Learn Hardcore Croatian: Matematika je teška, ali zanimljiva.

Matematika on its own can mean math, the math, mathematics, etc., depending on context.
If you need to show definiteness or specificity, you do it with word order, context, or demonstratives (e.g. ova matematika – this math), not with articles.

Why do teška and zanimljiva end in -a?

Because they agree with matematika in gender, number, and case.

Matematika is a feminine noun (most nouns ending in -a are feminine).
It is singular and in the nominative case (subject of the sentence).
Predicate adjectives must match: feminine + singular + nominative → teška, zanimljiva.

So you get:

Matematika je teška.
Matematika je zanimljiva.
Combined: Matematika je teška, ali zanimljiva.

What does teška literally mean, and why is it used for “difficult”?

Literally, teška is heavy (feminine form of težak = heavy).

By extension, just like in English you say a heavy book or a heavy topic to mean “demanding,” in Croatian težak/teška is very commonly used to mean difficult/hard:

teška matematika – hard/difficult math
težak ispit – a difficult exam
težak zadatak – a tough task

Why is there a comma before ali?

In standard Croatian, you always put a comma before ali (but) when it connects two parts of a sentence:

… je teška, ali zanimljiva.

This is tighter than English, where sometimes people omit the comma before but in short sentences. In Croatian, the comma is expected in writing.

Why is there no je before zanimljiva?

The verb je (is) is shared by both adjectives:

Matematika je teška
(Matematika je) zanimljiva

Instead of repeating je, Croatian normally uses it once:

Matematika je teška, ali zanimljiva.

So you understand the second part as ali (je) zanimljiva, even though je is not written or spoken.

Can I say Matematika je teška, ali je zanimljiva? Is it wrong?

It’s not wrong; it’s grammatically fine.

Matematika je teška, ali je zanimljiva.

Adding the second je can slightly emphasize the contrast or make the rhythm clearer in speech, but in neutral style the shorter version (without the second je) is more common:

Neutral: Matematika je teška, ali zanimljiva.
Slightly more emphatic/explicit: Matematika je teška, ali je zanimljiva.

Could I change the word order, for example: Teška je matematika, ali zanimljiva?

Yes. Croatian word order is more flexible than English. Some possible variants:

Matematika je teška, ali zanimljiva. – neutral, most common.
Matematika je zanimljiva, ali teška. – same meaning, but the emphasis shifts: first on interesting, then hard.
Teška je matematika, ali zanimljiva. – stylistic; puts stress on teška.

All of them are correct; the differences are emphasis and style, not basic grammar.

Why is Matematika capitalized? Is the subject name normally capitalized?

In Croatian:

School subjects are written with a lowercase letter: matematika, fizika, engleski.
The first word of a sentence is capitalized.

So here, Matematika is capitalized only because it is the first word of the sentence, not because it’s a subject name. In the middle of a sentence, you would write matematika.

What case is matematika, and what case are teška and zanimljiva?

All three are in the nominative singular feminine.

Matematika – nominative subject.
teška, zanimljiva – predicate adjectives, so they also use the nominative to match the subject.

Pattern:

[Nominative subject] + je + [predicate adjective in nominative]
→ Matematika je teška.
→ Matematika je teška, ali zanimljiva.

Can I drop je and say Matematika teška, ali zanimljiva?

In standard Croatian, you should keep je:

Correct standard: Matematika je teška, ali zanimljiva.

You might hear Matematika teška, ali zanimljiva in very informal speech, titles, or slogans, where verbs are often dropped for brevity or effect. But for normal, correct sentences, you should include je.

How do you pronounce š and j in this sentence?

Pronunciation tips:

š in teška: like sh in English.
teška ≈ tesh-ka.
j in je and zanimljiva: like y in yes.
je ≈ ye, zanimljiva ≈ za-neem-lyi-va (approximate).
lj in zanimljiva is a single sound, similar to the lli in million in many accents: a “soft l”.

So, roughly: ma-te-MA-ti-ka je TESH-ka, a-li za-nim-LYI-va (capital letters = stressed syllables, roughly on ma and te in matematika, and nim in zanimljiva in many pronunciations).

Are there other words for but besides ali, and could I use them here?

Yes, there are a few common contrast words:

ali – the most neutral but.
→ Matematika je teška, ali zanimljiva.
no – also but, often a bit more formal or stronger.
→ Matematika je teška, no zanimljiva.
međutim – closer to however, usually starts a new clause or sentence.
→ Matematika je teška, međutim zanimljiva. (sounds more formal/written)

In everyday speech, ali is by far the most natural choice in this sentence.

Is matematika countable in Croatian, like “a math” or “two maths”?

No. Matematika is normally treated as a mass/abstract noun, like mathematics in English:

Volim matematiku. – I like math / mathematics.
You don’t say jedna matematika / dvije matematike to mean one math, two maths.

When you want to count specific parts or types, you use other nouns:

dva zadatka iz matematike – two math problems
tri kolegija iz matematike – three math courses