Tartalia - the stammering and generous mathematician

The Italian who survived a kitchen as a child, but remained a stutterer as a result of his injury, contributed in the 16th century to mathematics a solution to a cubic equation

Over the years, I witnessed the wonders of the disabled person who managed to bring his healthy parts to capacities that most of us did not believe could be used so extensively. But what about the disability whose main difficulty is speech? How can this be compensated for? The best answer in my opinion was given by Shamai in tractate Avot: "Say little and do much". Indeed, the history standing at the center of the world stage has a number of people who preferred silence in deed to braggadocio in speech, one brings out with freedom labs, the second claims that man came from the monkey and the third writes about a caterpillar that smokes a hookah while sitting on a mushroom. This time I chose to bring the story of another mathematical genius who preferred the paper to the tongue, not necessarily in matters of equations as well as in "wars" of honor and intrigues of the kind that would not embarrass an average reality show. The world of mathematics looks closed and gray from the outside, but below the surface the boiling trend rages and breaks out sometimes as if it wanted to say - "Hey, I'm not what you thought all these years".

Niccolo Fontana was born in 1500 to a poor family in the city of Brescia in Italy and began attending school at the age of four, but the murder of his father two years later brought the family to a state of abject poverty, causing Fontana to leave his studies and essentially begin the mask of his unhappy and angry life. When he was 12 years old, a French legion managed to conquer the town and began a cold-blooded murder of the inhabitants of the place - 46 thousand in number; All of this came as a retaliatory action for the discrimination and humiliation they experienced as a result of the actions of underground people from the city of Brescia. Fontana and his family managed to find temporary shelter in one of the churches in the town but a French warrior managed to hit him in the face with the bayonet and caused a very serious injury to his jaw and palate. Fontana was left bleeding where he was, and even though his mother found him in this condition, she could not afford to finance his medical treatment, but she did everything she could to take care of his health and recovery and was indeed successful in doing so. Later in his life, Fontana used to regularly wear a thick beard to hide the scars on his face, but the thing that remains visible to all due to his injury is the problem with the fluency of speech, which led to the derogatory nickname that was attached to him - "Tartalia", which means in Italian - the stutterer.

Fontana was self-taught in mathematics and his prodigious abilities were revealed to all in the most obvious way which led a rich man named Ludovico Belvisonio to become the patron of the potential genius. Hela moved to the city of Padua but a conflict between the two led to a separation and Fontana had to finance himself through mathematics lessons and a teaching job at a local school in the city of Verona, where he was known to have special skills and even participated in several local mathematical competitions. One of these competitions raised its horn among the world of science at the time when it competed with a minor mathematician named Fior regarding solving cubic equations, that is, those that have a variable in the third power. It is necessary to precede and present two facts and an explanation concerning the popular perception at that time.

In order to try and explain what a general solution to equations of the first, second, third degree and so on means, we can think of a talented basketball player who stands some distance from the basket and has a number of balls in his hands according to the competition in which he participates. If he has one basketball in his hands, then the accepted method to score a basket is to simply grip the ball firmly on both sides and throw it at a certain angle and force, but what about the competition in which the basketball player has 2 balls in his hands and he is supposed to throw them into the basket at once? There are two options before him - to throw one ball in each hand or the more obvious option is to throw two at once with one hand, which will surely prove that he is a real professional if he scores.

Cubic equations behave as if the basketball player had 4, 5 or 6 balls in his hands and he is required with his sharp senses to understand how to throw combinations of 3 balls into the basket at once together with another ball in another hand or even more difficult - two balls in the other hand and still score every time. Surely every reader will agree with me that in order to do this a phenomenal talent is required, isn't it? Well, one fact out of the two I mentioned is that the first solution to this type of equation was already given in the past by an important Italian mathematician named del Ferro, but it was a limited solution to some specific situation and did not include the full range of possibilities that face the composition of such equations, and accordingly For the previous description - he knew how to throw 3 balls into the basket with one hand and one more ball with the other hand, while Fontana knew how to do it with 5 balls, 3 in one hand and 2 in the other.

The second fact is the perception that mathematicians were actually professionals and not people of theory as is customary today, therefore every discovery they discovered - which they revealed to themselves as a professional secret, which is, as we know - solving equations. This was known and can even be seen throughout the lifetime of other mathematicians such as Fermat, Newton and also Del Pero who jealously guarded this solution method. However, it was only when he was on his deathbed that he decided to share his personal secret with his student Fior. Fiore began to flourish as a peacock in his community when it became known that he was hoarding such important information in his mind at that time and even invited Fontana to the duel of minds in 1535 that I mentioned before. Each of the competition participants sent 30 questions to the other participant and he had to answer them in the shortest possible time; Pior thought that Fontana did not know the method for solving the beacons as he knew and surprisingly, that was indeed the case until the morning of the competition day when Fontana received a kind of flash special to geniuses who are in a stressful situation and managed to solve a third degree equation as was known to Pior.

Fontana was able to solve all the questions presented to him by Fiore in less than two hours, while the latter was unable to solve anything. Fontana, in a noble act, decided to give up the monetary prize and remains proud of his victory. The echoes that this competition evoked also reached the city of Milan, which was the seat of another mathematician named Girolamo Cardano, who held to the opinion of the elite mathematician Pacioli that there is no general solution for equations of the third degree. Naturally, Cardano wanted to get his hands on Fontana's method and at one point asked his permission to add this method to a new book he was about to publish. Fontana, for his part, completely refused the offer because he was about to publish a book himself where he would write in more detail about this method; Cardano said no desperately and continued to press him but was met with a high wall of constant refusal. However, at one point he gave in to Cardano's repeated entreaties when he offered him a meeting with one of the most important patrons in Milan claiming that this person would be able to get him out of the poor financial and professional situation he was in;

Fontana decided to accept the offer and paid a visit to Milan in 1539. Unfortunately, the patron was not in the city at the time, which caused a serious grumble, but he nevertheless decided to reveal his secret to Cardano after it exerted massive pressure on him. Fontana made him swear not to reveal the secret to another person even when he died and asked him to always write it down using a code that was hidden in the words of a poem. Fontana, eager to leave Cardano's house, received a letter of recommendation for that patron but for some reason decided to set his sights on his house. During the journey back, Fontana claimed that he was worried that he had made a mistake in his decision to share his findings with another person. When he arrived in Venice he was already sure that he had made a mistake and his anger burned in him.

In the same year, Cardano published two important mathematics books and recommended it to Fontana in a personal letter, he obsessively searched for hints to introduce the method for solving the equations in the books and was relieved when he was deceived, but the response letter he sent to his colleague was full of rage and belittled the books. Cardano and his brilliant student Ferrari succeeded in perfecting the method to solve any type of equation in the third power and even managed to solve the equations in which there is a variable that is in the fourth power, an achievement whose value is priceless in the mathematical world. And yet, even though it was known in the community that there was a clear and orderly solution, Fontana stood by his refusal to publicly give his method. The story takes a turn when Cardano and Ferrari take a trip to Bologna, where they learn that it was Del Pero who found the method for solving the equations and not Fontana; These words made Cardano understand that even though he swore not to reveal Fontana's method - he did not take another such oath placing Del Ferro's method at the center, and indeed in 1545 Cardano published his most important book and one of the pillars of mathematics in the Middle Ages - Ares Magna, in which It was good to describe the method of solving equations with the third and fourth power and all the other work he did with his student regarding Fontana's method.

Cardano did not forget to bring the names of Fontana, Del-Ferro and Ferrari in his book as the inventors of these methods. Despite all this, Fontana seethed with rage when he realized that Cardano had reneged on his oath and his hatred towards him became an obsession for her own sake as well described in his personal book printed about a year later in which he brings his side of the story and does not spare his tribe from Cardano through personal insults. Cardano, whose excellent book placed him as the greatest mathematician of his time, was not harmed by these things, but Ferrari decided to strike back and came out harshly against Fontana and even invited him to a public battle of minds on the subject of solving equations. Fontana, for his part, considered the competition with Ferrari a childish act, mainly because the latter was still a negligible mathematician, but a fight against Cardano, who at the time was also considered an elevation in poetry and medicine, would raise his prestige to the highest level. Cardano felt ashamed of his honor to conduct such a battle, but he and his student began to exchange letters with defamatory and venomous content with Fontana, and he for his part did not remain indebted until in 1548 he was offered a position as a senior lecturer in his city, but in order to accept it he was supposed to make a tour to Milan where he was required to compete against Ferrari. Such a competition was indeed held and surprisingly Fontana escaped on the second day because his opponent surpassed him in his knowledge of solving equations, which resulted in his important victory. Fontana's loss resulted in not easy sanctions, one of which is the termination of funding for his salary - which caused him to return to his previous job and financial problems as he was used to in the past.

Today we call the solution of the equation of the third power as the Tartellia-Cardano method, however Fontana (called Tartellia) contributed a lot to the world of mathematics also in other subjects such as its introduction to the artillery battlefield, in which he describes new shooting methods and wonderful mechanical inventions, a popular article about arithmetic (a wide field and fascinating in mathematics dealing with advanced techniques of multiplication, division, etc.), was also the first to translate into Italian one of the two most important mathematics books - Euclid's "Elements" and many of Archimedes' essays.

Niccolo "Tertaglia" Fontana, the man who solved the problem that occupied mathematicians for many centuries, died in abject poverty and loneliness in the city of Venice in 1557.

For the previous articles in the series

• Gauss - the prince of mathematicians
• Everest visible