István Hatvani's health was poor as a child. He was fortunate to make it through the first few years of life and it is interesting to remark at this point that he would later become the first Hungarian to undertake a statistical analysis of infant mortality and to make medical deductions from the data. Hatvani's parents wanted him to become a priest and his initial education was designed with this in mind.
Hatvani attended schools in Rimaszombat which today is named Rimavská Sobota and is in central Slovakia, Losonc which today is named Lucenec and is also in central Slovakia, Kecskemét which is the county town of Bács-Kiskun in central Hungary 80 km southeast of Budapest, and Komárom which lies on the south bank of the Danube across from Komárno in present day Slovakia on the other side. He then went to Debrecen, one of the most important cities in eastern Hungary, to study at the Protestant College there. This College had an excellent reputation and was by Hatvani's time an ancient institution being founded in the middle of the 16th century.
In late 1738 an epidemic of the plague swept through Transylvania and reached Debrecen. All who could afford to leave the town did so and most students at the College, including Hatvani, did just this. By the first months of 1739 only thirty students remained at the College, and by this time Hatvani had moved back to Losonc (Lucenec) where he had been at school and there he worked as a tutor. He remained there until 1741 when, the epidemic having passed, he returned to his studies at the Protestant College of Debrecen. He graduated from the College in 1745 and continued his studies abroad at Basel in Switzerland. He was able to undertake foreign studies since he was supported by a scholarship given to him by the town of Debrecen.
In Basel Hatvani studied theology and medicine and was awarded a doctorate in both these subjects. Most importantly for his future career, he attended lectures by Johann Bernoulli and Daniel Bernoulli. They lectured on mathematics, physics and medicine and under their guidance Hatvani soon gained a reputation as an outstanding scientist. Turning down offers of posts at the University of Heidelberg, at the University of Marburg, and at the University of Leiden, Hatvani returned to the Protestant College of Debrecen in 1748 and began his career as a lecturer there.
In 1749 he gave his inaugural lecture at College of Debrecen :-
Hatvani started his inaugural address by exposing the backwardness of mathematical culture in Hungary and went on to prove how important a role this science played in a whole range of exact sciences. He went so far as to declare that mathematics was the only science whose findings could surely be relied on and whose conclusions were beyond doubt.Hatvani made his most significant contribution when he published Introductio ad principia philosophicae solidioris in 1757. In this work Hatvani described the theory of probability, in particular basing his material on Jacob Bernoulli's Ars conjectandi . Here is a sample question he posed (see for example  or ):-
Let us suppose that a commander despatches 100 troops to defend a camp; 12 of them are German, 4 Hungarian and 84 Croatian. One of them deserts. Now, I wish to know the probability of the deserter being Hungarian or Croatian.In  Horváth looks at the Introductio seeing that this work makes Hatvani the first Hungarian to present work on statistics. For example Hatvani presents tables for the number of births in Debrecen for the years 1750 to 1753 inclusive. He records the number of children who died within a year of being born and, finding a mortality rate of 34.2% which was well above that in other European countries (around 19%), he seeks medical reasons to explain the findings.
In fact Hatvani used his medical skills not only in such investigations, but also in caring for the health of the students at the College of Debrecen. Outside the College he used his knowledge of religious matters to support the Protestant Church, and he also was appointed as a judge in the County Court in 1783.
Article by: J J O'Connor and E F Robertson