Apr 152018

Today is the birthday (1707) of Leonhard Euler, a Swiss-born mathematician, physicist, astronomer, logician and engineer, who was unquestionably the most prolific, and one of the most influential, mathematicians in the West of all time. His written works fill around 80 quarto volumes. He, like so many other great mathematicians of the past, is not a household name these days, although you may know what an Euler diagram is, or you may know that the mathematical constant e is also known as Euler’s number, because he was the first to prove that e is irrational (“e” stands for “Euler”). I am going to spare you a diatribe on mathematics, working on the assumption that most people’s eyes glaze over when I stray too far from 2 + 2 = 4. This fact of life is a great pity in my ever-humble opinion. Mathematics and mathematical logic are useful intellectual tools. They are not the only tools in the toolbox, nor necessarily the most useful, but deep thinking is difficult without them. Care to build a shed without a hammer? It can be done, but is easier with one. I’ll delve into Euler’s life and influence mostly, and just give you a taste of what his mathematics can (and cannot) do.

Euler was born in Basel in Switzerland to Paul Euler, a pastor of the Reformed Church, and Marguerite née Brucker, a pastor’s daughter. He had two younger sisters: Anna Maria and Maria Magdalena, and a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, where Euler spent most of his childhood. Paul Euler was a friend of the Bernoulli family. Johann Bernoulli was then regarded as Europe’s foremost mathematician, and would eventually be the most important influence on young Leonhard.

Euler’s formal education started in Basel, where he was sent to live with his maternal grandmother. In 1720, aged 13, he enrolled at the University of Basel, and in 1723 (aged 16), he received a Master of Philosophy with a dissertation that compared the philosophies of Descartes and Newton. During that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his pupil’s incredible aptitude for mathematics. At that time Euler’s main studies included theology, Greek, and Hebrew at his father’s urging in order to become a pastor, but Bernoulli convinced his father that Euler was destined to become a great mathematician.

In 1726, Euler completed a dissertation on the propagation of sound, titled De Sono. At that time, he was unsuccessfully attempting to obtain a position at the University of Basel. In 1727, he first entered the Paris Academy Prize Problem competition; the problem that year was to find the best way to place the masts on a ship. Pierre Bouguer, who became known as “the father of naval architecture,” won and Euler took second place. Euler later won this annual prize 12 times.

Around this time Johann Bernoulli’s two sons, Daniel and Nicolaus, were working at the Imperial Russian Academy of Sciences in Saint Petersburg. On 31st July 1726, Nicolaus died of appendicitis after spending less than a year in Russia, and when Daniel assumed his brother’s position in the mathematics/physics division, he recommended that the post in physiology that he had vacated be filled by his friend Euler. In November 1726 Euler accepted the offer, but delayed making the trip to Saint Petersburg while he unsuccessfully applied for a physics professorship at the University of Basel.

Euler arrived in Saint Petersburg on 17th May 1727. He was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he often worked in close collaboration. Euler mastered Russian and settled into life in Saint Petersburg. He also took on an additional job as a medic in the Russian Navy. The Academy at Saint Petersburg, established by Peter the Great, was intended to improve education in Russia and to close the scientific gap with Western Europe. As a result, it was made especially attractive to foreign scholars like Euler. The academy possessed ample financial resources and a comprehensive library drawn from the private libraries of Peter himself and of the nobility. Very few students were enrolled in the academy in order to lessen the faculty’s teaching burden, and the academy emphasized research and offered to its faculty both the time and the freedom to pursue scientific questions.

The Academy’s patron, Catherine I, who had continued the progressive policies of her late husband, died on the day of Euler’s arrival. The Russian nobility then gained power upon the ascension of the 12-year-old Peter II. The nobility was suspicious of the academy’s foreign scientists, and thus cut funding and caused other difficulties for Euler and his colleagues. Conditions improved slightly after the death of Peter II, and Euler swiftly rose through the ranks in the academy and was made a professor of physics in 1731. Two years later, Daniel Bernoulli, who was fed up with the censorship and hostility he faced at Saint Petersburg, left for Basel. Euler succeeded him as the head of the mathematics department.

Concerned about the continuing turmoil in Russia, Euler left St. Petersburg  in June 1741 to take up a post at the Berlin Academy, which he had been offered by Frederick the Great of Prussia. He lived for 25 years in Berlin, where he wrote over 380 articles. In Berlin, he published the two works for which he would become most renowned: the Introductio in analysin infinitorum, a text on functions, published in 1748, and the Institutiones calculi differentialis, on differential calculus, published in 1755.

Euler was asked to tutor Friederike Charlotte of Brandenburg-Schwedt, the Princess of Anhalt-Dessau and Frederick’s niece. Euler wrote over 200 letters to her in the early 1760s, which were later compiled into a best-selling volume: Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess. This work contained Euler’s exposition on various subjects pertaining to physics and mathematics, as well as offering valuable insights into Euler’s personality and religious beliefs. This book became more widely read than any of his mathematical works and was published across Europe and in the United States. The popularity of the “Letters” testifies to Euler’s ability to communicate scientific matters effectively to a lay audience.

Despite Euler’s immense contribution to the Academy’s prestige, he eventually incurred the wrath of Frederick and ended up having to leave Berlin. The Prussian king had a large circle of intellectuals in his court, and he found the mathematician unsophisticated and ill-informed on matters beyond numbers and figures. Euler was a simple, devoutly religious man who never questioned the existing social order or conventional beliefs, in many ways the polar opposite of Voltaire, who enjoyed a high place of prestige at Frederick’s court. Euler was not a skilled debater and often made it a point to argue subjects that he knew little about, making him the frequent target of Voltaire’s wit. Frederick also expressed disappointment with Euler’s practical engineering abilities:

I wanted to have a water jet in my garden: Euler calculated the force of the wheels necessary to raise the water to a reservoir, from where it should fall back through channels, finally spurting out in Sanssouci. My mill was carried out geometrically and could not raise a mouthful of water closer than fifty paces to the reservoir. Vanity of vanities! Vanity of geometry!

Euler’s eyesight worsened throughout his mathematical career. In 1738, three years after nearly dying from a fever, he became almost blind in his right eye, but Euler preferred to blame the painstaking work on cartography he performed for the St. Petersburg Academy for his condition. Euler’s vision in that eye worsened throughout his stay in Germany, to the extent that Frederick referred to him as “Cyclops”. Euler later developed a cataract in his left eye, which was discovered in 1766. Just a few weeks after its discovery, he was rendered almost totally blind. However, his condition appeared to have little effect on his productivity, as he compensated for it with his mental calculation skills and exceptional memory. Upon losing the sight in both eyes, Euler remarked, “Now I will have fewer distractions.” Euler could repeat Virgil’s Aeneid from beginning to end without hesitation, and for every page in the edition he could indicate which line was the first and which the last. With the aid of his scribes, Euler’s productivity on many areas of study actually increased. He produced, on average, one mathematical paper every week in the year 1775. The Eulers bore a double name, Euler-Schölpi, the latter of which derives from schelb and schief, signifying squint-eyed, cross-eyed, or crooked. This suggests that the Eulers may have had a genetic disposition to eye problems.

In 1760, with the Seven Years’ War raging, Euler’s farm in Charlottenburg was ransacked by advancing Russian troops. Upon learning of this event, General Ivan Petrovich Saltykov paid compensation for the damage caused to Euler’s estate, later Empress Elizabeth of Russia added a further payment of 4000 rubles – an exorbitant amount at the time. The political situation in Russia stabilized after Catherine the Great’s accession to the throne, so in 1766 Euler accepted an invitation to return to the St. Petersburg Academy. His conditions were steep – a 3000 ruble annual salary, a pension for his wife, and the promise of high-ranking appointments for his sons. All of these requests were granted. He spent the rest of his life in Russia. However, his second stay in the country was marred by tragedy. A fire in St. Petersburg in 1771 cost him his home, and almost his life. In 1773, he lost his wife Katharina after 40 years of marriage. Three years after his wife’s death, Euler married her half-sister, Salome Abigail Gsell (1723–1794). This marriage lasted until his death.

In St. Petersburg on 18 September 1783, after a lunch with his family, Euler was discussing the newly discovered planet Uranus and its orbit with a fellow academician Anders Johan Lexell, when he collapsed from a brain hemorrhage. He died a few hours later. French mathematician and philosopher Marquis de Condorcet, wrote: “il cessa de calculer et de vivre” (he ceased to calculate and to live). Euler was buried next to Katharina at the Smolensk Lutheran Cemetery on Goloday Island. In 1785, the Russian Academy of Sciences put a marble bust of Leonhard Euler on a pedestal next to the Director’s seat and, in 1837, placed a headstone on Euler’s grave. To commemorate the 250th anniversary of Euler’s birth, the headstone was moved in 1956, together with his remains, to the 18th-century necropolis at the Alexander Nevsky Monastery.

Here I am going to touch on Euler’s contributions to mathematics and related fields, so, if your eyes glaze over at this stuff, skip to the recipe. This section is not really technical (just a tiny bit). Euler worked in almost all areas of mathematics, such as geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is the only mathematician to have two numbers named after him: the Euler number, e, approximately equal to 2.71828, and the Euler–Mascheroni constant γ (gamma) sometimes referred to as just “Euler’s constant,” approximately equal to 0.57721.

Euler introduced and popularized several notational conventions, that are now commonplace, through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function and was the first to write f(x) to denote the function f applied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (not originally “e” for “Euler’s number”), the Greek letter Σ for summations, and the letter i to denote the square root of -1. The use of the Greek letter π to denote the ratio of a circle’s circumference to its diameter was also popularized by Euler, although it originated with Welsh mathematician William Jones.

The development of infinitesimal calculus was at the forefront of 18th-century mathematical research, and the Bernoullis—family friends of Euler—were responsible for much of the early progress in the field. Because of their influence, studying calculus became a major focus of Euler’s work. Newton and Leibniz got the ball rolling by showing that if you tolerated the concept of infinity (in mathematics) a giant new world opened up that had not been known in the West before. You have to grasp – maybe against your intuition, or common sense – that as you get closer and closer and ever closer to infinity with a series of numbers that are getting smaller and smaller and yet smaller, a simple answer (almost magically) pops out when you get all the way to infinity (known as the limit). Getting the answer is almost a leap of faith although mathematicians won’t admit this. The classic “explanation” is to take the number 1.999999999999999999999999999 with the 9s extending all the way to infinity. As the list of 9s gets longer and longer, the number gets closer and closer to 2. So, at the limit 1 followed by infinite 9s is the same as 2. There’s your leap of faith. It is not just a tiny bit smaller than 2, it is exactly equal to 2.

Brilliant mathematicians like Euler appear to be able, not only to grasp mathematical concepts intuitively, but also to see patterns between seemingly disparate mathematical expressions. The ratio pi, for example, concerning the diameter and circumference of a circle, shows up all over the place in expressions that do not seem to have anything to do with circles. It is almost mystical. Mathematicians like Euler are not worried by this oddity; they see much deeper into the structure of mathematics than ordinary mortals, in ways that seem obvious to them, but are opaque to the rest of us. For example, he derived the formula known as Euler’s identity:

e i π + 1 = 0

Richard Feynman called it the “most remarkable formula in all mathematics” because it pulls together fundamental, but rather quirky, constants of mathematics in one neat bundle combining the operations of addition, multiplication, exponentiation, and equality.

Euler also pioneered the use of analytic methods to solve number theory problems. Euler’s interest in number theory can be traced to the influence of Christian Goldbach, his friend in the St. Petersburg Academy. A lot of Euler’s early work on number theory was based on the works of Pierre de Fermat. Euler developed some of Fermat’s ideas and disproved some of his conjectures. He contributed significantly to the theory of perfect numbers, which had fascinated mathematicians since Euclid. A perfect number is a number that is the sum of all of its positive divisors (excepting itself). So, for example, 6 is a perfect number because its divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.

In 1735, Euler presented a solution to the problem known as the Seven Bridges of Königsberg. The city of Königsberg in Prussia was set on the Pregel River, and included two large islands that were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point. Euler proved it is not possible. This solution is considered to be the first theorem of graph theory, specifically of planar graph theory. Euler also discovered the formula V − E + F = 2 relating the number of vertices (V), edges (E) and faces (F) of a convex polyhedron, and hence of a planar graph.

One of Euler’s more unusual interests was the application of mathematical ideas in music. In 1739 he wrote the Tentamen novae theoriae musicae, hoping to eventually incorporate musical theory as part of mathematics. This part of his work, however, did not receive wide attention and was once described as too mathematical for musicians and too musical for mathematicians.

Euler helped develop the Euler–Bernoulli beam equation, which became a cornerstone of engineering. Aside from successfully applying his analytic tools to problems in classical mechanics, Euler also applied these techniques to celestial problems. His work in astronomy was recognized by a number of Paris Academy Prizes over the course of his career. His accomplishments include determining with great accuracy the orbits of comets and other celestial bodies, understanding the nature of comets, and calculating the parallax of the sun. His calculations also contributed to the development of accurate longitude tables.

In addition, Euler made important contributions in optics. He disagreed with Newton’s corpuscular theory of light in the Opticks, which was then the prevailing theory. His 1740s papers on optics helped ensure that the wave theory of light proposed by Christiaan Huygens would become the dominant mode of thought, at least until the development of the quantum theory of light.

Euler is also credited with using closed curves to illustrate syllogistic reasoning (1768). These diagrams have become known as Euler diagrams which are sometimes confused with Venn diagrams. Here is a series of images that might help explain the difference.

An Euler diagram is a diagrammatic means of representing sets and their relationships. Euler diagrams consist of simple closed curves (usually circles) in the plane that depict sets. Each Euler curve divides the plane into two regions or “zones”: the interior, which symbolically represents the elements of the set, and the exterior, which represents all elements that are not members of the set. In Venn diagrams every closed curve must intersect every other curve, but in Euler diagrams they do not.

Much of what is known of Euler’s religious beliefs can be deduced from his Letters to a German Princess and an earlier work, Rettung der Göttlichen Offenbahrung Gegen die Einwürfe der Freygeister (Defense of the Divine Revelation against the Objections of the Freethinkers). These works show that Euler was a devout Christian who believed the Bible to be inspired; the Rettung was primarily an argument for the divine inspiration of scripture.

The dish known as French Meat was developed in St Petersburg in Euler’s time – a time when the Russian aristocracy wanted to appear more cosmopolitan to the outside world. The dish is unknown in France, of course, but it has remained popular in parts of Europe.  Worth a try, I’d say. I like it, and it is simple to make. The order of layers in the dish may vary depending on your preferences. The bottom layer can be onions to create a stratum between the meat and the baking tray, or potatoes, which will result in the dish saturated with pork fat. Some people make French Meat without potatoes. In this case, the pork chunks should be larger. Some don’t use mayonnaise, but the cheese-mayonnaise layer should always be on top, creating an aromatic gratin cheese crust while the dish is in the oven.

French Meat


500 gm/ 1lb moderately fat pork, cut in small chunks
600 gm/ 1 ¼ lb potatoes, peeled and sliced
4 large onions, peeled and sliced
300 gm/ 10 ½ oz melting cheese, grated
200 grams/ 7 oz (approx.) mayonnaise
salt, pepper to taste


Pre-heat the oven to 200˚C/400˚F.

Grease a casserole and spread the pork in a layer on the bottom. Cover the pork evenly with a layer of onion slices. Put a layer of thin slices of potato on top of the onions. Season with salt and pepper to taste. Top with a layer of grated cheese smothered in mayonnaise using a tablespoon or a cooking brush.

Bake the dish  for about 30 minutes. The dish is ready when the top layer of cheese is golden and bubbly. Remove the casserole from the oven and let it cool for 10 minutes before serving in blocks or slices.

Mar 032016


Today is the birthday (1845) of Georg Ferdinand Ludwig Philipp Cantor a German mathematician of immense importance. He created set theory, which has become a fundamental theory in mathematics. Cantor’s work is of great philosophical interest, as well as being purely mathematical, a fact I want to dwell on after dribbling on a bit about his life.

Cantor’s theory of transfinite numbers (numbers larger than all finite numbers, yet not absolutely infinite) was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from his mathematical contemporaries and later from philosophers. Cantor, a devout Lutheran, believed the theory had been communicated to him by God. Some Christian theologians saw Cantor’s work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously rejected.

The objections to Cantor’s work were occasionally fierce: Henri Poincaré referred to his ideas as a “grave disease infecting the discipline of mathematics,” and Leopold Kronecker’s public opposition and personal attacks included describing Cantor as a “scientific charlatan”, a “renegade” and a “corrupter of youth” (shades of Socrates !!). Writing decades after Cantor’s death, Wittgenstein lamented that mathematics is “ridden through and through with the pernicious idioms of set theory,” which he dismissed as “utter nonsense,” “laughable” and “wrong”. Cantor’s recurring bouts of depression from 1884 to the end of his life have been blamed on the hostile attitude of many of his contemporaries, though some have explained these episodes as probable manifestations of a bipolar disorder.

Those whose eyes glaze over at the mere mention of mathematics might be amazed that mathematical propositions could engender such base emotions. But Cantor’s work had, and has, implications for some of the most basic, but enduring, human questions such as “what is real?” and “what is God?” I promise I won’t delve too deeply into mathematics, I’ll just use a few analogies, with apologies to those who know a bit more than the basics about number theory and set theory. I realize they are over-simplifications, as well as being vaguer than the underlying mathematics.


Georg Cantor was born in the western merchant colony in Saint Petersburg, Russia, and brought up in the city until he was eleven. Georg, the oldest of six children, was regarded as an outstanding violinist. His grandfather Franz Böhm (1788–1846) was a well-known musician and soloist in a Russian imperial orchestra. Cantor’s father had been a member of the Saint Petersburg stock exchange but when he became ill, the family moved to Germany in 1856, first to Wiesbaden then to Frankfurt, seeking winters milder than those in Saint Petersburg. In 1860, Cantor graduated with distinction from the Realschule in Darmstadt. His exceptional skills in mathematics, trigonometry in particular, were noted. In 1862, Cantor entered the University of Zürich. After receiving a substantial inheritance upon his father’s death in 1863, Cantor shifted his studies to the University of Berlin, and then spent the summer of 1866 at the University of Göttingen, a major center for mathematical research.

Cantor submitted his dissertation on number theory to the University of Berlin in 1867. After teaching briefly in a Berlin girls’ school, Cantor took up a position at the University of Halle, where he spent his entire career. Cantor was promoted to Extraordinary Professor in 1872 and made full Professor in 1879. To attain the latter rank at the age of 34 was a notable accomplishment, but Cantor desired a chair at a more prestigious university, in particular at Berlin, at that time the leading German university. However, his work encountered too much opposition for that to be possible.


Cantor suffered his first known bout of depression in 1884, which some scholars attribute to the constant criticism of his work by famous scholars that weighed heavily upon him. This crisis led him to apply to lecture on philosophy rather than mathematics. He also began an intense study of Elizabethan literature thinking there might be evidence that Francis Bacon wrote the plays attributed to Shakespeare (in my opinion a fruitless quest, but endlessly simmering at the fringes of Shakespeare scholarship). It never ceases to annoy me that such investigation is based on the premise that a poor grammar school boy can’t be a genius.

After Cantor’s 1884 hospitalization his youngest son Rudolph died suddenly (while Cantor was delivering a lecture on his views on Baconian theory and William Shakespeare), and this tragedy drained Cantor of much of his passion for mathematics. Cantor was again hospitalized in 1903. One year later, he was outraged and agitated by a paper presented by Julius König at the Third International Congress of Mathematicians. The paper attempted to prove that the basic tenets of transfinite set theory were false. Since the paper had been read in front of his daughters and colleagues, Cantor perceived himself as having been publicly humiliated. Although Ernst Zermelo demonstrated less than a day later that König’s proof had failed, Cantor remained shaken, and momentarily questioning the existence of God. Cantor suffered from chronic depression for the rest of his life, for which he was excused from teaching on several occasions and repeatedly confined in various sanatoria. The events of 1904 preceded a series of hospitalizations at intervals of two or three years. He did not abandon mathematics completely, however, lecturing on the paradoxes of set theory (I’ll get to it in a minute !!) to a meeting of the Deutsche Mathematiker–Vereinigung in 1903, and attending the International Congress of Mathematicians at Heidelberg in 1904.


Cantor retired in 1913, living in poverty and suffering from malnourishment during World War I. The public celebration of his 70th birthday was canceled because of the war. He died on January 6, 1918 in the sanatorium where he had spent the final year of his life.

The concept of the existence of an actual infinity was an important shared concern within the realms of mathematics, philosophy and religion. Differential calculus was not developed until the 17th century, even though the basic building blocks had been available to ancient Arab and Greek mathematicians. The problem was that calculus requires use of infinity and ancient mathematicians could not accept the existence of infinity. It turns out that you don’t have to accept the existence of infinity to use the concept mathematically. The square root of -1 cannot logically exist, because there does not exist a pair of identical numbers that when multiplied together produce -1. But if you just give it a name (the letter “i”) and use it in equations without worrying about whether it exists or not, the equations often work out when you cancel out i. For example, x – i = y – i simplifies to x = y, so you don’t need to worry about whether i exists or not. Infinity can work in much the same way mathematically. But dealing with infinity is both tricky and counterintuitive.

gc7 gc8

If you’re smart but not especially well versed in mathematics, I highly recommend George Gamow’s book, One, Two, Three . . . Infinity. It explores Cantor’s mathematics in simple terms. Gamow’s birthday is tomorrow and since I can’t very well celebrate a mathematician followed next day by a theoretical physicist (working in complex mathematics), I’ll tip my hat to Gamow today. He was an early advocate and developer of the Big Bang Theory. In the book he uses a thought experiment to help explain the weirdness of infinity. Imagine you have a hotel with finite rooms, all of which are full, and a new guest arrives. You have to send him away because there is no room. Now imagine you have a hotel with infinite rooms and a new guest arrives. “No problem,” you say. You move the person in room 1 to room 2, in room 2 to room 3, in room 3 to room 4 . . . and so on. The series of integers (whole numbers) is infinite, so you never run out at the upper end. Now room 1 is free for the new guest. Now suppose the infinity hotel is full and an infinite number of guests shows up. “No problem,” you say again. This time you put every guest in the room that is double the number of the room they are in now. The guest in room 1 goes to room 2, in room 2 goes to room 4, room 3 goes to room 6 . . . and so on. In this way you free up all the odd-numbered rooms (double ANY number is an even number). There is an infinite number of odd numbers, so you can accommodate an infinite number of new guests. Maybe now you are beginning to grasp the problem of the existence of infinity. This thought experiment is counter-intuitive, and, hence, why so many philosophers and mathematicians objected.

So . . . are mathematical objects (things) real or not? Mathematicians, philosophers, and theologians have been arguing about this question for millennia with no end in sight. Cantor believed that absolute infinity was God. I find this equation an admirable idea, but it does not answer the question as to whether absolute infinity exists any more than whether God exists. Even if infinity defines God it does not prove his existence. I can define unicorns, but they don’t exist.

Cantor’s set theory also can lead to paradoxes, and mathematicians don’t like paradoxes. The barber paradox is an informal version. Imagine a town in which all the men need to shave, but are clean shaven. Men either shave themselves OR are shaved by the barber. Who shaves the barber? The two sets “shaved by the barber” and “shave themselves” cannot logically be distinct sets.


If nothing else, I hope I have shown that mathematics prompts questions and puzzles that are more than of scientific or logical interest. They strike at the very heart of issues such as, “What is the meaning of life?” and “Is there a God?” or “What is existence?” Cantor died poor and believing he was a failure. How many giants have died likewise? We owe it to Cantor today to keep him in memory.

I’m going to give you a great Saint Petersburg recipe in Cantor’s honor, because he was born there, even though he spent most of his life in Germany. Germans will like this too. It is a version of stuffed cabbage, but not the kind that you are used to. Instead of peeling off the leaves and stuffing them individually, you stuff the whole cabbage intact. Herbs can be of your choosing.


St Petersburg Stuffed Cabbage.


1 small cabbage
1 carrot, peeled and sliced
3 onions, peeled and sliced
1 bouquet garni
1-2 bay leaves
2-3 cloves
5-8 peppercorns


14 oz veal
7 oz pork lard
2-3 slices stale white bread
1 cup milk
2 eggs, beaten
salt and pepper


To make the filling, grind the veal with the lard. Soak the bread in milk for several hours, then wring out the excess. Mix the bread thoroughly with the meat and lard, add the eggs and mix the whole filling uniformly. Season with salt and pepper to taste.

Remove the toughest outer leaves of the cabbage. Immerse fully in a large pot of water and simmer until the leaves are soft and pliant. Drain the cabbage and put the filling between the leaves without tearing them off. Tie the cabbage with strong (colorless) twine and simmer in water or stock. Add the carrot, onions and seasonings. Cook on low heat for around 30 minutes. Serve the cabbage whole with the vegetables to garnish, and with sour cream.

Mar 212014


Today is the birthday (1839) of Modest Petrovich Mussorgsky (Модест Петрович Мусоргский), a Russian composer, one of the group known as “The Five” — Mily Balakirev (the leader), César Cui, Modest Mussorgsky, Nikolai Rimsky-Korsakov and Alexander Borodin (Borodin post here). He was an innovator of Russian music in the Romantic period who strove to achieve a uniquely Russian musical identity, often in deliberate defiance of the established conventions of Western music.

Many of his works were inspired by Russian history, Russian folklore, and other nationalist themes. Such works include the opera Boris Godunov, the orchestral tone poem Night on Bald Mountain, and the piano suite Pictures at an Exhibition. For many years Mussorgsky’s works were known mainly in versions revised or completed by other composers. Many of his most important compositions have recently come into their own in their original forms, and some of the original scores are now also available.

Mussorgsky was born in Karevo, Toropets, Pskov Governorate, Imperial Russia, 400 km (250 mi) south of Saint Petersburg. His wealthy, land-owning family, the noble family of Mussorgsky, is reputedly descended from the first Ruthenian ruler, Rurik, through the sovereign princes of Smolensk. At age six Mussorgsky began receiving piano lessons from his mother, herself a trained pianist. His progress was sufficiently rapid that three years later he was able to perform a John Field concerto and works by Franz Liszt for family and friends. At 10, he and his brother were taken to Saint Petersburg to study at the elite Peterschule (St. Peter’s School). While there, Modest studied the piano with the noted Anton Gerke. In 1852, the 12-year-old Mussorgsky published a piano piece titled “Porte-enseigne Polka” at his father’s expense.


Mussorgsky’s parents planned the move to Saint Petersburg so that both their sons would renew the family tradition of military service. To this end, Mussorgsky entered the Cadet School of the Guards at age 13. His skills as a pianist made him much in demand by fellow-cadets; for them he would play dances interspersed with his own improvisations. In 1856 Mussorgsky – who had developed a strong interest in history and studied German philosophy – successfully graduated from the Cadet School. Following family tradition he received a commission with the Preobrazhensky Regiment, the foremost regiment of the Russian Imperial Guard.

In October 1856 the 17-year-old Mussorgsky met the 22-year-old Alexander Borodin while both men served at a military hospital in Saint Petersburg. The two were soon on good terms. More portentous was Mussorgsky’s introduction that winter to Alexander Dargomyzhsky, at that time the most important Russian composer after Mikhail Glinka. Dargomyzhsky was impressed with Mussorgsky’s piano skills. As a result, Mussorgsky became a fixture at Dargomyzhsky’s soirées. Over the next two years at Dargomyzhsky’s, Mussorgsky met several figures of importance in Russia’s cultural life, among them Vladimir Stasov, César Cui (a fellow officer), and Mily Balakirev. Balakirev had an especially strong impact. Within days he took it upon himself to help shape Mussorgsky’s fate as a composer. He recalled to Stasov, “Because I am not a theorist, I could not teach him harmony (as, for instance Rimsky-Korsakov now teaches it), but I explained to him the form of compositions, and to do this we played through both Beethoven symphonies [as piano duets] and much else (Schumann, Schubert, Glinka, and others), analyzing the form.” Up to this point Mussorgsky had known nothing but piano music; his knowledge of more radical recent music was virtually non-existent. Balakirev started filling these gaps in Mussorgsky’s knowledge.

In 1858, within a few months of beginning his studies with Balakirev, Mussorgsky resigned his commission to devote himself entirely to music. He also suffered a painful crisis at this time. This may have had a spiritual component (in a letter to Balakirev the young man referred to “mysticism and cynical thoughts about the Deity”), but its exact nature will probably never be known. In 1859, the 20-year-old gained valuable theatrical experience by assisting in a production of Glinka’s opera A Life for the Tsar on the Glebovo estate of a former singer and her wealthy husband; he also met Konstantin Lyadov (father of Anatoly Lyadov) and enjoyed a formative visit to Moscow – after which he professed a love of “everything Russian.”

In spite of this epiphany, Mussorgsky’s music still leaned more toward foreign models; a four-hand piano sonata which he produced in 1860 contains his only movement in sonata form. Nor is any ‘nationalistic’ impulse easily discernible in the incidental music for Serov’s play Oedipus in Athens, on which he worked between the ages of 19 and 22 (and then abandoned unfinished), or in the Intermezzo in modo classico for piano solo (revised and orchestrated in 1867). The latter was the only important piece he composed between December 1860 and August 1863: the reasons for this probably lie in the painful re-emergence of his subjective crisis in 1860 and the purely objective difficulties which resulted from the emancipation of the serfs the following year – as a result of which the family was deprived of half its estate, and Mussorgsky had to spend a good deal of time in Karevo unsuccessfully attempting to stave off their looming impoverishment.

By this time, Mussorgsky had freed himself from the influence of Balakirev and was largely teaching himself. In 1863 he began an opera – Salammbô – on which he worked between 1863 and 1866 before losing interest in the project. During this period he had returned to Saint Petersburg and was supporting himself as a low-grade civil-servant while living in a six-man “commune”. In a heady artistic and intellectual atmosphere, he read and discussed a wide range of modern artistic and scientific ideas – including those of the provocative writer Chernyshevsky, known for the bold assertion that, in art, “form and content are opposites”. Under such influences he came more and more to embrace the rather enigmatic ideal of artistic realism: the responsibility to depict life “as it is truly lived.” “Real life” affected Mussorgsky painfully in 1865, when his mother died. It was at this point that the composer had his first serious bout of alcoholicism. The 26-year-old was, however, on the point of writing his first realistic songs including “Hopak” and “Darling Savishna” (or, “Love Song of an Idiot), both of them composed in 1866 and among his first “realist” publications the following year. 1867 was also the year in which he finished the original orchestral version of his Night on Bald Mountain (which, however, Balakirev criticized and refused to conduct, with the result that it was never performed during Mussorgsky’s lifetime).

Mussorgsky’s career as a civil servant was by no means stable or secure: though he was assigned to various posts and even received a promotion in these early years, in 1867 he was declared ‘supernumerary’ – remaining ‘in service’ but receiving no wages. Decisive developments were occurring in his artistic life, however. Although it was in 1867 that Stasov first referred to the ‘kuchka’ (‘The Five’) of Russian composers loosely grouped around Balakirev, Mussorgsky was by then ceasing to seek Balakirev’s approval and was moving closer to the older Alexander Dargomyzhsky .

Since 1866 Dargomïzhsky had been working on his opera The Stone Guest, a version of the Don Juan story with a Pushkin text that he declared would be set “just as it stands, so that the inner truth of the text should not be distorted”, and in a manner that abolished the ‘unrealistic’ division between aria and recitative in favor of a continuous mode of syllabic but lyrically heightened declamation somewhere between the two.

Under the influence of this work (and the ideas of Georg Gottfried Gervinus, according to whom “the highest natural object of musical imitation is emotion, and the method of imitating emotion is to mimic speech”), Mussorgsky in 1868 rapidly set the first eleven scenes of Nikolai Gogol’s The Marriage (Zhenitba), with his priority being to render into music the natural accents and patterns of the play’s naturalistic and deliberately humdrum dialogue. This work marked an extreme position in Mussorgsky’s pursuit of naturalistic word-setting: he abandoned it after reaching the end of his ‘Act 1’ and though its characteristically ‘Mussorgskyian’ declamation is to be heard in all his later vocal music, the naturalistic mode of vocal writing more and more became formulaic.

A few months after abandoning Zhenitba, the 29-year-old Mussorgsky was encouraged to write an opera on the story of Boris Godunov. This he did, assembling and shaping a text from Pushkin’s play and Karamzin’s history. He completed the large-scale score the following year while living with friends and working for the Forestry Department. In 1871, however, the finished opera was rejected for theatrical performance, apparently because of its lack of any ‘prima donna’ role. Mussorgsky set to work producing a revised and enlarged second version. During the next year, which he spent sharing rooms with Rimsky-Korsakov, he made changes that went beyond those requested by the theatre. In this version the opera was accepted, probably in May 1872, and three excerpts were staged at the Mariinsky Theatre in 1873.


From this peak a pattern of decline becomes increasingly apparent. Already the Balakirev circle was disintegrating. Mussorgsky was especially bitter about this. He wrote to Vladimir Stasov, “The Mighty Handful has degenerated into soulless traitors.” In drifting away from his old friends, Mussorgsky had been seen to fall victim to ‘fits of madness’ that could well have been alcoholism-related. His friend Viktor Hartmann had died, and his relative and recent roommate Arseny Golenishchev-Kutuzov (who furnished the poems for the song-cycle Sunless and would go on to provide those for the Songs and Dances of Death) had moved away to get married. While alcoholism was Mussorgsky’s personal problem, it was also a behavior pattern considered typical for those of Mussorgsky’s generation who wanted to oppose the establishment and protest through extreme forms of behavior. One contemporary notes, “an intense worship of Bacchus was considered to be almost obligatory for a writer of that period. It was a showing off, a ‘pose,’ for the best people of the [eighteen-]sixties.” Another writes, “Talented people in Russia who love the simple folk cannot but drink. Mussorgsky spent day and night in a Saint Petersburg tavern of low repute, the Maly Yaroslavets, accompanied by other bohemian dropouts. He and his fellow drinkers idealized their alcoholism, perhaps seeing it as ethical and aesthetic opposition. This bravado, however, led to little more than isolation and eventual self-destruction.”

For a time Mussorgsky was able to maintain his creative output: his compositions from 1874 include Sunless, the Khovanschina Prelude, and the piano suite Pictures at an Exhibition (in memory of Hartmann). He also began work on another opera based on Gogol, The Fair at Sorochyntsi (for which he produced another choral version of Night on Bald Mountain).

In the years that followed, Mussorgsky’s decline became increasingly steep. Although now part of a new circle of eminent people that included singers, medical professionals, and actors, he was increasingly unable to resist drinking, and a succession of deaths among his closest associates caused him great pain. At times, however, his alcoholism would seem to be in check, and among the most powerful works composed during his last 6 years are the four Songs and Dances of Death. His civil service career was made more precarious by his frequent ‘illnesses’ and absences, and he was fortunate to obtain a transfer to a post (in the Office of Government Control) where his music-loving superior treated him with great leniency – in 1879 even allowing him to spend 3 months touring 12 cities as a singer’s accompanist.

The decline could not be halted, however. In 1880 he was finally dismissed from government service. Aware of his destitution, one group of friends organized a stipend designed to support the completion of Khovanschina; another group organized a similar fund to pay him to complete The Fair at Sorochyntsi. However, neither work was completed (although Khovanschina, in piano score with only two numbers uncomposed, came close to being finished).


In early 1881 a desperate Mussorgsky declared to a friend that there was ‘nothing left but begging’ and suffered four seizures in rapid succession. Though he found a comfortable room in a good hospital – and for several weeks even appeared to be rallying – the situation was hopeless. Repin painted the famous red-nosed portrait in what were to be the last days of the composer’s life: a week after his 42nd birthday, he was dead. He was interred at the Tikhvin Cemetery of the Alexander Nevsky Monastery in Saint Petersburg.


Mussorgsky’s works, while strikingly novel, are stylistically Romantic and draw heavily on Russian musical themes. He has been the inspiration for many Russian composers, including most notably Dmitri Shostakovich (in his late symphonies) and Sergei Prokofiev (in his operas).

Contemporary opinions of Mussorgsky as a composer and person varied from positive to ambiguous to negative. Mussorgsky’s eventual supporters, Stasov and Balakirev, initially registered strongly negative impressions of the composer. Stasov wrote Balakirev, in an 1863 letter, “I have no use whatever for Mussorgsky. All in him is flabby and dull. He is, I think, a perfect idiot. Were he left to his own devices and no longer under your strict supervision, he would soon run to seed as all the others have done. There is nothing in him.” Balakirev replied: “Yes, Mussorgsky is little short of an idiot.”

Mixed impressions are recorded by Rimsky-Korsakov and Tchaikovsky, colleagues of Mussorgsky who, unlike him, made their living as composers. Both praised his talent while expressing disappointment with his technique. About Mussorgsky’s scores Rimsky-Korsakov wrote, “They were very defective, teeming with clumsy, disconnected harmonies, shocking part-writing, amazingly illogical modulations or intolerably long stretches without ever a modulation, and bad scoring. …what is needed is an edition for practical and artistic purposes, suitable for performances and for those who wish to admire Mussorgsky’s genius, not to study his idiosyncrasies and sins against art.”

Rimsky-Korsakov’s own editions of Mussorgsky’s works met with some criticism of their own. Rimsky-Korsakov’s student, Anatoly Lyadov, found them to be weak, saying “It is easy enough to correct Mussorgsky’s irregularities. The only trouble is that when this is done, the character and originality of the music are done away with, and the composer’s individuality vanishes.” A very strange sentiment — essentially saying that Mussorgsky’s writing is all wrong, but if you make it “right” it is no good.  My advice would be to leave it alone, then.

Tchaikovsky, in a letter to his patroness Nadezhda von Meck was also critical of Mussorgsky: “Mussorgsky you very rightly call a hopeless case. In talent he is perhaps superior to all the [other members of The Five], but his nature is narrow-minded, devoid of any urge towards self-perfection, blindly believing in the ridiculous theories of his circle and in his own genius. In addition, he has a certain base side to his nature which likes coarseness, uncouthness, roughness…. He flaunts … his illiteracy, takes pride in his ignorance, mucks along anyhow, blindly believing in the infallibility of his genius. Yet he has flashes of talent which are, moreover, not devoid of originality.”

Western perceptions of Mussorgsky changed with the European premiere of Boris Godunov in 1908. Before the premiere, he was regarded as an eccentric in the west. Critic Edward Dannreuther, wrote, in the 1905 edition of The Oxford History of Music, “Mussorgsky, in his vocal efforts, appears willfully eccentric. His style impresses the Western ear as barbarously ugly.”However, after the premiere, views on Mussorgsky’s music changed drastically. Gerald Abraham, a musicologist, and an authority on Mussorgsky said, “As a musical translator of words and all that can be expressed in words, of psychological states, and even physical movement, he is unsurpassed; as an absolute musician he was hopelessly limited, with remarkably little ability to construct pure music or even a purely musical texture.”

I wish I had the time and space to provide a proper appreciation of Pictures at an Exhibition.  I have known the piece since I was a young teen and have always loved its rich complexity and evocative movements.  It has 10 separate movements sporadically interspersed with an interlude that is initially called “Promenade” but unmarked in the rest of the score.  The simple idea is that Mussorgsky (or some viewer) is walking around an exhibit of 10 paintings (Promenade), and when he stops in front of a piece the music changes to become a tonal depiction of the image. Then there is another promenade as he walks to the next painting.  Here’s what I did not know about the piece as a teen but which is self evident if I lay out the piece as I do below.  First, the exhibition is not a random assortment of paintings but, rather, 11 paintings by Mussorgsky’s friend Viktor Hartmann, to memorialize him.  Several are still extant and I attach them in the appropriate places.  The two for movement 6 were owned by Mussorgsky.



Second, there is not a simple alternation of promenade, painting, promenade, painting . . . etc.  In several spots Mussorgsky moves from one painting to the next without interlude.  Third, you will see that, with one exception, the promenade motif is not a simple restatement each time.  Time signatures and keys change (as do tempo markings which I have omitted for the sake of simplicity – they get complicated).  It is as if Mussorgsky is showing that with each new painting his mood changes as he leaves to go to the next. (Occasionally, too, there are echoes of the Promenade within the formal movements).

First Promenade
Key: B-flat major
Meter: originally 11/4. Published editions alternate 5/4 and 6/4.

No. 1 “Gnomus”
(Latin, The Gnome):

[Untitled] (Interlude, Promenade theme)
A-flat major
Meter: alternating 5/4 and 6/4

No. 2 “Il vecchio castello”
(Italian, The Old Castle):

[Untitled] (Interlude, Promenade theme)
Key: B major.
Meter: alternating 5/4 and 6/4

No. 3 “Tuileries” (Dispute d’enfants après jeux)
(French, Tuileries (Dispute between Children at Play))

No. 4 “Byd?o”(Polish, Cattle)

[Untitled] (Interlude, Promenade theme)
Key: D minor
Meter: alternating 5/4, 6/4, 7/4

No. 5 ” Балет невылупившихся птенцов” [Balet nevylupivshikhsya ptentsov]
(Russian, Ballet of the Unhatched Chicks)


No. 6 “Samuel” Goldenberg und “Schmuÿle”
(Yiddish, Samuel Goldenberg and Pauper)

MM6 mmpe6

Key: B-flat major.
Meter: originally 11/4. Published editions alternate 5/4 and 6/4.
A nearly bar-for-bar restatement of the opening promenade. Differences are slight: the second half is a little condensed and the block chords voiced more fully. Structurally the movement acts as a restart, giving listeners another hearing of the opening material before elements from the first half are developed in the second half.

Many arrangements, including Ravel’s orchestral version, omit this movement.

No. 7 “Limoges”, le marché (La grande nouvelle)
(French, The Market at Limoges (The Great News))

No. 8 “Catacombæ” (Sepulcrum romanum) and “Con mortuis in lingua mortua”
(Latin, The Catacombs (Roman sepulcher)) and (Latin, With the Dead in a Dead Language)
Note: The correct Latin would be Cum mortuis.
The movement is in two distinct parts. Its two sections consist of a nearly static largo made up of a sequence of block chords, with elegiac lines adding a touch of melancholy, and a more flowing, gloomy andante section that introduces the Promenade theme into the scene.


No. 9 Избушка на курьих ножках (Баба-Яга) [Izbushka na kuryikh nozhkakh (Baba-Yagá)]
(Russian, The Hut on Fowl’s Legs (Baba-Yagá))


No. 10 Богатырские ворота (В стольном городе во Киеве) [Bogatyrskiye vorota (V stolnom gorode Kiyeve)
(Russian: The Bogatyr Gates (in the Capital in Kiev))


Without question this is my favorite piano suite, bar none.  I listen to it sparingly because I find it exhausting.  Like any masterwork there are always hidden treasures to discover.

Pictures at an Exhibition has been arranged for orchestra dozens of times by the likes of Henry Wood, Leopold Stokowski, and, of course, Maurice Ravel whose orchestral score is perhaps the best known of all (video at the end of this post).  As far as I can tell – I have not been exhaustive – all these arrangements take liberties with the piano score, usually omitting sections. Ravel, as noted for example, omits the restatement of the Promenade.  No idea why.

Because each of the pieces in the suite can stand alone they are often played individually , and on a bewildering array of instruments in all genres imaginable – Duke Ellington with a big band sound, Emerson, Lake & Palmer as progressive rock, and Segovia for classical guitar, to name a few.  Here’s an ethereal version of movements 2 and 5 for glass harp duet.

To celebrate Mussorgsky I have chosen shchi (щи), a traditional Russian soup known since at least the 9th century, soon after cabbage was introduced from Byzantium. Its popularity in Russia originates from several factors. Shchi is relatively easy to prepare; it can be cooked with or without various types of meat that makes it compatible with different religions; and it can be frozen and carried as a solid on a trip to be cut up when needed. Finally, it was noticed that most people do not get sick of shchi and can eat it daily. This property is referenced in the Russian saying: “Pодной отец надоест, а щи – никогда!” (Rodnoi otets nadoyest, a shchi—nikogda! “One may become fed up with one’s own father, but never with shchi!”). As a result, by the 10th century shchi became a staple food of Russia, and another popular saying sprang from this fact: “Щи да каша — пища наша” (Shchi da kasha — pishcha nasha “Shchi and kasha are our food”). The major components of shchi were originally cabbage, meat (beef, pork, lamb, or poultry), mushrooms, flour, and spices (based on onion and garlic). Cabbage and meat were cooked separately and Smetana (very heavy sour cream) was added as a garnish before serving with rye bread.

The ingredients of shchi gradually changed. Flour, which was added in early times to increase the soup’s caloric value, was excluded for the sake of finer taste. The spice mixture was enriched with black pepper and bay leaf, which were imported to Russia around the 15th century, also from Byzantium. Sometimes fish was used in place of meat, and carrot and parsley could be added to the vegetables. Beef was the most popular meat for shchi in Russia, while pork was more common in Ukraine. The water to cabbage ratio varied and whereas early shchi were often so viscous that a spoon could stand in it, more diluted preparations were adopted later. Nowadays soup ingredients include: meat (mainly pork), cabbage, potato, tomato, carrot, onion (some people like to make a ??????? (obzharka) by roasting the carrot with onion before adding it to the soup) and spices (pepper, salt and parsley).  It is very common to make the soup 1 or 2 days ahead of time to let the flavors marry before serving.


Shchi (щи)

8 cups beef stock
1 ½ lbs green cabbage, cored and finely shredded
4 garlic cloves, peeled and finely chopped
3 medium potatoes, peeled and diced
2 medium onions, peeled and chopped
2 medium tomatoes, chopped
2 small radishes, washed and sliced thin
1 leek (white half only), sliced in thin rings
1 large carrot, peeled and grated
3 bay leaves
2 tablespoons butter
1 teaspoon black peppercorns
1 teaspoon caraway seed
2 tablespoons sour cream (or Smetana, per bowl)
1 teaspoon fresh dill (per bowl)
1 teaspoon parsley (per bowl)


Melt the butter in a large pot or pan. Add garlic, onion, radish, leek and carrot. Saute on high heat approximately 5-10 minutes until vegetables have softened.

Add beef stock (vegetable stock or water) and bring to a boil.

Add green cabbage, potatoes, tomatoes, bay leaves, black peppercorns, and caraway seed.

Reduce heat to low and cover. Simmer for approximately one hour or until all vegetables are done, stirring occasionally.

Remove and discard bay leaves.

Finely chop dill and/or parsley.

Either refrigerate for 1 to 2 days or ladle into bowls. Add a dollop of sour cream (or smetana) on top and sprinkle with chopped dill and/or parsley.

Serve with a dark rustic bread such as pumpernickel or rye bread optionally spread with butter.

Ideally, refrigerate after cooling and wait 1-2 days to serve as shchi is usually allowed to “cure” for a short time. In my opinion, it tastes great fresh or re-heated. It can also be served cold.