We have decided to share more interesting facts from the history of mathematics. We are starting with some interesting events that happened in August. Hope you will like these posts!

### 10 August 1548

Everything started with Tartaglia giving Cardan the method to solve the cubic. Cardan didn’t want to break his promise for a very long time. Everything was fine until another mathematical colleague, Annibale della Nave, showed Cardan that Tartaglia was not the only one to have solved this problem.

After that Cardan published both the solution to the cubic and Ferrari’s solution to the quartic in Ars Magna (1545) convinced that Tartaglia was not the first – or the only one – to solve the cubic. As expected, Tartaglia was furiou. At this point Ferrari (Cardan’s student) wrote to Tartaglia challenging him to a public debate. Tartaglia was extremely reluctant to dispute with Ferrari, still a relatively unknown youngster, against whom even a victory would do little material good.

Tartaglia wrote back to Ferrari, trying to bring Cardan into the debate. For more than a year Ferrari and Tartaglia wrote fruitlessly to each other, but they didn’t manage to solve the dispute. In 1548, Tartaglia received an offer of a lecturing position in Brescia. To establish he was the man for the job, he was asked to journey to Milan and conclude the contest with Ferrari.

On 10 August 1548, the contest which all Italy wanted to see, for the correspondence between the two antagonists had taken the form of open letters, took place in the Church in the Garden of the Frati Zoccolanti in Milan. A huge crowd had gathered, and the Milanese celebrities came out in force, with Don Ferrante di Gonzaga, governor of Milan, the supreme arbiter. Ferrari was confident of success, despite his inexperience in such matters, and brought a large crowd of friends and supporters. Alone but for his brother, Tartaglia was a vastly experienced disputant and also fancied his chances.

By the end of the first day, it was clear that things were not going Tartaglia’s way. He was unwilling to give Ferrari time to respond to his criticisms and when he did, it was Ferrari who got in the more telling blows. Ferrari clearly understood the cubic and quartic equations more thoroughly than his opponent who decided that he would leave Milan that very night and thus leave the contest unresolved, so victory went to Ferrari. On the strength of this challenge, Ferrari’s fame soared and he was inundated with offers of employment, including a request from the emperor himself, who wanted a tutor for his son.

Find out more: Ferrari Biography

### 10 August 1846

The Smithsonian Institution was founded “for the increase and diffusion of knowledge”.

The mathematics collection from the Institution holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

### 26 August 1735

Euler presented a solution to the problem known as the Seven Bridges of Königsberg. The city of Königsberg, Prussia was set on the Pregel River, and included two large islands that were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point. The solution to this problem is considered to be the first theorem of graph theory, specifically of planar graph theory.

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other.

### 31 August 1899

On 31st August 1899, Cantor wrote to Dedekind remarking that his diagonal process could be used to show that the power set of a set (A Power Set is a set of all the subsets of a set.) has more elements than the set itself.

In set theory, Cantor’s diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. Such sets are now known as uncountable sets, and the size of infinite sets is now treated by the theory of cardinal numbers which Cantor began.

### 31 August 1950

On 31st August 1950, Kurt Godel addressed the International Congress of Mathematicians in Cambridge, Massachusetts, on his work in relativity theory. The lecture was called “Rotating Universes in General Relativity Theory”.

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