Full Width [alt+shift+f] Shortcuts [alt+shift+k]
Sign Up [alt+shift+s] Log In [alt+shift+l]
125
Related writings: “Logic, Explainability and the Future of Understanding” (2018) » “The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics” (2022) » “Computational Knowledge and the Future of Pure Mathematics” (2014) » The Simplest Axiom for Logic Theorem (Wolfram with Mathematica, 2000): The single axiom ((a•b)•c)•(a•((a•c)•a))c is a complete axiom system for Boolean algebra (and […]
6 months ago

Improve your reading experience

Logged in users get linked directly to articles resulting in a better reading experience. Please login for free, it takes less than 1 minute.

More from Stephen Wolfram Writings

What Can We Learn about Engineering and Innovation from Half a Century of the Game of Life Cellular Automaton?

Metaengineering and Laws of Innovation Things are invented. Things are discovered. And somehow there’s an arc of progress that’s formed. But are there what amount to “laws of innovation” that govern that arc of progress? There are some exponential and other laws that purport to at least measure overall quantitative aspects of progress (number of […]

4 months ago 56 votes
Towards a Computational Formalization for Foundations of Medicine

A Theory of Medicine? As it’s practiced today, medicine is almost always about particulars: “this has gone wrong; this is how to fix it”. But might it also be possible to talk about medicine in a more general, more abstract way—and perhaps to create a framework in which one can study its essential features without […]

5 months ago 64 votes
Launching Version 14.2 of Wolfram Language & Mathematica: Big Data Meets Computation & AI

The Drumbeat of Releases Continues… Notebook Assistant Chat inside Any Notebook Bring Us Your Gigabytes! Introducing Tabular Manipulating Data in Tabular Getting Data into Tabular Cleaning Data for Tabular The Structure of Tabular Tabular Everywhere Algebra with Symbolic Arrays Language Tune-Ups Brightening Our Colors; Spiffing Up for 2025 LLM Streamlining & Streaming Streamlining Parallel Computation: […]

6 months ago 75 votes
Useful to the Point of Being Revolutionary: Introducing Wolfram Notebook Assistant

Note: As of today, copies of Wolfram Version 14.1 are being auto-updated to allow subscription access to the capabilities described here. [For additional installation information see here.] Just Say What You Want! Turning Words into Computation Nearly a year and a half ago—just a few months after ChatGPT burst on the scene—we introduced the first […]

7 months ago 124 votes

More in science

A Third of Slum Dwellers at Risk of 'Disastrous' Floods

Close to 900 million people across the Global South live in densely packed urban slums, which often sit in floodplains. A new study finds that one in three slum dwellers is at risk of "disastrous" flooding, a risk that is set to grow as warming spurs more intense rainfall around the world. Read more on E360 →

2 days ago 3 votes
Quantum Scientists Have Built a New Math of Cryptography

In theory, quantum physics can bypass the hard mathematical problems at the root of modern encryption. A new proof shows how. The post Quantum Scientists Have Built a New Math of Cryptography first appeared on Quanta Magazine

2 days ago 4 votes
On Controlling Fire, New Lessons from a Deep Indigenous Past

For centuries, the Native people of North America used controlled burns to manage the continent's forests. In an e360 interview, ecologist Loris Daniels talks about the long history of Indigenous burning and why the practice must be restored to protect against catastrophic fires. Read more on E360 →

3 days ago 5 votes
Research experience for teachers - why NSF education funds matter

The beginning of a RET poster session Research Experience for Teachers (RET) programs are an example of the kind of programs that the National Science Foundation funds which are focused on K12 (and broader) education. This summer I hosted a high school physics teacher in my lab for 6 weeks, where he worked on a brief project, with one of my doctoral students helping out in a mentoring role.  Just yesterday was the big poster session for all of the participants in the program, and it was very enjoyable to talk with a whole cadre of high school science teachers from across the greater Houston area about their projects and their experiences.   Readers may be more familiar with the sibling Research Experience for Undergraduates (REU) programs, which give undergraduate students the chance to work for 10 weeks or so in a lab that is very likely not at their home institution.  REUs are a great way for students interested in research to get broad exposure to new topics, meet people and acquire new skills, and for some, figure out whether they like research (and maybe which topics are exciting to them).  The educational goal of REUs is clear:  providing direct research experience to interested undergrads, ideally while advancing a research project and for some small fraction of students resulting in an eventual publication.   RET programs are different:  They are intended as professional development.  The teachers are exposed to new topics, hopefully a fun research environment, and they are encouraged to think carefully about how they can take the concepts they learn and translate those for the classroom.  I am very much not an expert in education research, but there is evidence (see here, for example) that teachers who participate in these programs get a great deal of satisfaction and have lower attrition from teaching professions.  (Note that it's hard to do statistics well on questions like that, since the population of teachers that seek out opportunities like this may be a special subset of the total population of teachers.)  An idea that makes sense to me:  Enhancing the motivation and job satisfaction of a teacher can have a larger cumulative impact on educating students than an individual research project for a single student. It would be a great shame if RET and REU programs are victims of large-scale cuts at NSF.  The NSF is the only science agency with education as part of its mission (at least historically).  All the more reason to try to persuade appropriators to not follow the draconian presidential budget request for the agency.

4 days ago 8 votes
Tram trains

How to build cheap transit in smaller towns

4 days ago 9 votes