zesteryoo

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[slender crystal]

It's not « avoir un mal », it's just « avoir mal ». « mal » here is acting like an adverb and it generally means 'to hurt, to ache'. Thus, « à + body part » just designates where the ache is. I can translate « J'ai mal à la tête » as 'I have a headache' but more literally it would be something like 'I have pain in my head'.

For the second part, the plural « maux », that's « mal » as a noun: « un mal de tête (a headache), un mal de dos (backache) ». The construction here is the descriptive « de » wherein it describes the part that has some pain.

[fervent minnow]

so diff body parties use diff prepositions?

[slender crystal]

It's not about the body part, it's about the construction

[wanton wren]

Avoir mal ≈ to be in pain (add à + body part to specify where)

Un mal (de tête, de dos) ≈ a [head/back/etc]ache

Somewhat similar to "my head hurts" vs "I have a headache", though the frequency is a bit different

[fervent minnow]

so you could say J'ai mal a tete and J'ai mal de tete?

[wanton wren]

À la tête

[fervent minnow]

Why?

[wanton wren]

Un mal de tête

[fervent minnow]

Ohhhh

OHHH, tysm,

[wanton wren]

À usually includes an article after it if one exists

[slender crystal]

J'ai mal à la tête (My head hurts)
J'ai un mal de tête (I have a headache)

I've just explained why there's a difference in my first comment

[fervent minnow]

Yeah sorry, tysm

[latent swift]

of course chatgpt would mix them up