Wolfram Alpha is mostly for "trivia" type problems. Or giving solutions to equations.

I was figuring out some mode decomposition methods such as ESPRIT and Prony and how to potentially extend/customize them. Wolfram Alpha doesn't seem to have a clue about such.

Wolfram Alpha is better at actually doing math, but far worse at explaining what it’s doing, and why.

What’s worse about it?

It never tells you the wrong thing, at the very least.

When you give it a large math problem and the answer is "seven point one three five ... ", and it shows a plot of the result v some randomly selected domain, well there could be more I'd like to know.

You can unlock a full derivation of the solution, for cases where you say "Solve" or "Simplify", but what I (and I suspect GP) might want, is to know why a few of the key steps might work.

It's a fantastic tool that helped get me through my (engineering) grad work, but ultimately the breakthrough inequalities that helped me write some of my best stuff were out of a book I bought in desperation that basically cataloged linear algebra known inequalities and simplifications.

When I try that kind of thing with the best LLM I can use (as of a few months ago, albeit), the results can get incorrect pretty quickly.

What book was it that you found helpful?

A survey on matrix theory and matrix inequalities - Marvin Marcus

https://www.amazon.com/gp/product/048667102X/ref=ppx_yo_dt_b...

Im reviewing linear algebra now and would also love to know that book!

It was this one (in case you miss sibling response): https://www.amazon.com/gp/product/048667102X/ref=ppx_yo_dt_b...

I make no claim about its usefulness for anyone else!

> [...], but what I (and I suspect GP) might want, is to know why a few of the key steps might work.

It's been some time since I've used the step-by-step explainer, and it was for calculus or intro physics problems at best, but IIRC the pro subscription will at least mention the method used to solve each step and link to reference materials (e.g., a clickable tag labeled "integration by parts"). Doesn't exactly explain why but does provide useful keywords in a sequence that can be used to derive the why.

Its understanding of problems was very bad last time I used it. Meaning it was difficult to communicate what you wanted it to do. Usually I try to write in the Mathematica language, but even that is not foolproof.

Hopefully they have incorporated more modern LLM since then, but it hasn’t been that long.

Wolfram Alpha's "smartness" is often Clippy level enraging. E.g. it makes assumptions of symbols based on their names (e.g. a is assumed to be a constant, derivatives are taken w.r.t. x). Even with Mathematica syntax it tends to make such assumptions and refuses to lift them even when explicitly directed. Quite often one has to change the variable symbols used to try to make Alpha to do what's meant.

I wish there was a way to tell Chatgpt where it has made a mistake, with a single mouse click.

What's surprising to me is that this would surely be in OpenAI's interests, too -- free RLHF!

Of course there would be the risk of adversaries giving bogus feedback, but my gut says it's relatively straightforward to filter out most of this muck.

Is the explanation a pro feature? At the very end it says "step by step? Pay here"

No. Wolfram Alpha can't solve anything that isn't a function evaluation or equation. And it can't do modular arithmetic to save its unlife.

WolframOne/Mathematica is better, but that requires the user (or ChatGPT!)to write complicated code, not natural language queries.

Wolfram Alpha can solve equations well, but it is terrible at understanding natural language.

For example I asked Wolfram Alpha "How heavy a rocket has to be to launch 5 tons to LEO with a specific impulse of 400s", which is a straightforward application of the Tsiolkovsky rocket equation. Wolfram Alpha gave me some nonsense about particle physics (result: 95 MeV/c^2), GPT-4o did it right (result: 53.45 tons).

Wolfram alpha knows about the Tsiolkovsky rocket equation, it knows about LEO (low earth orbit), but I found no way to get a delta-v out of it, again, more nonsense. It tells me about Delta airlines, mentions satellites that it knows are not in LEO. The "natural language" part is a joke. It is more like an advanced calculator, and for that, it is great.

You're using it wrong, you can use natural language in your equation, but afaik it's not supposed to be able to do what you're asking of it.

You know, "You're using it wrong" is usually meant to carry an ironic or sarcastic tone, right?

It dates back to Steve Jobs blaming an iPhone 4 user for "holding it wrong" rather than acknowledging a flawed antenna design that was causing dropped calls. The closest Apple ever came to admitting that it was their problem was when they subsequently ran an employment ad to hire a new antenna engineering lead. Maybe it's time for Wolfram to hire a new language-model lead.

It's not an LLM. You're simply asking too much of it. It doesn't work the way you want it to, sorry.

Correct, so it isn't a "ChatGPT of Math", which was the point.

Tell Wolfram. They're the ones who've been advertising it for years, well before LLMs were a thing, using English-language prompts like these examples: https://www.pcmag.com/news/23-cool-non-math-things-you-can-d...

The problem has always been that you only get good answers if you happen to stumble on a specific question that it can handle. Combining Alpha with an LLM could actually be pretty awesome, but I'm sure it's easier said than done.

Before LLMs exploded nobody really expected WA to perform well at natural language comprehension. The expectations were at the level of "an ELIZA that knows math".

No, “holding it wrong” is the sarcastic version. “You’re using it wrong” is a super common way to tell people they are literally using something wrong.

But they're not using it wrong. They are using it as advertised by Wolfram themselves (read: himself).

The GP's rocket equation question is exactly the sort of use case for which Alpha has been touted for years.