Его интерес к науке вырос.

Here его means his.

So Его интерес к науке = his interest in science.

A useful thing to know is that его is an unchanging form:

• его книга = his book
• я вижу его = I see him
• у его брата = at his brother’s / of his brother

So in this sentence, you understand from position and function that его is possessive, not him.

Because Russian normally uses the pattern:

интерес к + dative

This is the standard way to say interest in something.

Examples:

• интерес к музыке = interest in music
• интерес к истории = interest in history
• интерес к детям = interest in children

For an English speaker, this can feel odd because Russian uses к, which literally often means to/toward, not in. But with интерес, you should learn the whole pattern as a fixed combination:

интерес к чему? = interest in what?

Because the preposition к requires the dative case.

The dictionary form is наука.
Its dative singular form is науке.

So:

• наука = science
• к науке = toward science / in science, after интерес

This is why you get:

интерес к науке

not интерес к наука.

Вырос is the past tense, masculine singular form of the verb вырасти.

So:

• infinitive: вырасти = to grow, to increase
• past masculine: вырос
• past feminine: выросла
• past neuter: выросло
• past plural: выросли

In this sentence, it is masculine singular because the subject is интерес, and интерес is a masculine noun.

Because Russian verb forms in the past tense agree with the grammatical gender of the noun, not with biological sex.

Интерес is grammatically masculine, so the verb is:

• интерес вырос

Compare:

• цена выросла = the price went up
  (цена is feminine)
• число выросло = the number increased
  (число is neuter)

So вырос does not mean anything male is involved; it just matches the noun интерес.

Yes. Literally, вырос means grew, but in English this sentence is often translated more naturally as:

• His interest in science grew.
• His interest in science increased.

Both are good translations.

Russian often uses grow in places where English might prefer increase, especially with abstract things like:

• интерес вырос = interest grew / increased
• спрос вырос = demand grew / increased
• цены выросли = prices rose / increased

Because Russian does not form the past tense the way English does.

English can say:

• grew
• has grown

Russian simply uses the past tense form:

• вырос

So Его интерес к науке вырос can correspond to English:

• His interest in science grew
• His interest in science has grown

The exact English tense depends on context and translation style, not on an extra word in Russian.

The subject is the whole noun phrase:

Его интерес к науке

The main noun inside that phrase is интерес, and that is what the verb agrees with.

So the structure is:

• Его = his
• интерес = interest
• к науке = in science
• вырос = grew / increased

Even though науке comes right before the verb, it is not the subject. It is part of the phrase attached to интерес.

Yes. Russian word order is more flexible than English word order.

The neutral order here is:

Его интерес к науке вырос.

But other orders are possible, depending on emphasis. For example:

• Интерес к науке у него вырос.
• У него вырос интерес к науке.

These can sound more natural in certain contexts, especially if you are introducing interest as new information or emphasizing in him / on his part.

Very roughly:

• Его интерес к науке вырос = straightforward, neutral
• У него вырос интерес к науке = a bit more like He developed / came to have a growing interest in science

Yes, absolutely.

Both are natural, but they are built differently:

• Его интерес к науке вырос = his interest in science grew
• У него вырос интерес к науке = literally at him, an interest in science grew, meaning he developed an interest in science / his interest in science grew

The first version treats interest as the main thing from the start.
The second version often feels a little more dynamic, as if the interest arose or developed in him.

This is a question of aspect.

• вырос is perfective
• рос is imperfective

Here вырос presents the growth as a completed change or result:

• his interest grew / increased

Рос would focus more on the process:

• Его интерес к науке рос = His interest in science was growing / kept growing

So:

• вырос = result, change achieved
• рос = ongoing development

Usually yes.

In this sentence, наука means science in the general sense. So интерес к науке is naturally interest in science.

Depending on context, наука can also mean:

• science as a field of study
• scholarship / academic knowledge
• a particular science in some contexts

But in a sentence like this, the broad meaning science is the normal one.