After getting many failing grades in the first weeks, I came to understand that I had to work hard, and by the end of the first year I was near the top of my class. This was really the experience that started me on the path toward knowledge and science. My two most influential teachers were János Pogány, who taught mathematics, and Zoltán Fórián-Szabó, who taught physics and chemistry.

János Pogány was a very passionate person, he experienced every stupidity or ignorance of a pupil as a personal pain, or as an insult ... He was impressive and terrifying ..

He was terrifying and had a heart of gold. A lion and worthy of love. He roared, but if he was offended, he spoke so softly that you could hear the buzzing of a fly. ... Those who were captivated by him became outstanding scientists.

In 1948, R Frucht proved that, given a finite group $G$, there are infinitely many connected cubic graphs $X$ such that the automorphism group $Aut X$ is isomorphic to $G$. In a letter, Professor Frucht has proposed the problem, whether in addition $X$ can be required to be hamiltonian. One of the aims of the present note is to answer this question affirmatively.

Fried and Sichler have proved that the category of integral domains of characteristic zero is strongly binding. [Note. A category is said to be binding if every algebraic category can be fully embedded in it.] They conjectured (oral communication by E Fried) that no "natural" subcategory of this category is binding. The aim of this paper is to disprove this conjecture.

It is proved that to any finite group G there exists a finite algebraic extension of the field of rationals whose automorphism group is isomorphic to G. This answers in the affirmative a weakened form of a question of Emmy Noether on the existence of fields with prescribed Galois group.

László Babai and Ervin Fried told me that there was this large branch of mathematics, called algebraic geometry, which was completely unknown in Hungary at that time. So I decided to learn it. For two years I worked completely alone, with only a few books. It was slow going, with nobody to consult, but it resulted in my learning the foundations very well. After that I spent two semesters in Moscow as an exchange student, where I attended the lectures of Vasilii Iskovskikh and Yuri Manin, and the seminar of Igor Shafarevich.

I was very disheartened, but this turned out to be one of the great lucky twists in my life.

A direct collaboration with pure mathematicians is uncommon for a physicist, particularly an experimentalist. But Alicia Kollár is no stranger to mathematics. Raised by two mathematicians in Princeton, New Jersey, she was exposed to the discipline early on. However, Alicia Kollár said her parents didn't pressure her to pursue mathematics growing up.

"It never crossed my dad's mind to try to force me to do what he loved," Alicia Kollár said. "He considered that pointless, like 'You should go into research for you, not for somebody else's expectations.'"

Her father, János Kollár, a professor of mathematics at Princeton, had a slightly different take.

"She was always interested in science, so I didn't need to apply any influence," he said. "If she was only interested in rock music it might have been different."

This turned out to have a decisive influence on my work, both in our joint papers, books and in my work ever since.

... three intense Summer Seminars where dozens of young algebraic geometers came together to work on the rapidly developing minimal model programme, the moduli theory of canonical models and the early stages of the study of rationally connected varieties. These three topics have been the main areas of my research ever since.

For thirty years János Kollár has researched geometrically oriented algebraic geometry. Besides providing many positive results, he has worked to guide the direction of the field by locating and opening up productive new avenues of investigation. Among other areas, his work has focused on the study of minimal models and their singularities; the analysis of rational and rationally connected varieties; the study of fundamental groups and universal covering spaces of algebraic varieties; the topology of real algebraic threefolds; and compactifications of moduli spaces.

What I especially like is when I teach a class of non-mathematicians and then at the end of the year one or two students usually come to me and say "I would like to be a mathematician now."