Related papers: The Future of Set Theory
Science is a complex system comprised of many scientists who individually make decisions that, due to the size and nature of the academic system, largely do not affect the system as a whole. However, certain decisions at the meso-level of…
As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this paper, we analyze sessions with ChatGPT around topics in basic Linear Algebra. We reflect the…
ADASS has been a successful conference series for 24 years. If it is to continue to be successful and relevant we need to ensure that it provides what we as a community need from an annual conference. Earlier this year the ADASS Program…
What do we teach and what should we teach? An honest answer to this question is painful, very painful--what we teach lags decades behind what we practice. How can we reduce this `gap' to prepare a data science workforce of trained…
A survey is made of selected topics in flavour physics where real progress is expected in the coming half-decade, paying particular attention to those where New Physics signals may appear.
Notes of my lectures at the CIME (Levico Terme, june 2015). The lectures gave an overview of the L\"uroth problem, its history, the counter-examples found in the 70's, and the recent developments on stable rationality following the new…
In the first part of the talk, I give a low-resolution overview of the current state of particle physics - the triumph of the Standard Model and its discontents. I review and re-endorse the remarkably direct and (to me) compelling argument…
The use of language-model-based question-answering systems to aid humans in completing difficult tasks is limited, in part, by the unreliability of the text these systems generate. Using hard multiple-choice reading comprehension questions…
These are lectures notes prepared for a series of seminars I am invited to give at Princeton Philosophy Department in November 2024. They cover the conceptual structure of quantum gravity, the relational interpretation of quantum mechanics,…
Current speech translation systems, while having achieved impressive accuracies, are rather static in their behavior and do not adapt to real-world situations in ways human interpreters do. In order to improve their practical usefulness and…
Each year perhaps millions of young people face the following dilemma: should I continue my education or rather start working with already acquired skills. Right decision must take into account somebody's own abilities, accessibility to…
Knowledge sharing is an important aspect in most meetings. Personal characteristics of some participants, such as their (in)ability or (un)willingness to take the floor, may have a negative effect on the quality of knowledge sharing; some…
We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to…
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…
In this article the author claims that there is a paradigm shift from ZFC to NFUM and further to NACT - due to philosophical reasons, not mathematical ones. The goal is to construct systems where every "Not-Properclass" is a set! With help…
Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
Advances in artificial intelligence (AI) will transform many aspects of our lives and society, bringing immense opportunities but also posing significant risks and challenges. The next several decades may well be a turning point for…
Transformers replace recurrence with a memory that grows with sequence length and self-attention that enables ad-hoc lookups over past tokens. Consequently, they lack an inherent incentive to compress history into compact latent states with…