Related papers: Singularity: a Seventh Memo?
A system's apparent simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Each time we teach, our students communicate to us. They talk, write, and draw. How do we take in their expressions of self and mathematics? How do we listen? In this column, published in the Fall 2023 AWM Newsletter, I explore different…
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to…
Transcript of G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The notion of randomness is taken from physics and applied to pure mathematics in order to shed light on the…
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…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
Clarithmetics are number theories based on computability logic (see http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories represent interactive computational problems, and their "truth" is understood as existence of an…
In this paper the claim that Zeno's paradoxes have been solved is contested. Although no one has ever touched Zeno without refuting him (Whitehead), it will be our aim to show that, whatever it was that was refuted, it was certainly not…
Literary critics often attempt to uncover meaning in a single work of literature through careful reading and analysis. Applying natural language processing methods to aid in such literary analyses remains a challenge in digital humanities.…
We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy,…
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…