Learn Hardcore Croatian: Bez obzira na to što znanost ponekad izgleda teška, znanstvenica ostaje strpljiva. - Regardless of the fact that science sometimes looks hard, the scientist female remains patient.

So literally: “without regard to that that science sometimes looks difficult …” → idiomatically: “Even though science sometimes seems difficult, …”

It introduces a concessive clause (expressing contrast). It’s used a lot in both spoken and written Croatian.

Why isn’t znanost in the genitive after bez obzira? Shouldn’t bez take the genitive?

The preposition bez does indeed take the genitive (e.g. bez znanosti – without science).
But notice the structure here:

Bez obzira na to što [znanost ponekad izgleda teška], znanstvenica …

The word governed by bez is obzira (genitive singular of obzir).
Then we have na to, and što znanost ponekad izgleda teška is a subordinate clause introduced by što, explaining what “that” (to) refers to.

So znanost is not an object of bez. It is the subject of the verb izgleda in the embedded clause:

što znanost ponekad izgleda teška
→ “that science sometimes seems difficult”

As a subject, znanost is in the nominative.

What case is to in, and why?

To here is in the accusative singular neuter because it is governed by the preposition na:

na to = “on that / to that / regarding that”

Structure:

bez
- obzira (genitive)
na
- to (accusative)

Na to što… is a common pattern meaning roughly “(with regard) to the fact that…”. The što-clause explains what to is referring to.

What is što in this sentence: a question word, a relative pronoun, or a conjunction?

In this sentence, što functions essentially as a conjunction, similar to English “that” in:

“regardless of the fact that science sometimes seems difficult”

More technically:

It introduces a subordinate content clause:
što znanost ponekad izgleda teška
→ “that science sometimes seems difficult”

It is not a question word here (no question is being asked), and it isn’t a typical relative pronoun modifying a noun, but rather introducing the entire clause that completes the meaning of to (“that”).

Why is teška in the feminine singular form?

Teška is the feminine singular form of the adjective težak (“hard, difficult, heavy”).

It is in this form because it agrees with the subject znanost, which is:

znanost – feminine, singular, nominative
teška – feminine, singular, nominative

In Croatian, a predicative adjective (an adjective used with a verb like to be, to seem, to look) agrees in gender, number, and case with the subject:

znanost je teška – science is difficult
znanosti su teške – (many) sciences are difficult

Here:
znanost (F.SG.NOM) … izgleda teška (F.SG.NOM)

What’s the difference between izgleda teška and je teška?

je teška – “is difficult”
- uses the verb biti (to be)
- states a more direct fact: “science is difficult”
izgleda teška – “looks/seems difficult”
- uses the verb izgledati (to look, seem, appear)
- expresses appearance or impression:
  “science seems/appears difficult”

So:

Znanost je teška. – Science is (objectively) difficult.
Znanost izgleda teška. – Science seems difficult (maybe at first glance, or to some people).

In your sentence the nuance is: even if it seems difficult, the scientist remains patient.

Why is ponekad placed between znanost and izgleda? Could it go somewhere else?

Ponekad means “sometimes” and is an adverb of frequency. Croatian word order is relatively flexible, so several positions are possible:

Znanost ponekad izgleda teška. (used here)
Ponekad znanost izgleda teška.
Znanost izgleda ponekad teška. (possible, but less neutral)

All three are grammatical. The most neutral and common options are:

Ponekad znanost izgleda teška.
Znanost ponekad izgleda teška.

The chosen order (subject – adverb – verb) is very natural and lightly emphasizes that it is not always, but sometimes, that science appears difficult.

What tense and aspect is ostaje, and why this verb instead of just “to be”?

Ostaje is:

present tense, third person singular
of the verb ostajati (imperfective aspect), “to remain, to stay”

So znanstvenica ostaje strpljiva means:

“the scientist remains patient” / “stays patient”

Why not just je strpljiva (“is patient”)?

je strpljiva simply states a current quality.
ostaje strpljiva emphasizes continuity and persistence despite something (here: despite science seeming difficult).

It fits the concessive idea:
“Even though X, she remains Y.”

Why is it znanstvenica (feminine) instead of znanstvenik?

Croatian commonly marks grammatical gender on nouns referring to people.

znanstvenik – male scientist or generic “scientist” (traditionally masculine default)
znanstvenica – female scientist

The suffix -ica is a typical feminine ending for many professions and roles:

učitelj → učiteljica (male teacher → female teacher)
glumac → glumica (actor → actress)
znanstvenik → znanstvenica (male scientist → female scientist)

Your sentence explicitly refers to a female scientist.

Why is there a comma before znanstvenica ostaje strpljiva?

The part starting with Bez obzira na to što… is a subordinate (dependent) clause, expressing a condition/contrast:

Bez obzira na to što znanost ponekad izgleda teška,
→ “Even though science sometimes seems difficult,”

The comma separates this introductory dependent clause from the main clause:

znanstvenica ostaje strpljiva.

In Croatian, when a subordinate clause comes first, it is usually followed by a comma before the main clause.

Can we say Bez obzira na to da znanost ponekad izgleda teška instead of što?

No, that would not be natural Croatian here.

In this “bez obzira na to …” pattern, the subordinate clause is normally introduced by što, not da:

bez obzira na to što… – correct, natural
bez obzira na to da… – sounds wrong or at least very odd in standard Croatian in this usage

So you should keep što after na to in this structure.

What’s the difference between bez obzira na to što and iako or premda?

All of these introduce a concessive clause (similar to English “although / even though”), but they differ in formality and structure:

bez obzira na to što
- literally “without regard to the fact that”
- slightly more formal / emphatic
- used a lot in both speech and writing
- example:
  Bez obzira na to što je umoran, radi dalje.
  “Even though he is tired, he keeps working.”
iako
- simple, common “although / even though”
- very frequent in everyday speech
- example:
  Iako je znanost teška, znanstvenica ostaje strpljiva.
premda
- similar to iako, often a bit more formal or literary
- example:
  Premda znanost ponekad izgleda teška, znanstvenica ostaje strpljiva.

Your sentence could also be rewritten as:

Iako znanost ponekad izgleda teška, znanstvenica ostaje strpljiva.
Premda znanost ponekad izgleda teška, znanstvenica ostaje strpljiva.

All are grammatical; the nuance is mostly stylistic.

Could we drop na to and say Bez obzira što znanost ponekad izgleda teška?

You will sometimes hear bez obzira što… in spoken language, but:

Bez obzira na to što… is the standard, fully correct form.
Bez obzira što… may sound colloquial and less precise/standard.

For learners and in careful language, it’s safer to use the full pattern:

Bez obzira na to što znanost ponekad izgleda teška, …

Is there any difference between ponekad and katkad?

Both ponekad and katkad mean “sometimes” and are very close in meaning.

ponekad – very common, neutral in everyday speech and writing
katkad – also correct, can sound a bit more formal or stylistic in some contexts, but is widely used

You could say:

Znanost ponekad izgleda teška.
Znanost katkad izgleda teška.

Both are fine and mean the same thing.