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

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!

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 19^th-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.

Fibonacci Day

 

Biblioteca Ambrosiana, Milan*

November 23, which is 11/23 in month/day notation, always brings to mind the Fibonacci Numbers. I think some people even celebrate Fibonacci Day, though I haven't seen it get as much traction as Pi Day, which is March 14 or 3.14.

The Fibonacci Numbers are 1, 1, 2, 3, 5, 8, 13, 21 and so on, a sequence begun with 1, 1 and in which each succeding term is found by adding the previous two numbers. For example, the next number above would be 34, since 13+21=34.

As we'll see in a moment, this number sequence shows up in the natural world and in other places around us, which has made them popular, but first I want to spent a moment on their name and origin.

Fibonacci Memorial - Camposanto - Pisa, Italy

Because the number sequence 1, 1, 2, 3, 5, 8 . . . is called the Fibonacci Sequence, it is often thought that Fibonacci developed it. This is not true; it was known long before his time, going back well over a thousand years before his birth. Fibonacci did include a problem in his work Liber abbaci (Book of Calculating) that resulted in this number sequence. It was here that it became popularized and is why it bears his name.

Fibonacci Memorial (left-most sculpture) - Camposanto - Pisa, Italy

Despite knowing about this sequence for decades, what I didn't realize until recently is that Fibonacci's name was nearly lost in the mists of time. In fact, though he lived from about 1170AD to about 1250AD, he wasn't known as Fibonacci until 1838. His name was Leonardo, and he was from Pisa, so he was called Leonardo of Pisa (sort of like Leonardo da Vinci) or Leonardo Pisano. Fibonacci is a contraction of the term filius Bonacci ("son of Bonacci" or "of the house of Bonacci") that Leonardo refers to himself as in his book. Professor Keith Devlin, of Stanford University, went in search of Fibonacci's life and legacy beginning in about 2010, a journey that lasted about a decade and resulted in three very iteresting books: The Man of Numbers, Finding Fibonacci, and Leonardo and Steve - each of which I highly recommend if you want to learn more about about Fibonacci and the profound and ongoing impact of his work. For purposes of this post, we will not turn our attention to Fibonacci Numbers around us.

This number sequence often (though not always) shows up in the number of flower petals (or tepals).

The cala lily has 1 spathe.

The day lily had 3 petals and 3 sepals. (The three tepals with purple and yellow are petals; the other white tepals are sepals. Little did you know there would be botany terminology in this post!)

Many flowers display the "Fibonacci Five," as I like to call it. Here are a few examples:

Here we have 8 petals..

Daisies often display 13, 21, 34, or 55 petails; the daisy below has 21:

It's not just numbers of tepals that display Fibonacci Numbers but also numbers of spirals in natural objects. When I first learned this many years ago, I wasn't sure exactly what it was that I was supposed to be counting in order to find these numbers, so I'm including two explanatory photos below this pinecone, which has 8 spirals if you count the going clockwise and 13 spirals if you count them going counter-clockwise. Note that 8 and 13 are consecutive Fibonacci Numbers.

Pineapples too generally have a number of spirals that are Fibonacci. There are three spirals on a pineapple, and each of the three Fibonacci Numbers is consecutive.

And it's not just the amount of spirals that turn out to be Fiboacci. There are alsp spiral shapes that have the Fibonacci Numbers hidden in them.

The shape of the Chambered Nautilaus shell above can be modeled well by using the Fibonacci Numbers to create a grid - staritng with a square of side-length 1, then another square side-length one, and then a square next to those with side-length 2 and so on as shown below - and then spiraling out from the original square to the outermost square:

And, here are the Fibonacci Numbers 5, 8, and 13 showing up in an octave on a keyboard:

Whatever November 23 holds in store for you, I hope it's a happy Fibonacci Day!

_______
*The picture at the top of this post is of Milan's Biblioteca Ambrosiana. In their collection is a manuscript copy of the Liber abbaci. During a visit to Italy in autumn 2024 I consulted their copy, and I found it to be a deeply moving experience to handle an 800-year-old manuscript, a book that introduced the number system we used today into Europe in a way that merchants and others could make use of it. I would rank the importance of this book near the importance of the printing press for the impact it has had in ushering in the modern age.