Why do English speakers say ‘there is a problem’ and not ‘a problem exists’? For me they both mean the same.
(Hyun Il, Korea)

Thanks for the question Hyun Il, the use of ‘there is’ and ‘there are’ can be quite difficult for many learners of English. Let’s start with the basics.

English uses ‘there is/are’ to state that something does or does not exist. It is possible to say, as you asked, that ‘a problem exists’, but this is not what native speakers normally say.

There is or there are is a ‘preparatory’ subject, and the real subject follows after the verb, which is generally a form of ‘to be’

Eg. There is a hole in my pocket (more natural than ‘a hole is in my pocket’)
There isn’t a pen on the table (more natural than ‘a pen isn’t on the table’)

When the subject is a plural noun we use ‘there are’
Eg. There are four people in the queue (more natural than ‘four people are in the queue’)

There is and there are commonly introduce subjects that are not definite, often beginning with an indefinite article (a/an), no article, or with indefinite determiners (somebody, nothing, anywhere)
Eg. There are no people outside
There is someone waiting at the door
There isn’t anywhere to sit

When the subject is definite, for example it is a proper noun (a name) or it has a definite article (‘the’), then there is/are are not used
Eg. The door is open (NOT ‘there is the door open)
Susan was at work (NOT ‘there was Susan at work)

There is and there are can be used with all forms of to be, and with modal verbs that precede to be
Eg. There were a lot of people in the restaurant
There have been several accidents on the road this year
There is going to be a meeting this afternoon
There might be delays to your journey

So, in English, when we want to say that something exists, we introduce that something with there is or there are

Now complete these sentences with the correct form of ‘there + to be’

1. ……………… a man standing next to me.
2. Since I’ve been living here …………………. lots of times when I’ve got lost.
3. ……………………. any problems, everything was ok.
4. We can’t take the tube tomorrow, …………………… a strike. We’ll have to take the bus.