Related papers: Nature's Greatest Puzzles
Invited talk at the EPS-HEPP meeting in Krakow, July 2009. My first thought, and presumably the default expectation, was that I'd talk in a general way about the grandeur of high energy physics and the exciting future we anticipate,…
Many problems in science and engineering can be formulated as optimization problems, subject to complex nonlinear constraints. The solutions of highly nonlinear problems usually require sophisticated optimization algorithms, and traditional…
An expository lecture on the analogy between the subjects of the title. Delivered at the International Conference on Number Theory at the Korea Institute for Advanced Study in December 1997.
We describe how cosmology has converged towards a beautiful model of the Universe: the Big Bang Universe. We praise this model, but show there is a dark side to it. This dark side is usually called ``the cosmological problems'': a set of…
LLMs are increasingly used as seq2seq translators from natural language utterances to structured programs, a process called semantic interpretation. Unlike atomic labels or token sequences, programs are naturally represented as abstract…
We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e.,…
Science meets Engineering in Deep Learning took place in Vancouver as part of the Workshop section of NeurIPS 2019. As organizers of the workshop, we created the following report in an attempt to isolate emerging topics and recurring themes…
Recent decades have witnessed a dramatic shift in the cross-border collaboration mode of researchers, with countries increasingly cooperating and competing with one another. It is crucial for leaders in academia and policy to understand the…
We study the lattices of algebraic and transcendental cycles of cubic fourfolds.
Environmental fluid mechanics underlies a wealth of natural, industrial and, by extension, societal challenges. In the coming decades, as we strive towards a more sustainable planet, there are a wide range of grand challenge problems that…
We usually construct mathematical objects that are accessible, on which we can put our hands, but a huge part of the mathematical existing is actually wild. Here we explore part of the wild world: its inhabitants are knots that are…
This special issue cover the seventh and last conference of the CL&C series, started in 2006 in San Servolo. Topics are the computational content of logics between intuitionistic logic and classical logic, through normalization, and a new…
This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.
This is a resume of the talk delivered at the Symposium on Hodge theory, Degeneration and Complex surfaces, Tagajo, Miyagi, March 2004.
Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
This is the transcript of a lecture given at UMass-Lowell in which I compare and contrast the work of Godel and of Turing and my own work on incompleteness. I also discuss randomness in physics vs randomness in pure mathematics.
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
Scaling reasoning capabilities beyond traditional domains such as math and coding is hindered by the lack of diverse and high-quality questions. To overcome this limitation, we introduce a scalable approach for generating diverse and…
We live in a universe filled with galaxies with an amazing variety of sizes and shapes. One of the biggest challenges for astronomers working in this field is to understand how all these types relate to each other in the background of an…