations are generated in completely different ways, there are likely to be artifactual features that allow easy discrimination. Moreover, over the class of equations they consider, there is an extremely simple probabilistic procedure that solves the problem of equation verification with extremely high reliability. The usefulness of this problem in general as a testbed for AI systems is therefore doubtful.

It will be useful to setting up a general, abstract framework in which to discuss these issues. Generally speaking AI systems, and for that matter computer programs of any kind for a particular task, the actual ultimate objective can be formulated as follows. There is a class X of inputs that are "reasonable" problems for Q. There is a class Y of possible outputs. The task defines a relation Q(x, y) meaning "y is a good output [or an acceptable output, or the best possible output] on the task for input x." We assume that for every x X there is at least one y Y such that Q(x, y).

The First Winograd Schema Challenge at IJCAI-16

Six systems were entered, exploiting a variety of technologies. None of the systems were able to advance from the first round to the second and final round. The Winograd Schema Challenge is concerned with finding the referents of pronouns, or solving the pronoun disambiguation problem. Doing this correctly appears to rely on having a solid base of commonsense knowledge and the ability to reason intelligently with that knowledge. This can be seen from considering an example of a Winograd schema. The referent of it in sentence 1 is the backpack; the referent of it in sentence 2 is the water bottle.