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The thirty year long friendship between Imre Lakatos and the classic scholar and historian of mathematics Árpád Szabó had a considerable influence on the ideas, scholarly career and personal life of both scholars. After recalling some relevant facts from their lives, this paper will investigate Szabó's works about the history of pre-Euclidean mathematics and its philosophy. We can find many similarities with Lakatos' philosophy of mathematics and science, both in the self-interpretation of early axiomatic Greek mathematics as Szabó reconstructs it, and in the general overview Szabó provides us about the turn from the intuitive methods of Greek mathematicians to the strict axiomatic method of Euclid's Elements. As a conclusion, I will argue that the correct explanation of these similarities is that in their main works they developed ideas they had in common from the period of intimate intellectual contact in Hungarian academic life in the mid-twentieth century. In closing, I will recall some relevant features of this background that deserve further research.

The circumstance, that the text of Imre Lakatos' doctoral thesis from the University of Debrecen did not survive, makes the evaluation of his career in Hungary and the research of aspects of continuity of his lifework difficult. My paper tries to reconstruct these newer aspects of continuity, introducing the influence of László Kalmár the mathematician and his fellow student, and Sándor Karácsony the philosopher and his mentor on Lakatos' work. The connection between the understanding of the empirical basis of exact ideas—which is a common feature in the papers of the members of the Karácsony-circle—and Lakatos' way of thinking regarding mathematics is more direct and can be documented through his connection to Kalmár. The central element of Lakatos' philosophy of mathematics is criticism of formalism and his tendency is to use the empirical view. Discussions at the 1965 International Colloquium in the Philosophy of Science in London were very helpful in clarifying the quasi-empirical conception. Kalmár's lecture in London, based on one of his papers published by Karácsony in 1942, emphasized the empirical character of mathematics. After this colloquium some elements of the heritage of the Karácsony-circle were integrated again in the development of Lakatos' way of thinking. First I will analyze the Kalmár lecture of 1965 at the Colloquium of Philosophy of Science and Lakatos's reflections on the problem

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of the foundation of mathematics. Then I will present their common Hungarian background, their education and the beginning of their career, which have many important common features; third I draw attention to the network of contacts of Karácsony-disciples.

Lakatos is considered to be a Popperian who adapted his Hegelian-Marxist training to critical philosophy. I claim this is too narrow and misses Lakatos' goal of understanding scientific inquiry as heuristic inquiry—something he did not find in Popper, but found in Polanyi. Archival material shows that his 'new method' struggled to overcome what he saw as the Popperian handicap, by using Polanyi.

Heuristic is a central concept of Lakatos' philosophy both in his early works and in his later work, the methodology of scientific research programs (MSRP). The term itself, however, went through significant change of meaning. In this paper I study this change and the 'metaphysical' commitments behind it. In order to do so, I turn to his mathematical heuristic elaborated in Proofs and Refutations. I aim to show the dialogical character of mathematical knowledge in his account, which can open a door to hermeneutic studies of mathematical practice.