Learn Hardcore Russian: Математика кажется сложной, но мне нравится решать задачи. - Math seems difficult, but I like solving problems.

You can sometimes hear the nominative (Он кажется умный) in colloquial speech, but the instrumental (сложной) is more standard and stylistically neutral here.

What does the -ся at the end of кажется do?

The -ся ending is a reflexive/postfix particle that attaches to verbs. It can have several functions (true reflexive, reciprocal, “middle voice”, impersonal), but in казаться it’s basically part of the dictionary form of the verb and can no longer be “undone”.

Historically:

казать – “to show, to display” (now rare in this meaning)
казаться – “to show itself, to appear, to seem”

In modern Russian, казаться simply means “to seem / to appear (to be)”, and you should learn it as a fixed verb.
You cannot say *математика кажет сложной – that’s ungrammatical in modern standard Russian.

How does мне нравится express “I like”? Why not say я нравлюсь?

Russian нравиться literally means “to be pleasing”, not “to like”.

The construction is:

кому? (to whom? – dative)
что? / кто? (what/who? – subject in nominative)
нравится / нравятся

So in the sentence:

мне – “to me” (dative)
нравится решать задачи – “solving problems is pleasing”

So the literal structure is:
“To me is pleasing (to) solve problems.” → I like solving problems.

You do not say *я нравлюсь задачи for “I like problems”.
Я нравлюсь means “I am liked” (by someone), e.g.:

Я нравлюсь студентам. – Students like me.

Why is it нравится (singular) and not нравятся (plural)?

The form of нравиться agrees with its grammatical subject, not with the person who likes it.

In the sentence:

решать задачи – “to solve problems” is an infinitive phrase acting as the subject.
Infinitives in Russian are treated as neuter singular subjects.
Therefore the verb appears in 3rd person singular: нравится.

Compare:

Мне нравится задача. – I like the problem. (singular noun → нравится)
Мне нравятся задачи. – I like (the) problems. (plural noun → нравятся)
Мне нравится решать задачи. – I like solving problems. (infinitive phrase → нравится)

Why is the verb решать used and not решить?

This is a question of aspect:

решать – imperfective: ongoing, repeated, habitual action (to be solving / to solve in general)
решить – perfective: a one-time, completed action (to solve, finish solving)

With verbs of liking or preference (любить, нравиться, предпочитать) Russian almost always uses the imperfective to talk about general habits or activities:

Мне нравится решать задачи. – I like solving problems (as an activity).
Я люблю читать. – I love reading.
Он любит плавать. – He likes swimming.

If you said Мне нравится решить задачи, it would sound strange, as if you somehow “like the moment of having completed solving them” – not natural in ordinary speech.

What form and case is задачи, and why is it used?

Задачи here is:

feminine plural
accusative case

The noun is задача (a task / problem). Its forms:

Nominative plural: задачи
Accusative plural (inanimate): задачи (same as nominative)

Because решать is a transitive verb (“to solve something”), its direct object goes into the accusative:

решать задачу – to solve a problem (sg, acc: задачу)
решать задачи – to solve problems (pl, acc: задачи)

So in this sentence задачи is the direct object of решать.

Why is the conjunction но used instead of а?

Both но and а can be translated as “but”, but they are not identical.

но = “but, however” – introduces a stronger contrast or contradiction.
а = “but/whereas” – often used for a milder contrast or simple comparison.

Here, the two parts are in real opposition:

Math seems difficult (negative, intimidating)
but I still like solving problems (positive)

So но fits well:

Математика кажется сложной, но мне нравится решать задачи.

If you use а:

Математика кажется сложной, а мне нравится решать задачи.

it sounds a bit more like a neutral contrast (“Math seems difficult, whereas I like solving problems”), slightly weaker than the natural expectation of contradiction that но gives.

Why isn’t there any word for “is” (like есть) in Математика кажется сложной?

In Russian, the present tense of “to be” (есть) is usually omitted in simple statements:

Математика сложная. – literally “Math difficult.” → Math is difficult.
Он студент. – “He student.” → He is a student.

In your sentence, казаться already functions like a linking verb:

Математика кажется сложной. – Math seems difficult.

Adding есть would be ungrammatical here:

*Математика есть кажется сложной. – wrong.

Can I leave out мне and just say нравится решать задачи?

Yes, you can say:

Нравится решать задачи.

This then means something like:

“(It is) pleasant to solve problems.”
“Solving problems is enjoyable.”

It becomes a more general, impersonal statement – you’re not explicitly saying who likes it.

With мне:

Мне нравится решать задачи. – I like solving problems (specifically me).

So:

With мне – the speaker is specified.
Without мне – it sounds like a general remark or like you’re just mentioning the activity is enjoyable (often context will still make it clear you mean yourself).

How is the whole sentence pronounced, and where is the stress in each word?

Stresses (capital letter marks the stressed vowel):

МатемАтика – ma-te-MA-ti-ka
КАжется – KA-zhe-tsa
СлОжной – SLO-zhnoj
но – no (always stressed, it’s just one syllable)
мне – mne (also one syllable, stressed)
НРАвится – NRA-vi-tsa
решАть – re-SHATʹ
задАчи – za-DA-chi

So the full sentence with marked stress:

МатемАтика КАжется слОжной, но мне НРАвится решАть задАчи.

What’s the nuance difference between Математика кажется сложной and Математика сложная?

Математика сложная.
Direct statement: Math is difficult. You present it as a fact.
Математика кажется сложной.
More cautious/subjective: Math seems difficult / appears to be difficult.
This suggests:
- It’s your impression, not an absolute fact.
- It may be based on limited experience.
- It could change later (“it seems hard now”).

So кажется softens the statement and makes it sound more personal and subjective.