Are there any things which today's programming language can't solve or do?

Question

So, we can do a hell lot of things with programming languages. Then, are these languages not capable of doing some/more tasks which are hypothetically possible like simulating 4D,etc...?

Answer 1

Not gonna write so long because it's bedtime(GMT+05:30)
In short you can't do physical activities.

Answer 2

There is a class of "uncomputable numbers" that cannot be computed by a (finite) computer program. Most numbers are uncomputable in fact.
Even though it has infinitely many digits, π=3.141... for example is computable, since we can come up with a 5 lines of code program that would print out all the digits, given infinite time.
It's kind of cool that we know a few digits of some of the more famous uncomputables, don't ask me how that would even work.
By extension, there are infintitely many problems that a computer cannot and will never be able to solve.