Η φυσική χρειάζεται μαθηματικά.

Η is the definite article meaning the.

So η φυσική means physics as a school subject or field of study, literally the physics.

A few useful details:

• η is the article for feminine singular nouns in the nominative case.
• φυσική is treated as a feminine singular noun here.

Greek often uses the definite article in places where English does not. So even though English usually just says Physics, Greek often says η φυσική.

Because the noun φυσική comes from the adjective φυσικός / φυσική / φυσικό, meaning physical or natural, and in Modern Greek it is also used as a noun meaning physics.

As a subject name, it has become a feminine noun:

• η φυσική = physics
• η χημεία = chemistry
• η βιολογία = biology

So this is something you mostly learn as part of the word itself: φυσική is simply a feminine noun meaning physics.

It is in the nominative case because it is the subject of the sentence.

In Η φυσική χρειάζεται μαθηματικά, the subject is η φυσική = physics, and the verb is χρειάζεται = needs.

So the basic structure is:

• η φυσική = subject
• χρειάζεται = verb
• μαθηματικά = object

Great question. Yes, -εται is a form associated with the mediopassive set of endings in Modern Greek. But some Greek verbs use these endings while having an active meaning.

χρειάζομαι is one of those verbs. It means to need.

Its 3rd person singular form is:

• χρειάζεται = he/she/it needs

So in this sentence:

• Η φυσική χρειάζεται μαθηματικά.
• Physics needs mathematics.

Even though the form looks passive to an English speaker, here it is functioning with an active meaning.

Yes, in some contexts χρειάζεται can be understood as is needed or is necessary, depending on the structure.

For example:

• Χρειάζεται βοήθεια. = Help is needed / There is a need for help.

But in your sentence, the meaning is clearly:

• Η φυσική χρειάζεται μαθηματικά.
• Physics needs mathematics.

That is because η φυσική is the subject doing the needing.

So the same form can sometimes be translated differently depending on the sentence.

In Greek, μαθηματικά is a neuter plural noun in form.

This is very common for school subjects and languages:

• τα μαθηματικά = mathematics / math
• τα αγγλικά = English
• τα ελληνικά = Greek

So even though English may treat mathematics as singular, Greek uses a form that is grammatically plural.

Here, μαθηματικά is the direct object of the verb:

• Η φυσική χρειάζεται μαθηματικά.
• Physics needs mathematics.

Both article use and article omission can happen in Greek, depending on how specific or general the noun is meant to be.

Here, μαθηματικά without the article sounds more like:

• math
• mathematics in general
• some mathematical knowledge

If you said τα μαθηματικά, it could sound more like:

• mathematics as a recognized subject
• the math, more specifically

So:

• Η φυσική χρειάζεται μαθηματικά = Physics needs math / mathematical knowledge.
• Η φυσική χρειάζεται τα μαθηματικά = possible, but more specific or more emphatic in tone

In many learning contexts, the version without the article is a natural way to express the idea generally.

It is in the accusative case, because it is the direct object of χρειάζεται.

The tricky part is that for some neuter plural nouns, the nominative and accusative forms look the same.

So μαθηματικά could be nominative or accusative in form, but here it is accusative because it is the thing being needed.

Greek word order is more flexible than English word order.

The neutral order here is:

• Η φυσική χρειάζεται μαθηματικά.

But other orders are possible for emphasis, such as:

• Μαθηματικά χρειάζεται η φυσική.
• Η φυσική μαθηματικά χρειάζεται.

These alternatives change the emphasis, not the core meaning. For a learner, the original order is the safest and most neutral.

A rough pronunciation guide is:

• Η φυσική χρειάζεται μαθηματικά
• ee fee-see-KEE hree-A-ze-te ma-thee-ma-tee-KA

A few pronunciation notes:

• η sounds like ee
• φ sounds like f
• χρ in χρειάζεται can be hard for English speakers; χ is a throaty sound, somewhat like the ch in German Bach
• the stressed syllables are:
  • φυσική
  • χρειάζεται
  • μαθηματικά

Stress matters a lot in Greek because it is part of the correct form of the word and helps distinguish natural pronunciation.

In this sentence:

• φυσική
• χρειάζεται
• μαθηματικά

If you place the stress incorrectly, a native speaker will usually still understand you, but it will sound non-native and may sometimes cause confusion.

So it is worth learning each word together with its accent.

Yes. In translation, μαθηματικά can correspond to:

• mathematics
• math
• sometimes maths in British English

Which English word you choose depends mostly on style and dialect, not on a difference in the Greek word itself.

It can naturally refer to either, depending on context.

It could mean:

• Physics as a subject needs mathematics
• The field of physics requires mathematics

Greek often uses the same noun for both the school subject and the academic discipline, just as English does with words like physics and chemistry.

So the sentence works well in both a classroom context and a more general academic one.