He was most probably educated by the Jesuits at the Academy of Vilnius. As a lawyer, he managed the affairs of, for instance, Hetman Michał Kazimierz Ogiński. He was, however, unable to keep the chamberlainship and the office of ‘horodniczy’ (aedile) of Grodno. He did not manage to convince Ignacy Potocki to support him in his endeavours to obtain employment in the office of the city police or fire brigade. Equally unsuccessful were his efforts to secure for himself the stewardship of Jeziory, Skidel, or Skołubów in the Grodno region. Some of the setbacks in his professional and political career were due to the reservedness with which some of his view were perceived as expressed by Krzywkowski in his reputedly quite radical journalism. In 1790 he issued a pamphlet O sukcesji tronu i władzy stanów which was then extended in the next edition entitled O sukcesji tronu, władzy stanów i urzędach. In these works he postulated, among others, introducing a hereditary monarchy (after appointing the Elector of Saxony or a Royal Prince of Great Britain to the throne) and limiting the importance of magnates (through, for example, replacing the titles held for life with offices held for a predetermined term). In 1791 he published another pamphlet Gospodarstwo polityczne, in which he proposed a plan for obtaining the funds and resources for the army from the sales of the larger ‘starosties’ (i.e., crown lands). Following the adoption of the Constitution of the 3rd of May, he proclaimed that it was necessary to support it. He also praised the endeavours of the Americans, who were building their new order under the leadership of George Washington. Trying to escape from the Targowica Confederation, Krzywkowski crossed the Prussian border. His last letter addressed, as was his habit, to King Stanisław II Augustus, dates back to just that period. His further fate remains unknown.