News, Views & Insights
The Drumbeat of Releases Continues… Just under six months ago (176 days ago, to be precise) we released Version 14.1. Today I’m pleased to announce that we’re releasing Version 14.2, delivering the latest from our R&D pipeline. This is an exciting time for our technology, both in terms of what we’re now able to implement, […]
Nearly a year and a half ago—just a few months after ChatGPT burst on the scene—we introduced the first version of our Chat Notebook technology to integrate LLM-based chat into Wolfram Notebooks. For the past year and a half we’ve been building on those foundations. And today I’m excited to be able to announce that we’re releasing the fruits of those efforts: the first version of our Wolfram Notebook Assistant.
Most calculus students might think that if one could compute indefinite integrals, it would always be easy to compute definite ones. After all, they might think, the fundamental theorem of calculus says that one just has to subtract the values of the indefinite integral at the end points to get the definite integral.
So how come inside Mathematica there are thousands of pages of code devoted to working out definite integrals---beyond just subtracting indefinite ones? The answer, as is often the case, is that in the real world of mathematical computation, things are more complicated than one learns in basic mathematics courses. And to get the correct answer one needs to be considerably more sophisticated. In a simple case, subtracting indefinite integrals works just fine. Consider computing the area under a sine curve, which equalsIt’s not easy to make a big software system that really fits together. It’s incredibly important, though. Because it’s what makes the whole system more than just the sum of its parts. It’s what gives the system limitless possibilities—rather than just a bunch of specific features. But it’s hard to achieve. It requires maintaining consistency […]
I do love gadgets, linkages, clockworks, all that 19th-century cogs-and-wheels technology. So much easier to see than our 21st-century nanotubes and zillion transistors on a chip.
Sándor Kabai has written many Demonstrations illustrating such mechanisms.
What makes these interesting is that playing with the various parameters lets you vary both the geometric setup and the controls that make the mechanism go through its motion.
Not a lot gets written in the general press about foundational issues in mathematics, but this afternoon I found myself talking to a journalist about the subject of certainty in mathematics. It turned out to be a pretty interesting conversation, so I thought I’d write here about a few things that came up. Mathematics likes […]
“And although it will no doubt be very difficult to prove, it seems likely that this Turing machine will in the end turn out to be universal.” So I wrote on page 709 of A New Kind of Science (NKS). I had searched the computational universe for the simplest possible universal Turing machine. And I […]