Back

The document discusses the work of Piero della Francesca, a painter from the Italian Renaissance, and his painting “The Brera Madonna.” This painting reflects the shift in art during the Renaissance, where figures are represented as human beings without halos and stand solidly on the ground. The document also discusses the break between the new spirit of the fifteenth century and the spirit of the Middle Ages.

The document then transitions to discuss the development of mathematics during the Renaissance. Luca Paccioli, a mathematician born in the mid-15th century, played a significant role in advancing mathematics during this time. He wrote a book called “Summa de arithmetic, geometria et proportionalità” in 1494, which set out the basic principles of algebra and contained multiplication tables up to 60 × 60. The book also introduced the concept of double-entry bookkeeping, which had significant economic consequences.

Paccioli’s work caught the attention of Leonardo da Vinci, who became a close friend of Paccioli. Leonardo, known for his talents in art and various sciences, was particularly interested in the relationship between mathematics and art. Paccioli encouraged Leonardo to master mathematical concepts, and Leonardo provided complex drawings for Paccioli’s other famous work, “De Divine Proportione.”

The document then explores the history of probability and how it relates to mathematics. Paccioli’s book also addressed the concept of probability, specifically through a brain-teaser about dividing stakes in an uncompleted game. This problem, known as the problem of the points, marked the beginning of a systematic analysis of probability. The document discusses the ancient Greeks’ lack of interest in probability and how the Renaissance marked a shift towards experimentation and investigation.

Girolamo Cardano, a 16th-century physician and gambling addict, made significant contributions to the field of probability. He wrote a book called “Liber de Ludo Aleae” in 1525, which was the first serious effort to develop the statistical principles of probability. Cardano introduced the concept of expressing probability as a fraction and explored the probability of various outcomes in games of chance, such as dice-throwing.

The document also mentions Galileo, who wrote an essay on gambling in 1623 called “Sopra le Scoperte dei Dadi.” Galileo’s essay drew on Cardano’s work and further explored the frequency of outcomes in games of chance. The document concludes by discussing the advancements in probability analysis made in the 17th and 18th centuries and the importance of understanding how humans recognize and respond to probabilities in risk management and decision-making.

Words: 406