Tartaglia: VENICE

Gondolas near St. Mark's Square, Venice

For much of my life I had heard of mathematician Nicolo Tartaglia only in the context of his feud with Girolamo Cardano, a story in which he seems to be merely a foil who comes off poorly against the more well-known mathematician. We only have so much time in math history courses, so I fear that this unfair portrayal is the norm, and I'd like to right that wrong at least a little bit in this space.

Venice and the Bridge of Sighs

The pictures here are only from Venice, as I have not had a chance to visit his birthplace of Brescia nor Verona where he lived from his late teens to his early thirties. He did spend the last 23 years of his life in Venice, a place at the forefront of printing during the Renaissance and where books were widely available even even to those without a lot of money, and he was certainly one without a lot of money.

Clock in St. Mark's Square, Venice

Clock in St. Mark's Square, Venice

But let's step back in time a moment. 

Nicolo was born in Brescia in 1499 or 1500. His father was a postman known as 'Micheletto the Rider' who rode out to take messages to surrounding towns. Micheletto was murdered while out on delivery when Nicolo was 6 years old. And this family that had been poor sunk into abject poverty.

Nicolo Tartagalia - Rijksmuseum via Wikipedia - Public Domain

And, if things weren't hard enough already, when Nicolo was about 12 years old, the French invaded his home town. Nicolo's mother hid the family in a cathedral for refuge, but the soldiers were out for blood and killed 46,000 residents of the city - including civilians seeking sanctuary in churches. Nicolo's head was slashed with a saber, and he was left for dead. His jaw and palate were sliced through. Nicolo's mother could not afford medical help, so she nursed him back to health best she could on her own. Miraculously, he lived, but he was left with a stammer, hence his nickname 'Tartaglia,' which means stammerer in Italian. He kept a full beard all his adult life in order to cover the scars.

From Correr Museum, Venice

When he was 14, there was a little bit of money to provide him with at least enough education to be able to write the alphabet, but the money ran out by the time he reached the letter K. From that day on, he was self-taught. He wrote, "I never returned to a tutor, but continued to labor by myself over the works of dead men, accompanied only by the daughter of poverty that is called industry."

Despite these harsh conditions, he rose to a level of mastery in mathematics that was such that he wrote one of the most fundamental books on mechanics (applications of mathematics to artillery fire) in the Renaissance. He was also the first Italian translator (from the Greek) and publisher of Euclid's Elements. He also developed a method for solving certain forms of cubic equations - something prominent mathematician of the era, tutor to Leonardo da Vinci, Luca Pacioli had declared impossible.

The Winged Lion of Venice

In some sense it was controvery over the cubic that was his "downfall," and why he is often unfairly characterized, but that is another story for another post (which I will link here once posted). As far as I can tell, Tartaglia has never truly received the degree of credit he deserves for his work or for how he overcame the many serious obstacles of his early life. His time in Venice often saw him teaching arithmetic/practical mathematics in order to eke out a living. He sometimes had to take his customers to court when they "paid" him with something like a worn-out cloak rather than the agreed-upon monetary compensation.

Near Chiesa di San Francesco della Vigna, Castello, Venice

Venice, Italy

Venice, Italy

Venice, Italy

Below is an image of St. Mark's Square in Venice very near the time of Tartaglia's life. Other than the style of clothing, I can attest that not much has changed - at least not from this view - between his time and ours.

"Processione in Piazza San Marco" by Cesare Vecellio (1586) Correr Museum

Not a great picture, nor perfectly lined up, but a quick snap of my lunchtime view of this same piazza in May 2024 posted for comparision:

View over St. Mark's Square from the Correr Museum cafe May 2024

In Venice, Tartaglia lived on Calle del Sturion in the San Polo sestiere (neighborhood) roughly between the Rialto Bridge and Campo di San Silvestro.

Map showing C. del Sturion, Campo di San Silvestor, and the Rialto Bridge

Rialto Bridge

Rialto Bridge

View from the Rialto Bridge

Tartaglia expressed in his will that he wished to be buried in Chiesa di San Silvestri. While many churches in Venice are freely open to the public, I found I was unable to get into San Silvestri - at least not the main sanctuary. I was able to get into a small chapel on the southeast side that was open for prayer. I do not know for certain if Tartaglia was buried in this church. I'm assuming he was, and we know that this was his wish. He died at age 57 or 58 in 1557.

Chiesa di San Silvestri

Chiesa di San Silvestri

Chiesa di San Silvestri

Chiesa di San Silvestri

Chiesa di San Silvestri

This math history trip to Venice was to have taken place in spring 2020 as part of a sabbatical, but we all know what happened that shut down our world at that time. When I was planning that trip and looking into Tartaglia's life and work, I came across a poem written in the form of a letter to Tartaglia that moved me deeply. The author is Jessica Huey, who was a student at Cal State Fullerton at that time, and the poem was published in The Journal of Humanistic Mathematics (Volume 10, Issue 1, January 2020). I wrote Jessica asking permission to share her poem, and she graciously gave that permission. I think she has given here a beautiful tribute to Tartaglia, and I believe he more than deseves it!

A Letter to Niccolo Fontana de Brescia 

by Jessica Huey

Dear Niccolo,

How are you?

I have heard much about you.

I wish I could say it was all good things,

But I cannot.


I heard about your solution to the cubic.

How it must hurt to gain so much knowledge,

Yet not be credited for sharing it with the world.

Or, to be more accurate, when Cardano shared it with the world.


I heard about your other contributions to math,

Like arithmetic and number theory, the tetrahedron’s volume, and translating Euclid’s Elements.

How it must hurt to master math to such depth,

Yet not be honored for it.


I heard about how you got your scars,

The ones that you hide behind your beard, as well as the ones inside that no one can see.

How it must hurt to go through what you did,

And speak but not be heard.


I heard about the loneliness.

I know it hurts.

It hurts me too.


I don’t want to sympathize

Because sympathy can hurt,

And it can add to the pain that may already be there.


I want to empathize

Because empathy can heal.

With understanding comes relief

And with relief comes healing.


I too have spoken and not been heard.

I too have shared and not been credited.

I too have lived and been hurt.


I hope this brings you some relief.

I hope this doesn’t pain you to hear this, all these years (and centuries) later.

Your deathday happens to be in exactly a week.

I hope that by remembering you and sharing your story, this brings strength to you

As well as to others.

Someday we may meet, in the sky,

And you can tell me your story,

Yourself.


From,

Jessica


P.S. I wish I could’ve been at your math battles. Will you tell me about them someday?

Here is a link to the journal pages with the poem: https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1595&context=jhm

UPDATE - Temporary Post

I've been in Italy 16 days now on the path of mathematician Gerolamo Cardano (Cardano primarly, but others as well). I only have one post so far about the history of mathematics of the lives of mathematicians. I've been too busy tracking down places, details, and information - and posting on facebook and writing in my journal - to keep up at all with blogging. Some posts need pictures from multiple cities, so I've had to put off posting. I'll have quite a few posts to put up, but I think this will be it until I am home (end of May), at which point I can pull it all together. But I'll put a few "teasers" here.

Bologna Duomo

Cardano lived in Bologna between the time his son was executed for murdering his wife in 1560 and the time he himself was arrested by the Inquisition in 1570. He taught at the university here, which is pictured below.

University of Bologna - oldest in the world - founded 1088

There's a big mathematical feud that took place between mathematicians Gerolamo Cardano and Nicolo Tartaglia - part of which has to do with information Cardano got in Florence from the son-in-law of another mathematician.

Florence Duomo

This relates to earlier work by mathematician Scipione del Ferro who used to participate in mathematical duels in the quadriportico behind the Basilica of Santa Maria dei Servi:

Quadriportico of the Basilica of Santa Maria dei Servi

And how could I be following in the footsteps of Girolamo Cardano were I not to have gone to Sirmione surrounding which is a story of him nearly being shipwrecked in a storm?

Scaliger Castle, Sirmione, Italy

Scaliger Castle, Sirmione

And in Padua (Padova) I have checked out the second-oldest university in Italy and one of the oldest in the world. It is where Girolamo Cardano graduated with a medical degree (yes, he was a doctor as well as mathematician) and where Galileo spent 18 years teaching and holding the position of chair of mathematics. He called these years the best years of his life. The pictures below relate to Galileo.

Galileo's Teaching Podium

Galileo's Classroom

I hope you'll check back in again in June 2024 to see the lives of 16th-century mathematicians unfold in more interesting ways than I've had time to post here! For now, I'm pounding the pavement and finding everything I can!

Girolamo Cardano: VENICE

In his 20s and early 30s, Girolamo Cardano lived in the Veneto (i.e. near Venice). He finished his medical degree in Padua, having studied first in Pavia until the university there was closed due to French invasion and war. After graduating from Padua with his medical degree (and for prejudicial reasons being denied a license by the College of Physicians in Milan), Cardano moved to the small town Piove di Sacco just east of Padua. He practiced medicine independently there. In his autobiography, he writes of his days in Sacco being the happiest of his life. 

There was at least one one not-so-happy event during this time, however. It involves a run-in with a Venetian senator.

Senate Hall, Doge's Palace, Venice

The ceiling of Senate Hall, Doge's Palace, Venice

Cardano was one of the greatest mathematical minds of his era. He also spent large chunks of his life in poverty and had to turn to gambling to make ends meet. Due to his mathematical skill, he did well at gambling. In fact, he was the first to make a study of probability as something that could be measured. He predated Pascal and Fermat by about 100 years on that, but he left his book in manuscript form and didn't publish. Anyway, back to the story. Cardano was gambling with a Venetian Senator - no one knows the senator's name for sure at this point* - nor where he lived, but senators were wealthy, so let's imagine the pallazo pictured below as representative of the senator's home - very imposing.

Door to Palazzo Van Axel

Palazzo Van Axel

As they played, Cardano was losing money. They continued the next day, and he lost the rest of his money. This was not normal for Cardano, given that he had an understanding of probability that others in his day did not have. Eventually he realize the cards were marked, and he struck out at the senator with a dagger, leaving a gash on his face. Despite having done this and despite the senator having two young bodyservants in the room, they kept on playing. Now that Cardano knew that the cards were marked, he began winning and recovered all the money (his own and that of the senator) - along with clothes and rings that he had lost the previous day. Wanting to make amends for having harmed the senator, he threw some of the money back and then escaped the house - fighting his way through the house-servants who were unable to use weapons. The senator, weighing what he had to gain or lose, having defrauded Cardano, ordered the door opened and Cardano let go.

Of the rest of the evening Cardano writes in his memoirs: 

"On that same day about eight o'clock in the evening, while I was doing my best to escape from the clutches of the police because I had offered violence to a Senator, and keeping meanwhile my weapons beneath my cloak, I suddenly slipped, deceived in the dark, and fell into a canal. I kept my presence of mind even as I plunged, threw out my right arm, and, grasping the gunwale of a passing boat, was rescued by the passengers. When I scrambled aboard the skiff, I discovered in it, to my surprise, the Senator with whom I had just gambled. He had the wounds on his face bound up with a dressing; yet he willingly enough brought me out a suit of garments such as sailors wear. Dressed in these clothes, I traveled with him as far as Padua."**

So, the "not-so-good" situation had a happy ending!

Having walked all around Venice the last 4 days, I can certainly see how he could have slipped. The walkways can be very narrow - or can dead-end unexpectedly into a canal - and some canals are edged in marble, which is very slippery.

In order to "walk in the same footsteps" or "sail the same waters" as Cardano, I took a gondola ride today. I imagine that his experience was much different than mine. For one thing, I wasn't soaking wet. For another, I'm sure the senator had a fancy gondola with an enclosure.

*In his uniquely wonderful novel, The Quantum Astrologer's Handbook, author Michael Brooks gives the Senator's name as Thomas Lezun. I believe this comes from an early biography of Cardano.

**Quote taken from Cardano's The Book of My Life, chapter 30, titled: "Perils, Accidents, and Manifold, Diverse, and Persistent Treacheries." The book is quite the read - very eccentric. It's a biography like what I would want to write about myself!

Introduction to Sabbatical 2 REDUX

 

Girolamo Cardano (1501-1576) and Nicolo Tartaglia (1499-1557)

This post is coming to you from Venice. Four years after the initial attempt at this "sabbatical," I am finally able to finish what I started. I'd been granted a sabbatical for spring 2020. At this point we all know what spring 2020 held in store for our world. I was able to do a snippet of sabbatical that semester before Covid-19 closed our world down, but I never did make it to Italy. Here is a link to the description of "Sabbatical 2" from January 2020 if you're interested in the original intent.

St. Mark's Basilica as seen from the Doge's Palace

These travels will involve a different itinerary than that of the original plan and post - especially since the UK part of that plan has been completed. I'm doing a big triangle in northern Italy with the intent of following the life of mathematician Girolamo Cardano. Other mathematicians and scientists will come into this as well, including but not limited to: Tartaglia, Cavalieri, Bombelli, Dee, Galileo, Copernicus, and del Ferro.

San Giorgio di Maggiore as seen from the Doge's Palace

While in Venice I'll be focused mainly on Caradano and Tartaglia whose mathematical feud is the stuff of legend. I know that British mathematician John Dee also spent time here - as is testified to in his signature and note in the book pictured below. The book is Opus novum by Jacopo Silvestri and is either the first or second book ever printed on cryptography, a favorite subject (among many) of Dee.

British Library - 8495.a.9 - Silvestri, Jacopo - Opus novum

As well as what I've mentioned above, there's a story about Cardano that I'll have to tell in a future post that has to do with him being fished out of Venetian canal he'd fallen into, saved by passers-by in a gondola. I'll wait until I've taken a gondola ride myself so I can write a little more first-hand on that. 

My posts may be a bit slow in coming, but there will eventually be many of them. It may even be that I finish this project once I'm back home early this summer. Blogging takes lots of time, especially if internet gets slow, and I need to be out there following in these footsteps (or oar strokes as the case may be!) while I'm here and have the chance. If you know me, and if you are following in May 2024, you can find lots more pictures on facebook, which is much faster for me to upload to, so those posts will go up daily. But I do hope you'll stick around and not give up on this math history journey even if some days pass between posts. Welcome along and ciao! :-)