Related papers: Our Mathematical Universe?
Speculations and theories about the existence of other worlds have a long history. In recent times, the arguments have shifted away from their typical philosophical and theological character to supposedly become more objective thanks to…
In a recent article, M. Tegmark poses the hypothesis that our known universe is a ``baggage free'' mathematical structure among many other possible ones, which also correspond to other physical universes --Mathematical Universe Hypothesis,…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
Traditionally, mathematical knowledge is published in printed media such as books or journals. With the advent of the Internet, a new method of publication became available. To date, however, most online mathematical publications do not…
Over the past 20 years, Wikipedia has gone from a rather outlandish idea to a major reference work, with more than 60 million articles across all languages, including nearly 7 million in English [Wiki01]. Around 27,000 of these articles…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
We carry out a thorough bibliometric analysis of recent publications in mathematics based on the database Web of Science. The individual relations between various features and the citations are provided, and the importance of the features…
The mathematisation of the socio-economic sphere, where mathematics actively constructs social reality, presents a challenge for studies on ethics in mathematics and its education. While existing scholarship on ethics in mathematics offers…
I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the…
Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
I know better than to come between the experts here assembled and their research programs, so I confine these remarks to lessons to be drawn on the state of our subject from the histories of research in three Windows on the Universe:…
The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…
The mathematical universe discussed here gives models of possible structures our physical universe can have.
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
This is an expanded version of my review of Nina Engelhardt's book "Modernism, Fiction and Mathematics", Edinburgh University Press 2018. A considerably shortened version will appear in the Notices of the AMS.
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…
We propose to address the problem of how to know students' knowledge in an entirely new approach called ?epistemography? which is, roughly, an attempt to describe the structure of this knowledge. We claim that what is to be known is made of…
Three years ago, we initiated a programme of research in which ideas and tools from statistical physics and network theory were applied to the field of comparative mythology. The eclecticism of the work, together with the perspectives it…