Saturday, March 14, 2026

Einstein and Pavia

Ponte Coperto, River Ticino, Pavia, Italy
Normally on today's date - March 14 - I'm encouraging people to celebrate Pi Day. But this year I've decided to post in honor of the birthday of Albert Einstein. I'm choosing to write about one slice of his life :-)

Ponte Coperto, River Ticino, Pavia, Italy

Ponte Coperto, River Ticino, Pavia, Italy

Ponte Coperto, River Ticino, Pavia, Italy - dome of Duomo di Pavai in background
Einstein's family moved to Pavia from Munich, seeking better possibilities for his father's electrical business. Einstein was a teenager at this time, and still in gymnasium (high school), so he stayed behind in Munich to finish his schooling and joined his family during school holidays. Young Albert quickly fell in love with this beautiful city. Because of this, much of my post is simply pictures of the beauty of Pavia - with a splash of humor at the end.
Duomo di Pavia

Pavia University

Pavia University

Ancient Towers outside Pavia University

Walking through Pavia

Walking through Pavia
Einstein would take walks through the city with his sister Maja - something he still reminisced about decades later and looked back on fondly. He especially enjoyed the covered bridge, Ponte Coperto, over the River Ticino that flows through Pavia, which is why I opened this post with so many pictures of the covered bridge.
Riverside walk in Pavia, Italy - Ponte Coperto in the distance

View from Ponte Coperto, Pavia, Italy
More than 50 years later, Einstein mentioned Pavia in a letter. A phrase from that letter is engraved on a plaque inside the bridge memorializing Einstein's time in Pavia:

AN DIE SCHÖNE BRÜCKE IN PAVIA HABE ICH OFT GEDACHT . . .

I have often thought of the beautiful bridge in Pavia . . .

Einstein Plaque, Ponte Coperto, Pavia, Italy
And now for the silly ending that I can't help but include. 

Just a bit of a walk down-river from the bridge is an intriguing sight that I like to believe inspired some of Einstein's whimsy.
Walking alongside the Ticino River, Pavia, Italy

Walking alongside the Ticino River, Pavia, Italy


 La Linguacciona, Pavia, Italy


 La Linguacciona, Pavia, Italy


 La Linguacciona, Pavia, Italy

 La Linguacciona, Pavia, Italy
I mean, he was still thinking of his time in Pavia half a century later, so might La Linguacciona have inspired Einstien's pose in a picture taken many years later? We'll never know for sure, but I like to think it did.
Albert Einstein on his birthday in 1951



Monday, January 26, 2026

The Humble Grave of Henry Briggs

 

Grave of Henry Briggs (Henricus Briggius) in the chapel of Merton College, Oxford.
Today's post honors mathematician Henry Briggs who died on this date, January 16, in the year 1630. He was a man who held two prominent professorships and who contributed tremendously to the development and speedy adoption of logarithms - an invention that revolutionized calculation so dramatically that they were said to have "doubled the life of the astronomer."

Despite his prominence, Briggs was modest, humble, uninterested in wealth, and content with a quiet life of study. Fittingly, his tombstone in the chapel floor of Merton College bears only his name: no dates, no titles, no heraldic sheild, no list of achievements. Just the Latin form of his name: Henricus Briggius. Compare this with the memorial - also in Merton Chapel - of his contemporary and patron Henry Savile - heraldic sheild around his head, bust situated atop the world and flanked by Chrysostom, Ptolemy, Euclid, and Tacitus, and above it all, an angel playing a trumpet.
Memorial to Henry Savile (1549-1622) - Merton College, Oxford
Prior to teaching in Oxford, Briggs was the first professor at Gresham College, London, from which later arose the Royal Society. It was during his time at Gresham that he made the arduous journey to Edinburgh to meet the inventor of logarithms, John Napier; the journey today is about 4 hours by train; back then it was a formidable 4-day-long journey by horse and coach.
Gresham College, London today

Lion atop the gates to Napier's castle of Merchiston (Edinburgh)

Napier's Home, Merchiston Castle, from above
Briggs first visited and collaborated with Napier in the summer of 1615 and then went back in the summer of 1616 - each time staying for a month. He had plans to return in the summer of 1617, but Napier died in April. Briggs picked up the baton, constructing tables of base-10 logarithms, and promoting them in the scientific community, leading to their wide adoption.
Merton College, Oxford
A few years after these visits with Napier, Briggs moved from Gresham College, London to Merton College, Oxford, when he was appointed first Savilian Professor of Geometry at Oxford by Henry Savile himself. When I visit here, I feel I've traveled back in time - all the way back to the time of Briggs himself.

Merton College, Oxford

Merton College, Oxford
Chapel Tower, Merton College, Oxford
Chapel Door (left), Merton College, Oxford
Merton College, Oxford
The magnificence of the organ in Merton College Chapel never fails to take my breath away, but this organ, of course, was not there in Briggs's time (was installed only about a decade ago).
Merton College, Oxford
Merton College, Oxford

Merton College, Oxford
Barely visible on the left and right of the pillars on either side of the organ are the elaborate memorials to Henry Savile, pictured earlier in this post, and of Thomas Bodley, he of the Bodleian Library. About 15 feet to the left of where I'm standing to take this picture is the simple stone of the humble, yet brilliant man, Henry Briggs, and it is from my vigil at his stone that I take my leave of you today.
Tomb of Henry Briggs, Merton College, Oxford



Tuesday, December 30, 2025

Time to Raise a Glass

 

Guinness Storehouse - "Tick Followed Tock" - Guinness Advertisement 1999

As the clock winds down on 2025, as we toast the old year and look forward to the new, I find myself remembering my mathematical visit to the Guinness Storehouse in Dublin, Ireland earlier this year. Mathematics certainly provides great excuses to visit a wide variety of places!

A Visit to Guinness Storehouse - Dublin, Ireland
The Storehouse is a 7-story extravaganza of all things Guinness from ingredients to brewing to adverisiting to shipping and more! It includes a restaurant and multiple bars, including the Gravity Bar that makes up the entirety of the 7th floor, which has one of the best views over the city of Dublin. Most tickets include a pint in the Gravity Bar at the end of your tour.
Guiness Storehouse - Dublin, Ireland
One floor is enirely devoted to Guiness's famously whimsical ads.
Guiness Storehouse - Dublin, Ireland
All of my travels involve mathematics in some way, so what's the math connection here? 
Guiness Storehouse - Dublin, Ireland
Guinness faced a practical quality-control problem: testing barley to ensure consistent brewing required destroying some of the product; therefore, only small samples could be used. Traditional statistical methods required large sample sizes and didn’t work well with such limited data. William Sealy Gosset, a brewer at Guinness with training in mathematics and chemistry, developed a new way to draw reliable conclusions from small samples. 
Guiness Storehouse - Dublin, Ireland
This method became what we now call the Student’s t-test. The name is due to a company policy. Guinness allowed Gosset to publish his work only under a pseudonym. The name he chose to use was “Student.” That pseudonym is why the test still bears that name today.
St. James's Gate Brewery - Dublin, Ireland

Guinness Storehouse - Dublin, Ireland

Guinness Storehouse - Dublin, Ireland

Guinness Storehouse - Dublin, Ireland
More than a century later, the Student's t-test still matters because it remains one of the most widely used tools for making sense of small data sets, from scientific research to medicine, economics, and more! So, if you raise a glass this New Year's Eve - especially if it's a pint of Guinness - be sure to remember the name William Sealy Gosset.
Heidi &Toby at Gravity Bar - Guinness Storehouse - Dublin, Ireland
To all my reader's - I wish you a happy, healthy, and prosperous New Year!

Thursday, December 4, 2025

Omar Khayyam

This post is in honor of mathematician Omar Khayyam who died on this date, December 4, in the year 1131AD. As well as having been a mathematician, Khayyam was a poet, astronomer and philosopher. His astronomial work lives on through his development of the Jalali calendar, which forms the basis for the Persian calendar still in use today. In mathematics, he is most remembered for his work on solving cubic equations, involving a geometrical approach including conic sections. But he is probably best known generally for the poetry attributed to him, which was translated into English in the mid-19th century by British poet Edward FitzGerald.

This is a mathematical travel blog, and, sadly, I have not had opportunity to travel to Khayyam's hometown of Neyshabur (Nishapur), Iran where his magnificent mausoleum stands, made of marble and calligraphied with his poems. But I was reminded of him in some of my other travels, including a visit to London's Highgate Cemetery where I saw a tombstone with one of his famous "rubaiyat" (quatrains) on it.
The poem jumped out at me immediately, as it was one of my grandmother's favorites - and subsequently one of my favorites. You can also see the attribution to Omar Khayyam below the lines and to the right. I find it to be a good reminder of how to live.

“The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.”

I cannot tell whose tombstone this is, as the letters identifying the person and their dates have become dislodged from the stone, as have the last three words of the first line of the poem.

Another of my favorites among his writing is the following, for which I created a photographic illustration many years ago using my chess pieces and a wooden chessboard and jewelry box my grandfather made for me:

“Tis all a Chequer-board of nights and days
Where Destiny with men for Pieces plays:
Hither and thither moves, and mates, and slays,
And one by one back in the closet lays.”

I have a special place in my heart for mathematicians who are also poets. And, as the great 19th-century mathematician Karl Weierstrass once said, “A mathematician who is not also something of a poet will never be a complete mathematician.” This is echoed by his student, Sophia Kovalevskaya, who said, “It is impossible to be a mathematician without being a poet in soul.”
The amazing 'lines' of Khayyam's life have all been written; he has left the 'chequer-board.' I can only hope that the finger writing my life and that my checkerboard of nights and days can leave behind even the tiniest fraction of what the great Omar Khayyam accomplished - and if not that, then my hope would be that when I come to my final square on the board I don't feel a need to weep in an attempt to wash out any of the lines I'll leave behind.