Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates
From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson
The Victory and the Parties
The political parties of Rome continued their pitiful quarrels over the carcase, without troubling themselves about the great chapter in the world's history the first page of which was thus opened, without even giving way to the pure feeling that on this day Rome's aristocrats as well as Rome's democrats had done their duty. The rivalry of the two generals--who were not only political antagonists, but were also set at variance in a military point of view by the so different results of the two campaigns of the previous year--broke out immediately after the battle in the most offensive form.
Catulus might with justice assert that the centre division which he commanded had decided the victory, and that his troops had captured thirty-one standards, while those of Marius had brought in only two, his soldiers led even the deputies of the town of Parma through the heaps of the dead to show to them that Marius had slain his thousand, but Catulus his ten thousand.
Nevertheless Marius was regarded as the real conqueror of the Cimbri, and justly; not merely because by virtue of his higher rank he had held the chief command on the decisive day, and was in military gifts and experience beyond doubt far superior to his colleague, but especially because the second victory at Vercellae had in fact been rendered possible only by the first victory at Aquae Sextiae.
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Reference address : https://www.ellopos.net/elpenor/rome/4-05-peoples-north.asp?pg=51