Learn Hardcore Russian: Интересно думать не только о будущем, но и о прошлом. - It is interesting to think not only about the future but also about the past.

Интересно думать... literally: “(It is) interesting to think...”
There is no word for “it”; интересно works like “it is interesting” by itself.
This is very common with words like интересно, трудно, легко, приятно, скучно
- infinitive.

So Интересно думать... = “It is interesting to think...” without an explicit subject.

Why is it думать and not думаю?

Думать is the infinitive (“to think”).
In impersonal sentences like this, Russian typically uses an infinitive after the predicate:
- Интересно читать. – It’s interesting to read.
- Трудно понять. – It’s hard to understand.
If you said Я думаю, that means “I think” (I am thinking), which is a different idea.
Интересно думать focuses on the activity in general (“thinking is interesting”), not “I am thinking” right now.

Can I say Мне интересно думать не только о будущем...? What’s the difference?

Yes, and it’s very natural:

Интересно думать...
- General statement: “It’s interesting to think…” (in general, for people, or context-dependent).
Мне интересно думать...
- Personal: “It is interesting for me to think…” / “I find it interesting to think…”

So Мне in dative marks for whom it is interesting. You can also say:

Нам интересно думать... – We find it interesting to think...
Им интересно думать... – They find it interesting to think...

Why do we use о here? What about об or про?

The basic rule:

о + prepositional case = about (neutral, standard)
- о будущем, о прошлом – about the future, about the past

о / об / обо are the same preposition; the form depends on pronunciation:

о before most consonants and vowels:
- о прошлом, о будущем, о нём
об before words starting with several consonants where о is hard to pronounce:
- об университетЕ, об этом
обо before a few specific words (like мне, мнём, всех in some forms).

Here, о будущем, о прошлом are easy to pronounce, so we just use о.

Про can also mean “about” but is more colloquial:

думать про будущее – think about the future (more informal, spoken)
думать о будущем – neutral/standard, good in both speech and writing.

Why are будущем and прошлом in that form? What case is that?

They are in the prepositional case, singular:

будущее (n. sg., nominative) → о будущем (prepositional)
прошлое (n. sg., nominative) → о прошлом (prepositional)

Pattern for many neuter adjectives used as nouns: -ое → -ом in prepositional:

новое → о новом (the new [thing])
старое → о старом

The preposition о almost always takes the prepositional case when it means “about”.

How does the construction не только ... но и ... work here?

Не только ... но и ... = “not only ... but also ...”

It pairs two parallel elements:

не только о будущем, но и о прошлом
- not only about the future, but also about the past

Key points:

The two parts should be grammatically similar:
- не только о X, но и о Y
- не только читать, но и писать
The и after но is standard in this construction; it emphasizes “also”:
- не только о будущем, но и о прошлом sounds more natural than dropping и.

Why is there a comma before но?

In Russian, a comma is normally used before но (“but”) when it connects two parts:

Интересно думать не только о будущем, но и о прошлом.

Even though they are short and parallel, the contrastive conjunction но still takes a comma here. The pattern не только ..., но и ... is usually written with a comma.

Could I say Думать не только о будущем, но и о прошлом интересно? Does that change the meaning?

You can say that; it’s grammatically correct:

Думать не только о будущем, но и о прошлом интересно.

Meaning is basically the same, but:

Интересно думать... – more neutral, typical order.
Думать ... интересно. – emphasizes the thinking part a bit more, has a slightly more “bookish” or “stylistic” feel.

Both are possible, but the original word order is more common in everyday speech.

What’s the difference between думать о будущем and думать о своём будущем?

думать о будущем – think about the future in general (could be one’s own, humanity’s, the world’s, etc.).
думать о своём будущем – think about one’s own future specifically.

Своём is the reflexive possessive “one’s own” and is used instead of моём/твоём/нашем etc. when the owner is the subject of the verb:

Я люблю думать о своём будущем. – I love to think about my (own) future.

Why is the verb думать (imperfective) and not подумать?

думать (imperfective) – an ongoing, repeated, or general activity: “to think (in general)”.
подумать (perfective) – to think for a while, to have one act/episode of thinking: “to think (for a bit), to consider”.

In this sentence we talk about thinking as an activity, in general:

Интересно думать... – “It’s interesting to think (in general).”

If you said Интересно подумать, it would sound more like:

“It’s interesting to have a think / to think for a bit” – a bit unusual in this context and less natural.

Could we drop думать and just say Интересно не только о будущем, но и о прошлом?

That would sound incomplete or strange in most contexts.
You need a verb or activity for Интересно:

Интересно думать... – It is interesting to think...
Интересно говорить... – It is interesting to talk...

If the verb is very clear from context, Russians sometimes omit it, but as a standalone sentence it’s better to keep думать.

How would I stress the words when saying this sentence?

Main stresses (capital letters show stressed syllable):

ИнтерЕсно дУмать не тОлько о бУдущем, но и о прОшлом.

Typical intonation:

Slight emphasis on ИнтерЕсно (what is interesting),
then on the contrast: бУдущем vs прОшлом.

You might slightly raise your voice on бУдущем, then contrast with прОшлом.