> Personally, I've found numeric computation more useful in 99% of the cases; do others have a different experience?
Yes, of course they do. For example, if they want to obtain a general, symbolic, solution to a problem, rather than estimates of particular numerical values. I'm sorry to sound a bit dismissive, but on HN it is common to hear people say stuff like "Oh, I find code much more helpful than math" and it's a bit embarrassing.
Just to give one example out of the entire universe of human mathematical activity, suppose you're doing statistical inference. You've developed a likelihood model for the data-generating process, and now it's time to implement the actual inference, say in a Bayesian MCMC, or a rejection sampler, or importance sampler, or whatever. Those are numerical algorithms of course; but they need to repeatedly evaluate the likelihood function at millions of different points in parameter space. Now, your likelihood function, was developed to model the real world. And perhaps the resulting equations are a little complicated. You may be able to achieve a vast speed-up of your numerical algorithm if you use a symbolic algebra system to find/confirm a symbolic simplification of your likelihood function.
A dumbfounded example . All you need for this is a cas system or some gruelling head computation that can solve
This step or formula nothing more and not wolfram specifically .
Yes, of course they do. For example, if they want to obtain a general, symbolic, solution to a problem, rather than estimates of particular numerical values. I'm sorry to sound a bit dismissive, but on HN it is common to hear people say stuff like "Oh, I find code much more helpful than math" and it's a bit embarrassing.
Just to give one example out of the entire universe of human mathematical activity, suppose you're doing statistical inference. You've developed a likelihood model for the data-generating process, and now it's time to implement the actual inference, say in a Bayesian MCMC, or a rejection sampler, or importance sampler, or whatever. Those are numerical algorithms of course; but they need to repeatedly evaluate the likelihood function at millions of different points in parameter space. Now, your likelihood function, was developed to model the real world. And perhaps the resulting equations are a little complicated. You may be able to achieve a vast speed-up of your numerical algorithm if you use a symbolic algebra system to find/confirm a symbolic simplification of your likelihood function.