וַיַּעְפִּ֕לוּ לַעֲל֖וֹת אֶל־רֹ֣אשׁ הָהָ֑ר וַאֲר֤וֹן בְּרִית־יְהוָה֙ וּמֹשֶׁ֔ה לֹא־מָ֖שׁוּ מִקֶּ֥רֶב הַֽמַּחֲנֶֽה׃
Ma presumevano di salire sulla cima della montagna; nondimeno l'arca dell'alleanza dell'Eterno e Mosè non partirono dal campo.
Rashi on Numbers
ויעפלו is an expression for “strength” (doing a thing by insolent force). Similar is, (Habakkuk 2:4) “Behold it is insolent (עפלה)”, engres in O. F., an expression for insolent force. Similar also is, (Micah 4:8), “stronghold (עפל) of the daughter of Zion”; (Jes. 32:14) “the forts (עפל) and towers”. The Midrash Tanchuma 4:4:19, however, explains it (ויעפלו) to be of the same meaning as אופל, darkness, i.e. they went in darkness — without permission.
Sforno on Numbers
ויעפילו, they stiffened their attitude, similar to Exodus 6,13 where Pharaoh is reported as stiffening his attitude, and as a result not paying heed to Moses’ and Aaron’s warning.
Or HaChaim on Numbers
ויעפילו לעלות אל ראש ההר, But they presumed to go up to the top of the mountain, etc. They erred in thinking that by ascending the mountain they could demonstrate their faith in G'd and that as a result G'd would save them. G'd was not impressed, 1) for their punishment was still too recent to have run its course, and 2) the decree had been made absolute so that G'd could not reverse it. Please compare what I have written on this subject in Deut. 1,43.