A Little Closer to Finding What Became of Moses Schönfinkel, Inventor of Combinators

A Little Closer to Finding What Became of Moses Schönfinkel, Inventor of Combinators

For most big ideas in recorded intellectual history one can answer the question: “What became of the person who originated it?” But late last year I tried to answer that for Moses Schönfinkel, who sowed a seed for what’s probably the single biggest idea of the past century: abstract computation and its universality.

I managed to find out quite a lot about Moses Schönfinkel. But I couldn’t figure out what became of him. Still, I kept on digging. And it turns out I was able to find out more. So here’s an update….

To recap a bit: Moses Schönfinkel was born in 1888 in Ekaterinoslav (now Dnipro) in what’s now Ukraine. He went to college in Odessa, and then in 1914 went to Göttingen to work with David Hilbert. He didn’t publish anything, but on December 7, 1920—at the age of 32—he gave a lecture entitled “Elemente der Logik” (“Elements of Logic”) that introduced what are now called combinators, the first complete formalism for what we’d now call abstract computation. Then on March 18, 1924, with a paper based on his lecture just submitted for publication, he left for Moscow. And basically vanished.

It’s said that he had mental health issues, and that he died in poverty in Moscow in 1940 or 1942. But we have no concrete evidence for either of these claims.

When I was researching this last year, I found out that Moses Schönfinkel had a younger brother Nathan Scheinfinkel (yes, he used a different transliteration of the Russian Шейнфинкель) who became a physiology professor at Bern in Switzerland, and later in Turkey. Late in the process, I also found out that Moses Schönfinkel had a younger sister Debora, who we could tell graduated from high school in 1907.

Moses Schönfinkel came from a Jewish merchant family, and his mother came from a quite prominent family. I suspected that there might be other siblings (Moses’s mother came from a family of 8). And the first “new find” was that, yes, there were indeed two additional younger brothers. Here are the recordings of their births now to be found in the State Archives of the Dnipropetrovsk (i.e. Ekaterinoslav) Region:

Birth records—click to enlarge

So the complete complement of Шейнфинкель/Schönfinkel/Scheinfinkel children was (including birth dates both in their original Julian calendar form, and in their modern Gregorian form, and graduation dates in modern form):

And having failed to find out more about Moses Schönfinkel directly, plan B was to investigate his siblings.

I had already found out a fair amount about Nathan. He was married, and lived at least well into the 1960s, eventually returning to Switzerland. And most likely he had no children.

Debora we could find no trace of after her high-school graduation (we looked for marriage records, but they’re not readily available for what we assume is the relevant time period).

By the way, rather surprisingly, we found nice (alphabetically ordered), printed class lists from the high-school graduations (apparently these were distributed to higher-education institutions across the Russian Empire so anyone could verify “graduation status”, and were deposited in the archives of the education district, where they’ve now remained for more than a century):

Graduation records—click to enlarge

(We can’t find any particular trace of the 36 other students in the same group as Moses.)

OK, so what about the “newly found siblings”, Israel and Gregory? Well, here we had a bit more luck.

For Israel we found these somewhat strange traces:

Admission records—click to enlarge

They are World War I hospital admission records from January and December 1916. Apparently Israel was a private in the 2nd Finnish Regiment (which—despite its name—by then didn’t have any Finns in it, and in 1916 was part of the Russian 7th Army pushing west in southern Ukraine in the effort to retake Galicia). And the documents we have show that twice he ended up in a hospital in Pavlohrad (only about 40 miles from Ekaterinoslav, though in the opposite direction from where the 7th Army was) with some kind of (presumably not life-threatening) hernia-like problem.

But unfortunately, that’s it. No more trace of Israel.

OK, what about the “baby brother”, Gregory, 11 years younger than Moses? Well, he shows up in World War II records. We found four documents:

WWII documents—click to enlarge

Document #4 contains something interesting: an address for Gregory in 1944—in Moscow. Remember that Moses went to Moscow in 1924. And one of my speculations was that this was the result of some family connection there. Well, at least 20 years later (and probably also much earlier, as we’ll see), his brother Gregory was in Moscow. So perhaps that’s why Moses went there in 1924.

OK, but what story do these World War II documents tell about Gregory? Document #1 tells us that on July 27, 1943, Gregory arrived at the military unit designated 15 зсп 44 зсбр (15 ZSP 44 ZSBR) at transit point (i.e. basically “military address”) 215 азсп 61А (215 AZSP 61A). It also tells us that he had the rank of private in the Red Army.

Sometime soon thereafter he was transferred to unit 206 ZSP. But unfortunately he didn’t last long in the field. Around October 1, 1943, he was wounded (later, we learn he has “one wound”), and—as document #2 tells us—he was one of 5 people picked up by hospital train #762 (at transit point 206 зсп ЗапФ). On November 26, 1943, document #3 records that he was discharged from the hospital train (specifically, the document explains that he’s not getting paid for the time he was on the hospital train). And, finally, document #4 records that on February 18, 1944—presumably after a period of assessment of his condition—he’s discharged from the military altogether, returning to an address in Moscow.

OK, so first some military points. When Gregory arrived in the army in July 1943 he was assigned (as a reserve or “replacement”) to the 44th Rifle Brigade (44 зсбр) in the 15th Rifle Division (15 зсп) in the 61st Army (61A)—presumably as part of reinforcements brought in after some heavy Soviet losses. Later he was transferred to the 206th Rifle Division in the 47th Army, which is where he was when he was wounded around October 1, 1943.

What was the general military situation then? In the summer of 1943 the major story was that the Soviets were trying to push the Germans back west, with the front pretty much along the Dnieper River in Ukraine—which, curiously enough, flows right through the middle of Ekaterinoslav. On October 4, 1943, here’s how the New York Times presented things:

October 4, 1943—click to enlarge

But military history being what it is, there’s much more detailed information available. Here’s a modern map showing troop movements involving the 47th Army in late September 1943:

1943 Map—click to enlarge

The Soviets managed to get more than 100,000 men across the Dnieper River, but there was intense fighting, and at the end of September the 206th Rifle Division (as part of the 47th Army) was probably involved in the later stages of the fight for the Bukrin Bridgehead. And this is probably where Gregory Schönfinkel was wounded.

After being wounded, he seems to have been taken to some kind of service area for the 206th Rifle Division (206 зсп ЗапФ), from which he was picked up by a hospital train (and, yes, it was actually a moving hospital, with lots of cars with red crosses painted on top).

But more significant in our quest for the story of Gregory Schönfinkel is other information in the military documents we have. They record that he is Jewish (as opposed to “Russian”, which is how basically all the other soldiers in these lists are described). Then they say that he has “higher education”. One says he is an “engineer”. Another is more specific, and says he’s an “engineer economist” (Инж. Эконом.). They also say that he is not a member of the Communist Party.

They say he is a widower, and that his wife’s name was Evdokiya Ivanovna (Евдокия Иван.). They also list his “mother”, giving her name as Мария Григ. (“Maria Grig.”, perhaps short for “Grigorievna”). And then they list an address: Москва С. Набер. д. 26 кв. 1ч6, which is presumably 26 Sofiyskaya Embankment, Apartment 1-6, Moscow.

Where is that address? Well, it turns out it’s in the very center of Moscow (“inside the Garden Ring”), with the front looking over the Moscow River directly at the Kremlin:

Here’s a current picture of the building

26 Sofiyskaya Embankment, Apartment 1-6, Moscow

as well as one from perhaps 100 years earlier:

26 Sofiyskaya Embankment, Apartment 1-6, Moscow

The building was built by a family of merchants named the Bakhrushins in 1900–1903 to provide free apartments for widows and orphans (apparently there were about 450 one-room 150-to-300-square-foot apartments). In the Russian Revolution, the building was taken over by the government, and set up to house the Ministry of Oil and Gas. But some “communal apartments” were left, and it’s presumably in one of those that Gregory Schönfinkel lived. (Today the building is the headquarters of the Russian state oil company Rosneft.)

OK, but let’s unpack this a bit further. “Communal apartments” basically means dormitory-style housing. A swank building, but apparently not so swank accommodation. Well, actually, in Soviet times dormitory-style housing was pretty typical in Moscow, so this really was a swank setup.

But then there are a couple of mysteries. First, how come a highly educated engineering economist with a swank address was just a private in the army? (When the hospital train picked up Gregory, along with four other privates, one of the others was listed as a carpenter; the others were all listed as “с/хоз” or “сельское хозяйство”, basically meaning “farm laborer”, or what before Soviet times would have been called “peasant”).

Maybe the Russian army was so desperate for recruits after all their losses that—despite being 44 years old—Gregory was drafted. Maybe he volunteered (though then we have to explain why he didn’t do that earlier). But regardless of how he wound up in the army, maybe his status as a private had to do with the fact that he wasn’t a member of the Communist Party. At that time, a large fraction of the city-dwelling “elite” were members of the Communist Party (and it wouldn’t have been a major problem that he was Jewish, though coming from a merchant family might have been a negative). But if he wasn’t in the “elite”, how come the swank address?

A first observation is that his wife’s first name Evdokiya was a popular Russian Orthodox name, at least before 1917 (and is apparently popular again now). So presumably Gregory had—not uncommonly in the Soviet era—married someone who wasn’t Jewish. But now let’s look at the “mother’s” name: “Мария Григ.” (“Maria Grig.”).

We know Gregory’s (and Moses’s) mother’s name was Maria/“Masha” Gertsovna Schönfinkel (née Lurie)—or Мария (“Маша”) Герцовна Шейнфинкель. And according to other information, she died in 1936. So—unless someone miswrote Gregory’s “mother’s” name—the patronymics (second names) don’t match. So what’s going on?

My guess is that the “mother” is actually a mother-in-law, and that it was her apartment. Perhaps her husband (most likely at that point not her) had worked at the Ministry of Oil and Gas, and that’s how she ended up with the apartment. Maybe Gregory worked there too.

OK, so what was an “engineer economist” (Инженер Экономист)? In the planning-oriented Soviet system, it was something quite important: basically a person who planned and organized production and labor in some particular industry.

How did one become an “engineer economist”? At least a bit later, it was a 5-year “master’s level” course of study, including courses in engineering, mathematics, bookkeeping, finance, economics of a particular sector, and “political economy” (à la Marx). And it was a very Soviet kind of thing. So the fact that that was what Gregory did presumably means that he was educated in the Soviet Union.

He must have finished high school right when the Tsar was being overthrown. Probably too late to be involved in World War I. But perhaps he got swept up in the Russian Civil War. Or maybe he was in college then, getting an early Soviet education. But, in any case, as an engineer economist it’s pretty surprising that in World War II he didn’t get assigned to something technical in the army, and was just a simple private in the infantry.

From the data we have, it’s not clear what was going on. But maybe it had something to do with Moses.

It’s claimed that Moses died in 1940 or 1942 and was “living in a communal apartment”. Well, maybe that communal apartment was actually Gregory’s (or at least his mother-in-law’s) apartment. And here’s a perhaps fanciful theory: Gregory joined the army out of some kind of despondency. His wife died. His older brother died. And in February 1942 any of his family members still in Ekaterinoslav probably died in the massacre of the Jewish population there (at least if they hadn’t evacuated as a result of earlier bombing). Gregory hadn’t joined the army earlier in the war, notably during the Battle of Moscow. And by 1943 he was 44 years old. So perhaps in some despondency—or anger—he volunteered for the army.

We don’t know. And at this point the trail seems to go cold. It doesn’t appear that Gregory had any children, and we haven’t been able to find out anything more about him.

But I consider it progress that we’ve managed to identify that Moses’s younger brother lived in Moscow, potentially providing a plausible reason that Moses might have gone to Moscow.

Actually, there may have been other “family reasons”. There seems to have been quite a lot of back-and-forth in the Jewish population between Moscow and Ekaterinoslav. And Moses’s mother came from the Lurie family, which was prominent not only in Ekaterinoslav, but also in Moscow. And it turns out that the Lurie family has done a fair amount of genealogy research. So we were able, for example, to reach a first cousin once removed of Moses’s (i.e. someone whose parent shared a grandparent with Moses, or 1/32 of the genetics). But so far nobody has known anything about what happened to Moses, and nobody has said “Oh, and by the way, we have a suitcase full of strange papers” or anything.

I haven’t given up. And I’m hoping that we’ll still be able to find out more. But this is where we’ve got so far.

One More Thing

In addition to pursuing the question of the fate of Moses Schönfinkel, I’ve made one other potential connection. Partly in compiling a bibliography of combinators, I discovered a whole collection of literature about “combinatory categorial grammars” and “combinatory linguistics”.

What are these? These days, the most common way to parse an English sentence like “I am trying to track down a piece of history” is a hierarchical tree structure—analogous to the way a context-free computer language would be parsed:

But there is an alternative—and, as it turns out, significantly older—approach: to use a so-called dependency grammar in which verbs act like functions, “depending” on a collection of arguments:

In something like Wolfram Language, the arguments in a function would appear in some definite order and structure, say as f[x, y, z]. But in a natural language like English, everything is just given in sequence, and a function somehow has to have a way to figure out what to grab. And the idea is that this process might work like how combinators written out in sequence “grab” certain elements to act on.

This idea seems to have a fairly tortuous history, mixed up with attempts and confusions about connecting the syntax (i.e. grammatical structure) of human languages to their semantics (i.e. meaning). The core issue has been that it’s perfectly possible to have a syntactically correct sentence (“The flying chair ate a happy semicolon”) that just doesn’t seem to have any “real-world” meaning. How should one think about this?

I think the concept of computational language that I’ve spent so many years developing actually makes it fairly clear. If one can express something in computational language there’s a way to compute from it. Maybe the resulting computation will align with what happens in the real world; maybe it won’t. But there’s some “meaningful place to go” with what one has. And the point is that a computational language has a well-defined “inner computational representation” for things. The particular syntax (e.g. sequence of characters) that one might use for input or output in the computational language is just something superficial.

But without the idea of computational language people have struggled to formalize semantics, tending to try to hang what they’re doing on the detailed structure and syntax of human languages. But then what should one do about syntactically correct structures that don’t “mean anything”? An example of what I consider to be a rather bizarre solution—embodied in so-called Montague grammars from the 1970s—is essentially to turn pieces of certain sentences into functions, in which there’s nothing “concrete” there, just “slots” where things could go (“x_ ate y_”)—and where one can “hold off meaninglessness” by studying things without explicitly filling in the slots.

In the original formulation, the “functions” were thought about in terms of lambdas. But combinatory categorial grammars view them instead in terms of combinators, in which in the course of a sentence words in a sense “apply to each other”. And even without the notion of slots one can do “combinatory linguistics” and imagine finding the structure of sentences by taking words to “apply themselves” “across the sentence” like combinators.

If well designed (as I hope the Wolfram Language is!) computational language has a certain clean, formal structure. But human natural language is full of messiness, which has to be untangled by natural language understanding—as we’ve done for so many years for Wolfram|Alpha, always ultimately translating to our computational language, the Wolfram Language.

But without the notion of an underlying computational language, people tend to feel the need to search endlessly for formal structure in human natural language. And, yes, some exists. But—as we see all the time in actually doing practical natural language understanding for Wolfram|Alpha—there’s a giant tail that seems to utterly explode any all-encompassing formal theory.

Are there at least fragments that have formal structure? There are things like logic (“and”, “or”, etc.) that get used in human language, and which are fairly straightforwardly formalizable. But maybe there are more “functional” structures too, perhaps having to do with the operation of verbs. And in combinatory linguistics, there’ve been attempts to find these—even for example directly using things like Schönfinkel’s S combinator. (Given S f g xf[x][g[x]] one can start imagining—with a slight stretch—that “eat peel orange” operates like the S combinator in meaning “eat[orange][peel[orange]]”.)

Much of the work on this has been done in the last few decades. But it turns out that its history stretches back much further, and might conceivably actually intersect with Moses Schönfinkel himself.

The key potential link is Kazimierz Ajdukiewicz (1890–1963). Ajdukiewicz was a Polish logician/philosopher who long tried to develop a “mathematicized theory” of how meaning emerges, among other things, from natural language, and who basically laid the early groundwork for what’s now combinatory linguistics.

Kazimierz Ajdukiewicz was born two years after Moses Schönfinkel, and studied philosophy, mathematics and physics at the University of Lviv (now in Ukraine), finishing his PhD in 1912 with a thesis on Kant’s philosophy of space. But what’s most interesting for our purposes is that in 1913 Ajdukiewicz went to Göttingen to study with David Hilbert and Edmund Husserl.

In 1914 Ajdukiewicz published one paper on “Hilbert’s New Axiom System for Arithmetic”, and another on contradiction in the light of Bertrand Russell’s work. And then in 1915 Ajdukiewicz was drafted into the Austrian army, where he remained until 1920, after which he went to work at the University of Warsaw.

But in 1914 there’s an interesting potential intersection. Because June of that year is when Moses Schönfinkel arrived in Göttingen to work with Hilbert. At the time, Hilbert was mostly lecturing about physics (though he also did some lectures about “principles of mathematics”). And it seems inconceivable that—given their similar interests in the structural foundations of mathematics—they wouldn’t have interacted.

Of course, we don’t know how close to combinators Schönfinkel was in 1914; after all, his lecture introducing them was six years later. But it’s interesting to at least imagine some interaction with Ajdukiewicz. Ajdukiewicz’s own work was at first most concerned with things like the relationship of mathematical formalism and meaning. (Do mathematical constructs “actually exist”, given that their axioms can be changed, etc.?) But by the beginning of the 1930s he was solidly concerned with natural language, and was soon writing papers with titles like “Syntactic Connexion” that gave formal symbolic descriptions of language (complete with “functors”, etc.) quite reminiscent of Schönfinkel’s work.

So far as I can tell Ajdukiewicz never explicitly mentioned Schönfinkel in his publications. But it seems like too much of a coincidence for the idea of something like combinators to have arisen completely independently in two people who presumably knew each other—and never to have independently arisen anywhere else.


Thanks to Vitaliy Kaurov for finding additional documents (and to the State Archives of the Dnipropetrovsk Region and Elena Zavoiskaia for providing various documents), Oleg and Anna Marichev for interpreting documents, and Jason Cawley for information about military history. Thanks also to Oleg Kiselyov for some additional suggestions on the original version of this piece.