Related papers: Remembering Leo
This year is the 100th birth anniversary of Richard Philips Feynman. This article commemorates his scientific contributions and lasting legacy.
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Since Alan Turing envisioned Artificial Intelligence (AI) [1], a major driving force behind technical progress has been competition with human cognition. Historical milestones have been frequently associated with computers matching or…
I want to write about what I know and remember about the activities of Leonid Vital'evich Kantorovich, an outstanding scientist of the 20th century; about his dramatic struggle for recognition of his mathematical economic theories; about…
Interacting particle systems and percolation have been among the most active areas of probability theory over the past half century. Ted Harris played an important role in the early development of both fields. This paper is a bird's eye…
Linear regression is a fundamental tool for statistical analysis. This has motivated the development of linear regression methods that also satisfy differential privacy and thus guarantee that the learned model reveals little about any one…
Citations are a key indicator of research impact but are shaped by factors beyond intrinsic research quality, including prestige, social networks, and thematic similarity. While the Matthew Effect explains how prestige accumulates and…
This article concerns the life and work of Lucjan Emil B\"ottcher (1872-1937), a Polish mathematician. Besides biographical and bibliographical information, it contains a survey of his mathematical achievements in the theory of iteration…
We briefly recount the long friendship that developed between Ludwig and us (Moshe Flato and I), since we first met at ICM 1966 in Moscow. That friendship extended to his school and family, and persists to this day. Its strong personal…
In 1965 the Nobel Foundation honored Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman for their fundamental work in quantum electrodynamics and the consequences for the physics of elementary particles. In contrast to both of his…
One uniquely human trait is our inability to be random. We see and produce patterns where there should not be any and we do so in a predictable way. LLMs are supplied with human data and prone to human biases. In this work, we explore how…
Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is…
Some reflections on the role in the development of Mathematics of our unconscious perception of the world and just as unconscious organizing pulsions for those perceptions.
Value alignment, which aims to ensure that large language models (LLMs) and other AI agents behave in accordance with human values, is critical for ensuring safety and trustworthiness of these systems. A key component of value alignment is…
Joel Scherk (1946--1980) was an important early contributor to the development of string theory. Together with various collaborators, he made numerous profound and influential contributions to the subject throughout the decade of the 1970s.…
Large Language Models (LLMs) have demonstrated the ability to adopt a personality and behave in a human-like manner. There is a large body of research that investigates the behavioural impacts of personality in less obvious areas such as…
Translated from the Latin original, "De numeris amicabilibus" (1747). E100 in the Enestroem index. Euler starts by saying that with the success of mathematical analysis, number theory has been neglected. He argues that number theory is…
How does society work? How do groups emerge within society? What are the effects of emotions and memory on our everyday actions? George Homans, like us, had a perspective on what society is, except that he was a sociologist. Homans theory,…
The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems,…
The Binomial Theorem has long been essential in mathematics. In one form or another it was known to the ancients and, in the hands of Leibniz, Newton, Euler, Galois, and others, it became an essential tool in both algebra and analysis.…