"Każdy człowiek umie liczyć."
Translation:Each person knows how to count.
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"mogę" is 1st person singular (as you wrote), so perhaps it makes more sense to focus on 3rd person singular "może" here.
"może" would either mean that he/she/it is allowed to, or at least 'able to' do it.
"umie" means that he/she/it 'knows how to do' something, possesses the knowledge and skills. Like "Mój syn ma pięć lat i już umie czytać" = My son is five and he already [knows how to/can] read.