IMHO: Deliver products/services can get paid for. For this, move to new areas with no competition, that is, move products/services forward. For this, use new, powerful, valuable technology.
For that, broadly, supply new, valuable information. For that, take in available data, manipulate it, and report the new information as the results.
So, with all this data, find where some new, valuable information will make a good, new product/service. Then to have the first good or a much better offering, do use much more powerful data manipulations. For that, the secret is, and the candidates are, object oriented programming, processors with 1000+ cores, processors with clocks at 50 GHz+, new programming languages, new computer architectures exploiting, say, solid state disks addresses as a slower version of main memory, processors communicating with optical instead of electrical signals, quantum processors, massive parallelism of the cloud, original derivations with theorems and proofs in applied math exploiting appropriate advanced prerequisites, and may I have the envelope please [drum roll], and the winner is -- applied math!
Sorry 'bout that. Here the applied math is replacing the current ubiquitous elementary techniques, intuitive heuristics, fitting to large data sets, and copying what was long done manually.
This answer will not serve everyone or please everyone, but IMHO it is the most promising, single path forward.
IMHO, might look at ML as based heavily on the Leo Breiman work in random forests and classification and regression trees (CART).
Breiman was a first class applied mathematician, a student of M. Loeve at Berkeley and later a professor, of, say, statistics, at Berkeley.
So, one way to get valuable information is to take in some data, manipulate it, and report the results. IMHO, by far the best way to get powerful data manipulations is applied math, possibly with some advanced pure math prerequisites.
E.g., some of the best applied math long on the shelves of the research libraries for manipulating data to get valuable information is just astoundingly powerful stuff, and I don't see computer science work in ML and AI as an effective way to compete. E.g., how to do as well as Wiener filtering, linear programming, optimal control without just programming what is already known? Or, if we didn't have the simplex algorithm for linear programming, I don't see the
approaches of ML or AI as
replacing them. E.g., ML and AI are supposed to be good at games, but their approaches to just a large example of just the two person game of paper, scissors, rock would be very clumsy. Why? The solution is a nice application of linear programming, and that is darned clever. Or, want to assign workers to jobs on a production line. Sure, can try AI type approaches, but there is a super nice, fast, exact algorithm, darned clever, and a long way from ML or AI.
I'm out of school -- got my Ph.D. in applied math, stochastic optimal control.
I'm doing a startup, and the crucial core of the work and its value is some applied math I derived based on some advanced prerequisites.
I've published in AI, but my view is that so far there is nothing in AI that is at all close to actual intelligence as we see it in humans.
Theorems and proofs are a heck of a powerful methodology and tough to beat. For AI, a super big problem is to define in any meaningful way just what the heck intelligence is, say, enough to get started on a solution. That is, we don't really have a problem statement -- the Turing test might be a test on a candidate solution but is, still, not a problem statement. IMHO, once we do get a problem statement, then the most powerful approach will be via applied math.
I agree that ML and AI are applied math. It is a, duh, no-brainer.
But you might want to revise this:
> IMHO, might look at ML as based heavily on the Leo Breiman work in random forests and classification and regression trees (CART).
There is a whole lot more to ML than decision forests. We have talked about this before, I suggest that you get started with Vapnik's books. They are not light reading but I can promise you will enjoy them. No seriously, just get those books. In fact his main result is bigger than ML, its a non-asymptotic distribution independent _uniform_ law of large numbers.
ML is now in, what can be described as, a post-Vapnik era, but for someone steeped in probability and functional analysis that is the place to start.
For that, broadly, supply new, valuable information. For that, take in available data, manipulate it, and report the new information as the results.
So, with all this data, find where some new, valuable information will make a good, new product/service. Then to have the first good or a much better offering, do use much more powerful data manipulations. For that, the secret is, and the candidates are, object oriented programming, processors with 1000+ cores, processors with clocks at 50 GHz+, new programming languages, new computer architectures exploiting, say, solid state disks addresses as a slower version of main memory, processors communicating with optical instead of electrical signals, quantum processors, massive parallelism of the cloud, original derivations with theorems and proofs in applied math exploiting appropriate advanced prerequisites, and may I have the envelope please [drum roll], and the winner is -- applied math!
Sorry 'bout that. Here the applied math is replacing the current ubiquitous elementary techniques, intuitive heuristics, fitting to large data sets, and copying what was long done manually.
This answer will not serve everyone or please everyone, but IMHO it is the most promising, single path forward.