Galileo: PADUA

Part of Galileo - His Fifth Lumbar Vertebra

While walking in the footsteps of mathematicians in northern Italy, I couldn't help but also come across religious relics housed in churches and cathedrals - the tongue of St. Anthony in Padua, the skeleton of St. Ambrose flanked by skeletons of two other saints in a glass coffin in Milan, various bones of Beothius the Martyr in Pavia, the ossuary of St. Augustine also in Pavia. But in Padua I learned that even in the sciences we have our relics. The image above and the two below are of a vertebra of Galileo Galilei. From what I understand, one of Galileo's teeth and three of his fingers are on display elsewhere.

Display of Galileo's Fifth Lumbar Vertebra, University of Padova

Display of Galileo's Fifth Lumbar Vertebra, University of Padova

This display wasn't actually pointed out on our tour, but as we were all looking at the podium that Galileo had taught from, I turned around briefly and noticed that part of Galileo himself was right there outside his classroom as well. I found a translation online of the Latin incription above:

"I am the fifth lumbar vertebra and I permitted the flexion of the back of Galileo Galilei, who taught the new philosophy at this great University."

Galileo's Teaching Lectern, Pallazo Bo, University of Padua

In the days before projection units and microphones and speakers and screens, such a lectern was a way in which a professor could best be heard and seen. My understanding is that it would have been covered by decorative fabrics rather than having been merely bare wood at the time.

Galileo's Teaching Lectern, Pallazo Bo, University of Padua

Initially this classroom belonged to the law faculty of Padua University, but because Galielo had such a large following, the university extended the extraordinary privilege of making this classroom, which was the largest and is known as Aula Maga (The Great Hall), available for his classes. 

Aula Magna, Palazzo Bo, University of Padua

Ceiling, Aula Magna, Palazzo Bo, University of Padua

Detail of Back Wall, Aula Magna, Palazzo Bo, University of Padua

1892 Plaque Commemorating 300 Years Since Galileo Began Teaching Here

Galileo was the chair of mathematics and also taught astronomy at the University of Padua from 1592 to 1610, and he later wrote of these years as the happiest of his life.

Looking Toward the Door of the Aula Magna across the Plazzo Bo Quandrangle

Door of the Aula Magna

Detail in Palazzo Bo

Door of the Aula Magna

Door of the Aula Magna

During Galileo's time here (1595), the famous anatomy theatre - the first permanent anatomical theatre in the world - was constructed just across the quad. Galileo was a mathematician and astronomer, not a physician, but since the room is so close, I thought it would make for an interesting inclusion here. Given the timing and the proximity, I imagine Galileo saw the inside of this room, though I cannot positively state that as a certainty.

View Across Palazzo Bo from Galileo's Classroom Door

Modeo of Padua's Anatomical Theatre

Looking Up from the Bottom of Padua's Anatomical Theatre

On a narrow street a 10-minute's walk away from Palazzo Bo is Galileo's house, Casa di Galileo Galilei. It is well-marked and is on a street that is now named for him: Via Galileo Galilei.

House of Galileo Galilei, Padua, Italy

House of Galileo Galilei, Padua, Italy

House of Galileo Galilei, Padua, Italy

House of Galileo Galilei, Padua, Italy

On my way back to my hotel from Galileo's house, I walked through the city gate that was part of my route every day, but on this day, I noticed some signage that I hadn't notice before - signage relating to Galileo - a nice discovery for me that rounded out the day very well.

Porta di Ponte Molino

Google Translate tells me that this plaque says "From this tower Galileo reveals many ways of the heavens," so I take it that Galileo used this tower for astronomical observations

Porta di Ponte Molino

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!