#### Forword

Bill Howard is a noted figure in mathematical logic. Studying under Saunders Mac Lane and Andre Weil, he took his PhD at the U of Chicago in 1956 with the thesis ‘k- Fold Recursion and Well-Ordering’. Now Professor Emeritus at UIC, Bill is largely recognized in the mathematical world for his establishment of the relation between intuitionist logic and simply typed lambda calculus, referred to as the Curry – Howard Correspondence.

Stemming from their student days at the U of Chicago in the early 50’s, Bill was a lifelong

friend and intimate of Stan’s up until 1991. As such they saw and were in touch with each other

frequently in various circumstances (eg U of C, the farm in Michigan, Penn State, Yeshiva U,

IAS, UIC).

The quintessential ‘one who was there’, Bill provides a fascinating account of his association

with Stan over the years in a fulsome email correspondence during 2015/16. This includes not

only his address ‘My Life With Stan’ delivered at Stan’s memorial conference in April 2006 but

further a large, wide-ranging, body of recollections, stories, comments, reflections covering

among other things Stan’s early life, his student days, and his connections with Bettelheim,

psychoanalysis, Ray Smullyan, Paul Halmos, Andre Weil, the IAS, John Myhill, the Bourbaki….and so on.

#### My Life with Stan

Subject: Re: STANLEY TENNENBAUM MEMOIR

From: Howard, William A.

To: robtully;

Date: Tuesday, 25 August 2015, 7:39

#### Forty Years of Adventures with Stan

By William A Howard.

(This is the talk I gave at the Conference in Memory of Stanley Tennenbaum at the Graduate Center of the

City University of New York, April 7, 2006.)

I met Stan in the spring of 1950, when we were graduate students at the University of Chicago. Stan was a

handsome young man in a Brooks Brothers suit who had an obsession with Gödel’ incompleteness theorem.

If he spotted you crossing the campus, he would back you up against a tree and compulsively explain

Gödel’s incompleteness theorem, like the ancient mariner in Coleridge’s poem, The Rime of the Ancient

Mariner. I think he got this bug from Carnap, for whom the incompleteness theorem was a source of great

unhappiness. (It refuted the positivistic view that the meaning of a sentence was to be given by a procedure

for determining its truth or falsity.)

During the period 1950-1953, my relationship with Stan was rather casual. I was trying to become a great

mathematician like Andre Weil, and I had only a casual interest in logic. In the fall of 1953, Myhill and Dekker

had visiting appointments at the U. of C. Stan was occupying Prof. Bergstrasser’s house and holding a

#### Further thoughts, Stan's effect

Subject: Re: Stan

From: Howard, William A.

To: robtully

Date: Tuesday, 15 September 2015, 23:30

Dear Rob,

A few years after Stan’s memorial, I was talking to Juliette Kennedy, who was a close friend of Stan, and, in fact, had been responsible for the memorial itself. I told her that my presentation at the memorial had not mentioned an essential aspect of Stan’s influence on me; namely, that he had expanded my horizons. Here are two examples:

(1) The liberal education. He had gone through the U of C College during its prime (actually, it was still at its prime when I arrived in 1949). Great Books and all that. From him I learned all about the liberal education. I am not saying that the liberal education is suitable for state universities, but knowing what it is all about has given me a valuable perspective on the academic world and education as a whole.

(2) Psychoanalysis. He spent a few months at Bettelheim’s Orthogenic School (a school for really really disturbed kids), and from Bettelheim he acquired a deep understanding of psychoanalysis. So he taught me some of this, indicated how it helped to understand various people. He occasionally analyzed a dream of mine or the people we hung out with. I was so impressed that I made a thorough study of Freud’s book, “The interpretation of dreams.”

Actually, I think I have put my finger on the two most important ways in which he expanded my horizons. Good.

Item #2 did not have much effect on my career, but it helped me understand who I am, so it would go under the heading: metaphysical journey. Item #1 helped me understand who I am academically, and this has been a great help in my career.

But the above is just a summary. In regard to item #1, you have given an excellent summary in the Spring 1965 –

Fall 1965 section of your memoir, starting with “When you entered Stan’s class, you entered the totality of his

Cardinal Newman’s ‘Idea of a University’ scholastic world, …” and ending with “one of the most interesting

episodes being when Stan asked Bonnie Gold in a number theory course whether she would bet her life on

something she had just stated, …” Incidentally, I met Bonnie in the summer of 1968 (the month-long conference at Buffalo university); very smart, very nice.

Also relevant to #1 are the two paragraphs in in the Spring 1965 – Fall 1965 section of your memoir, starting with “I always had the impression that Stan’s life started at 16 at the U of Chicago, …”.

As I say in my memorial presentation: the decline of his physical health and psychological condition from (say) 1972 onward distressed me more than I can say. I have often pondered this change in Stan. I find the following passage, in the first of your two paragraphs mentioned above, particularly interesting: “I also had the feeling that it was here that he ‘constructed’ himself, block by block, building an intellectual, philosophical, metaphysical foundation, of course informed by the Chicago curricula, out of his own rational thought”. The result was certainly impressive, but maybe he was trying to do something impossible.

Let me end this email with the following story bearing on educational matters. In the spring of 1991 (or possibly a year or two earlier), Stan suddenly appeared on campus (U. of Illinois, Chicago). I was running to teach a class, a large lecture section on Finite Math for Business Students. Stan asked if he could sit in. I was happy to have him do so. He sat in the back and observed.

It was a typical lecture. Halfway through, a couple of students decided to leave, causing a commotion by making their way across the aisle (auditorium style lecture room). A few minutes later, someone dropped an empty Coke can: clank, clank, clank as it made its way down the tiers. And so on. Afterwards, I said to Stan: “I don’t know how to handle this. Will you be a guest lecturer in Friday’s class so I can pick up some pointers as to what to do?”

Stan’s reply was: “Sure, under two conditions. First, the students’ parents need to be present, so that they will see how immature their children are. Secondly, the Dean needs to be present, so he can see what the educational situation is at his university”

ME: “Okay, Stan, I get your point. But I really need advice. Tell me something practical.”

STAN: “Bill, this course is bad for your mental health. You should go to the chancellor and ask, on grounds of

mental health, that you be relieved from the duty of teaching this course, and, to make up for this, that you will spend an equivalent amount of time cleaning latrines.”

I did not take this specific advice, but it helped me understand that courses of this kind were indeed bad for my mental health. One way or another, I managed to avoid them for the next ten years, at which time the math. dept. administration was beginning to catch on, so I retired.

One strategy was to concentrate on the math. ed. courses. The math. dept. had an excellent program of courses for prospective or already practicing high school teachers, and I had already found these courses pleasant to teach, in particular because they were taught in small classrooms holding at most 32 students. In fact, on the same day as the above episode, Itaught one of these classes in the evening and Stan came along. He got so excited that he could not restrain himself and took over the class. It was a typical Tennenbaum performance; I don’t know what the students thought.

What I thought was: Well, it was good for them.

Best regards,

Bill

#### Reply to Bill, Freud and Bettelheim

Subject: Re: Stan

From: Rob Tully

To: Bill Howard

Date: Monday, 21 September 2015, 15:46

dear bill,

it was with great pleasure that i received your account of the effects and influences stan had on you, those so

in concert with those he had on me.

leaving the house one morning to go to the U of R campus, apropos of i forget what, he commented over the

top of the car, he getting in one side, me the other, on the genius of freud’s ‘interpretation of dreams’, ‘real

science’ as he put it, a book that would take a minimum of two years to really comprehend. i of course

immediately put it in my mental ‘to do’ list (though as yet have not set aside the demanded two years)…. his

regard of freud (as you note, through bettelheim) might have been responsible for my taking later a freud

seminar though i can’t be sure of that….. he spoke often of bettelheim which did indeed cause me to (1) read

much of bettelheim’s work and (2) seek summer employment at the orthogenic school (it turned out that

bettelheim would not be there that summer)…… a few years later dick cavett on his talk show was hosting

bettelheim followed by a very minor comedian, doc something or other. coming on after bettelheim and sitting

next to him, the comedian, abject fool, tried with lame arrows at psychiatry to elicit some cheap laughs at

bettelheim’s expense. within two or three scathing sentences, bettelheim demoralized the pretender to such an

extent he ended up staring at his shoes, head bowed, for the remainder of his interview, from which position

he never recovered. i was astonished. when i mentioned this to stan who had also seen the segment in 1971(the

last time i saw him), he said ‘see, an expert’ ….. many many years later i saw a lecture by bettelheim at the u of

new mexico, not too long before he committed suicide.

i hugely regret not being in touch with stan in his later years, not least because of his financial straits which

by that time i could easily have helped with and would have very happily done so. lamenting this on a visit to

peter in rochester, peter said no, it was far better that i didn’t know stan then as he had markedly deteriorated

physically and psychologically, peter noting that he was having all of the john nash symptoms of

schizophrenia, reading arcane messages into everyday events and so on. perhaps his pot habit might have had

some effect. indeed, looking at peter’s wedding pictures, i had to ask who a certain man was in the photos, only

to be told that it was stan, shockingly unrecognizable to me….. my friend john flavin, a couple of years ahead of

me, after talking to stan at length one morning in ’67 or ’68 when stan was through rochester, said that stan

was deeply haunted by something which would never let him be deeply at ease.

i have a particularly hard time trying to imagine stan when he was young, a student with you at chicago……i

knew him when he was a mature 39, masterfully assured in all aspects, a mantle of intellectual virtuosity lying

easily about his shoulders…….if you would like to relate something of him during this time, i would be

gratified…..

at some point (in the 70’s?), stan lived with bonnie gold and her husband until that point the he and the

husband had an irreconcilable contretemps.

though i did write to juliette kennedy, i’ve not heard from her. should it not be presumptuous, i would be

appreciative if you mentioned the existence of the memoir to her.

my best wishes,

#### FORTY YEARS OF ADVENTURES WITH STAN

#### To Jazmin Arellano, the Bourbaki

Subject: Re: Bourbaki

From: Howard, William A.

To: jazmin

Cc: robtully

Date: Thursday, 24 September 2015, 10:35

Dear Jazmin,

Maybe you are referring to Tully’s passages:

Spring 1965 – Fall 1965 “distrustful of Lang (or at least Lang was of him), who was at the

University of Chicago at the same time, perhaps because of his association with the

Bourbaki, red rag to a bull anathema to Stan.”

Spring 1966 – Winter 1966 “For Stan mathematics should be concrete, hands-on, the proof

of any statement, no matter how complex, could, if the keys were found, be written on a

single sheet, most often attended with the right ‘picture’ ….. it was this persuasion,

prejudice if you will, that leaned him towards Klein, Hilbert (Geometry and the

Imagination), Courant, Polya, Poincare, made him dismissive of, distrustful of the Bourbaki,

an effort he philosophically opposed as being inimical to the creative and continuing

flowering of mathematics. (Andre Weil, at Chicago when Stan was there, was the

purported head of the Bourbaki. Much of his life spent trying to solve the Riemann

Hypothesis, Stan claimed that he used to walk around the commons room asking new

students how old they were, and if they were over 21, used to cackle ‘Ha!! … It’s too late for

you!!’)”

Bourbaki’s approach emphasizes abstractions: no diagrams or pictures. As V. I Arnold says

at the beginning of (*) http://math.sun.ac.za/wp-content/uploads/2013/03/Bourbaki.pdf

(http://math.sun.ac.za/wp-content/uploads/2013/03/Bourbaki.pdf) it is left-brained, no

right brain. Also no concrete examples. So Stan did not like this.

The Bourbaki group wrote a number of volumes intended for students at about the first

year of graduate school. The style is very austere. I did not like them much, except for the

historical passages (obviously written by Weil), which are superb. As indicated in the

second paragraph of page 2 of (*), this series of volumes was meant to do for today’s

mathematics what Euclid’s Elements did for the mathematics of his time, an impossible

goal. The next couple of paragraphs describe one of Bourbaki’s pranks. By “the truth”, Weil

meant that Bourbaki was an actual person. As Mac Lane says in his autobiography (p. 202):

“Wow!” Mac Lane goes on to say, “I wrote an ambiguous letter to the editor; fortunately,

Weil did not stop speaking to me.” Bourbaki then spread the rumor that Boas did not exist;

rather Boas was an acronym, B.O.A.S., for a group of Americanmathematicians. I was a

student there at the time, and we were all gossiping about it. My impression at the time

was that Boas was quite peeved. Maybe he got over it; he talks about it in an article,

Bourbaki and Me, in the Mathematical Intelligencer, 1986 (use to be available for free online;

now they want to charge for it; so to hell with them).

I got a kick from Grothendieck’s remark, col. 1, page 2 of (*), near bottom.

Tully (above) reports that Stan claimed that Weil used to walk around the commons room

asking new students how old they were, and if they were over 21, used to cackle ‘Ha!! … It’s

too late for you!!’)” Maybe this was Stan’s version of the following story, which I

undoubtedly told him. In the fall of 1953, when Weil and I were walking in the park, he

suddenly had a thought:

WEIL: “How old are you?”

ME: “26.”

WEIL: “When Newton was 26, he had already discovered the theory of gravitation, invented

the calculus, etc., etc.”

I wondered what this was all about. I already knew that Weil had been a child prodigy, and

in his teens had been told that he was expected to be Poincaré’s successor. When I arrived

at the U. of C., there was gossip that Weil was unhappy at not having reached the level of

creativity of Poincaré, and that this explained some of Weil’s behavior. So, I thought at the

time: maybe that was it. The explanation is plausible, but, in pondering this episode in

subsequent years, I felt that this was not the whole explanation. In 2003 or 2004, I

recounted the episode to Jill. Her reply: “How old was he?” I made a quick calculation and

replied: “46 or 47” (actually, he was 47). Then I immediately thought: Well, of course, the

retirement age for membership in the Bourbaki group is 50! Jill’s intuition about what was

on Weil’s mind was correct. He was thinking that his own time was running out.

Actually, in 1967 he came up with the Taniyama–Shimura-Weil conjecture (which eventually

led to Andrew Wiles’ proof of Fermat’s Last Theorem in 1994); so there was still some life in

the old horse. It is past my bedtime, so I’ll stop here

. B

ill

#### The early Stan

Subject: Re: The early Stan

From: Howard, William A.

To: robtully

Cc: jazmin

Date: Friday, 25 September 2015, 7:58

Dear Rob,

Stan did not speak very much about his early life. He grew up in Cincinnati; his father owned a large

furniture store or company, already established by the grandfather. He spoke to me about this a couple of

times. My impression is that there was quite a bit of money in the family. I met his mother when she paid a

visit to Chicago in the mid 1950s. Cincinnati socialite, very domineering.

He was on his high school’s football team. I remember him telling me that when they played against the

local Catholic high school, he would be out on the field and the members of the opposing team would be

calling to one another: “Get the Jew-boy.”

After the following episode, there was no doubt in my mind that he had been a serious player in the high

school football scene. In the fall of 1953, we were walking down the street. There was a group of young kids

(around age 12) playing football in the middle of the street. STAN: “Give me the ball. I’ll show you how it

should be done.” He punted the ball expertly, high in the air. While we were leaving, the kids were saying,

“Who is he?”

So, at age 16 there was a big step in Stan’s life: from Cincinnati bourgeoisie to the Hutchins program. In

your memoir, Spring 1966 – Winter 1966, you say: “I always had the impression that Stan’s life started at 16

at the U of Chicago, that an unknown world yawned before him, one courtesy of Hutchins’ vision, …. I also

had the feeling that it was here that he ‘constructed’ himself, block by block, building an intellectual,

philosophical, metaphysical foundation, of course informed by the Chicago curricula, out of his own rational

thought.”

I find your observation very perceptive. It may help explain the changes in his behavior that began to

manifest in the late 1960s. He had built one personality on top of another that was radically different, and

the contradictions began to make themselves felt.

He had a sister approximately his own age. Here is an amusing story. I met him through his pal Raymond

Smullyan in, I think, 1951. Raymond also had a sister approximately his own age. Raymond knew a lot about

psychoanalysis (it is my impression that he himself had undergone psychoanalysis for a number of years,

but I don’t know this as a fact). Shortly after Raymondhad introduced me to Stan, I witnessed the following

conversation between Raymond and Stan.

RAYMOND: “Do you think that it would have been therapeutic if you had slept with your sister?”

The discussion went on for some time, considering the therapeutic pros and cons for sleeping (ie., having

sex) with one’s sister. Unfortunately, I cannot remember the details because I was sitting there openmouthed. I had never seen anything like this. I was a hick from the sticks, having grown up in the

mountains near Vancouver. So, for me, this was very avant garde. Of course, after a few months of

conversation with Stan, in which he passed on some of the knowledge of psychoanalysis he had acquired

from Dr. B., I would have regarded the above conversation as completely normal. I’ll break off here. I

assume that you got the cc of my email to Jasmin. She is a friend of mine, on the humanistic side of the

cultural divide, interested the Weil, Bourbaki, and my relationship with Stan.

Bill

#### Jonathan, Stan and education

Subject: Re: Jonathan’s paper

From: Howard, William A.

To: robtully

Date: Friday, 17 June 2016, 8:37

Dear Rob,

Thanks for Jonathan’s paper. I had not seen it before. There was nothing about it at the

memorial conference. I hope Juliette has a copy.

I am still pondering the paper. As an initial step, I have zeroed in on some items that call

up concrete memories.

“Another very important influence was my father’s experience working as a voluntary

assistant in Bruno Bettelheim’s school for autistic and schizophrenic children in

Chicago. By understanding the extreme case of the damage done to those children, and

how they could be helped, and comparing with many other experiences, he gained an

extraordinary insight into the emotional side of education generally.”

Yes, sometime before I met him, Stan worked for a few months as a counselor in

Bettelheim’s Orthogenic School. We talked about it quite a lot. From his experience as a

counselor, and from Bettelheim himself, Stan became an expert on psychoanalysis; and

I learned a lot from Stan, studied Freud’s “Interpretation of Dreams”, and in fact use a

version of this (due to Ira Progoff) at appropriate times in my own life. Also, Stan

analyzed two or three of my own dreams. Very impressive.

Agreed that what Stan learned from the Bettelheim experience strongly influenced his

ideas about education.

“Indeed, one could say, that the greater part of scientific education at the University of

Chicago in the 1950s, did not go on in classrooms, but rather in places like Steinway’s

coffeehouse on 57th Street, where my father used to hang out a lot of the time, often

with me tagging along; and where young people could learn most of their physics,

mathematics and chemistry by just sitting at the table with scientists, many of them

already famous ones, arguing and fighting over ideas.”

Yes indeed. I was there. It was Stineway’s drugstore with tables for snacks and coffee,

corner of 57th and Kenwood. More generally, both the undergraduates and the graduate

students learned more from their informal interaction with the faculty and with each

other than they did from actual classroom experience. The educational environment at

the Univ. of Chicago at that time was very unusual.

High school math textbooks: “incoherent, kaleidoscopic, broken up with countless

colored boxes, irrelevant cartoons and arbitrary symbols, supposedly to make them

“interesting” (i.e. distracting) to the child.”

I remember, on the farm, Stan showing me one of them. It was, indeed, pretty bad.

“But then, in Michigan, I fell into trouble, especially in mathematics, and the teachers got

to me. I did not have my father’s defiant character. Instead of fighting back, I caved in.

My father was furious! He saw me being destroyed and finally decided to take me out of

school entirely. That brought him into serious conflict with my mother, …”

I visited Stan’s farm in Michigan a few times, 1960-1962. Jonathan was being “home

schooled”. It did not seem like such a big deal to me. I did not realize that his mother,

Carol, had misgivings about the situation.

“I was lazy and rather spoiled, and spent most of my time running around outside on

the farm.”

He is exaggerating. He was a serious person, mature for his age (9-11). The last time I

saw Jonathan was when I visited Stan at Stony Brook. This was probably 1964.

“(In the sequel, I hopped and jumped in and out of school and home, without finishing

either grade school or high school, sat in on some university courses, finally got

interested in mathematics — particularly Riemann’s theory of functions of a complex

variable and analytical number theory –, learned to work hard, finished a doctorate at

the University of California and left, at the age of 22, for a teaching position in Europe. …

)”

Jonathan got his doctorate under Bishop in 1973. I would like to know more about his

experience with Bishop. Stan was talking a lot about Bishop during those years, in

particular in connection with the project of creating a new university. Stan recounted

some of this to me (ie., his conversations with Bishop) during the late 1960s.

“One of the people who felt particularly resentful and threatened by my father was the

wife of a faculty colleague, who was trying to build herself a career in “computer

science”. The particular colleague, while very brilliant, had a history of mental illness.

Now, his wife went to my mother and confided to her, that she recognized the same

symptoms of “manic-depressive psychosis” in my father, as her own husband had

suffered from! …

To make a long story short, my mother demanded that he go with her to see a

university psychiatrist for “consultation”. Smelling an attempt by Wallis et al. to obtain a

pretext for removing him from his tenured position at the University — mental illness

being one of the two legal justifications for such a move — my father demanded that I

go along as a witness ..

.” Wow! Reads like a novel; but also has the ring of truth.

The educational films: Stan talked to me about this but I found it hard to relate to; it was

not the sort of thing that I was very interested in. I remember him recounting a

conversation with Gödel, who said, concerning the opposition he would encounter from

the entrenched commercial interests, “They will destroy you *instantly*.”

Concerning the importance of fostering the ability of children to “think things through

by and for themselves — the sovereignty of their minds –“: well, of course. I don’t

recall Stan emphasizing this, but he probably did; it is just so obvious to me that I would

not have noticed.

The fight at the IAS: As mentioned in my talk to the memorial conference, I was there

during the year 1972-1973. Lots of memories from that year.

I have not had any contact with Jonathan since Stony Brook, 1964. I should send him an

email. Could you give me the address?

Bill

#### Paul Halmos

Subject: Halmos

From: Howard, William A.

To: robtully

Cc: hulin

Date: Wednesday, 27 July 2016, 8:41

Dear Rob,

Re your mention of the tension between Stan and Paul Halmos (Winter 1966 section of your memoir): it goes back to

(at least) the fall of 1953, when Halmos was giving a course on a method of subsuming Gödel’s Completeness

Theorem into a variant of Tarski’s cylindrical algebras. Stan’s reaction to this was: “Paul is trying to destroy logic by

subsuming it into ordinary mathematics. In this, he is being egged on by Saunders Mac Lane.”

Also, in the fall of 1953, Jim Dekker was giving a seminar on recursion theory. I was not interested in Paul’s course

or Dekker’s seminar but I often came around when the seminar let out. One day, I heard Halmos down the hall say:

“There go the logic cadets.” Maybe he was annoyed that most of the seminar participants were ignoring his course.

Also, he told me that he thought that logic attracted some pretty weird people; e.g., Stan, Smullyan, Myhill.

Re your remark in Winter 1966 section, “Logic students included Bill Howard, Ray Smullyan, and Anil Nerode”:

Michael Morley should be included. When I mentioned to him, in 2004, “We had an exciting logic group at U. of C. in

the 1950s,” his reply was, “We had logic students but no logic professors.”

As for Halmos’ book (1960), ‘Naïve Set Theory’, I did not understand why Stan’s reaction against the book was so

negative. I seem to remember him saying: “It’s fraudulent. He does not know what he is talking about.” My

explanation now would be twofold: (1) Stan did not like Halmos very much, and (2) he thought that the book was

unphilosophical. In reply to #2, I would say that it was not meant to be philosophical; it was just an exposition,

meant for a certain audience. Apparently, even today, this audience has found it helpful:

http://www.goodreads.com/book/show/558194.Naive_Set_Theory

(http://www.goodreads.com/book/show/558194.Naive_Set_Theory)

Halmos was Errett Bishop’s thesis adviser. Stan talked to Bishop a lot about his plans for a new university. I got to

know Bishop pretty well. Jonathan got his Ph.D. under Bishop in 1973. Small world!

I am sending a cc. to my colleague Fred Thulin, who is interested in these matters. Reminder to Fred: The memoir,

on Google, is “Stanley Tennenbaum: American Original.”

Best,

Bill

#### Logic according to Halmos and Weil

Subject: Logic according to Halmos and Weil

From: Howard, William A.

To: hulin

Cc: robtully

Date: Saturday, 30 July 2016, 8:30

Dear Fred,

After Friday’s conversation I remembered another Halmos episode.

Sometime in 1954 I mentioned to Halmos that I was working on a finitary consistency proof for Peano

arithmetic. From then on, for months afterward, whenever I passed Halmos in the hallway, he would

say, with a show of anxiety, “Bill, have you proved the consistency of mathematics yet? We need to

know, so we can get on with our research without being afraid that it is all inconsistent.”

Also, he liked to go around saying, “Intuitionistic mathematics? Doing mathematics without the use of

the law of the excluded middle is like taking a centipede, cutting off all but one its legs and seeing how

far it gets.” I wonder what he thought when Errett Bishop, one of his best students, from 1965 onward

devoted his life to developing constructive mathematics which avoids use of the law of the excluded

middle?

Here are a couple of Weil episodes. In the fall of 1951 I mentioned to him that I was taking a course from

Carnap on The Axiomatic Method. From that time onward, Weil kept asking me, “Well, are you through

with your axiomatic nonsense yet?” Once, when we were out for a walk, he said, “I hope you are not

involved with Brouwer’s intuitionistic mathematics, which is an *abomination*.” He said “abomination”

with great emphasis, stamping his foot on the sidewalk.

So that was logic at the U. of C. in the 1950s. Not that I found episodes of this sort discouraging. It just

increased my resolve to keep doing what I was doing.

From the above, and also Stan’s remarks quoted in my email of 7/27/16 to Rob Tully, one would conclude

that Halmos was unfriendly towards logic. A different perspective is provided by Nerode in his

obituary of Hartley Rogers in the Bulletin of Symbolic Logic, June 2016, p. 295. Nerode is talking about

what led to the five week NSF Summer Institute in Symbolic Logic at Cornell in August, 1957. He says

that it was this meeting that created the mathematical logic community. Halmos played a crucial role:

“Halmos, then at the University of Chicago, had the motto, `Mathematics is a social science’, and

suggested to Tarski a meeting of all those doing research in mathematical logic.” Tarski and Rosser

then got funding, etc. But I found a much more detailed account of this:

https://math.stanford.edu/~feferman/papers/cornell.pdf

(https://math.stanford.edu/~feferman/papers/cornell.pdf)

Alfred Tarski and a watershed meeting in logic: Cornell, 1957, by Solomon Feferman.

Feferman says that Halmos got the ball rolling when he contacted Edwin Hewitt in 1955. In his letter to

Hewitt, he says:

“In regard to the non-availability of other support, I think little need be said. Although logic is one of

the oldest subjects of mathematical interest and although I am convinced that its continued study is of

tremendous mathematical value, the subject is not such as to capture the imagination of an admiral of

the navy or a tycoon of industry.”

Hey Paul, right on!

As ever,

Bill

#### Stan, Myhill, Weil, and me

Subject: Stan, Myhill, Weil and me.

From: Howard, William A.

To: robtully

Date: Thursday, 18 August 2016, 8:47

Dear Rob,

Feel free to make use of my emails about Stan and company in any way you want (unless

there is something that might offend somebody, but there is nothing of that sort in the

emails I have sent you up to now).

You mention Weil and Bourbaki in your section Spring 1966 – Winter 1966. Here is something

that will amuse you, especially since it includes Myhill and (in a separate story) Mac Lane. It

is a post, by my colleague John Baldwin, of a couple of emails I sent him.

http://homepages.math.uic.edu/~jbaldwin/pub/howonbour.pdf

(http://homepages.math.uic.edu/~jbaldwin/pub/howonbour.pdf) Recollections of some

connections of Bourbaki with logicians, by William A. Howard, July 27, 2013.

I don’t know how much personal contact Stan had with Weil during our student days, but in

the late 1960s, when Weil was at the IAS, Stan had established a personal relationship with

him. At U. of C., Weil pronounced his name as in “Vile” but later changed it to Vey, possibly to

avoid confusion with Hermann Weyl; also there was his famous sister, Simone, but that is

another story. In any case, in the late 1960s and early 1970s, Stan used to go up to Weil and

say, “Oy, it’s Mr. Oy Vey!” They got a kick out of each other.

Weil’s learning was formidable. He studied Sanscrit in India, could quote Plato in the

classical Greek, etc., etc. One day, in the fall of 1972, Stan and I were at the IAS tea, when

Weil and a group of formally dressed elderly men came through the door. Stan said to me,

“That’s the archaeology seminar. They are terrified of him.”

Jonathan describes the fight at the IAS against Kaysen’s plan to create a new “School of

Social Science” alongside the existing three faculties of mathematics, physics and history,

with Robert Bellah as head. Weil was in the vanguard of the opposition. In an interview with

the New York Times, Weil said, “Yes, I have read Bellah’s worthless book,” etc. It was probably

“Tokugawa Religion: The Values of Pre-Industrial Japan.” Weil could be impulsive, at times.

Stan used to tell me what went on in the faculty meetings; e.g., Gödel got up and made a

convoluted analysis of Bellah’s theory, the upshot being (in Stan’s words, not Gödel’s): “It is

wrong.” I asked Stan, “How do you know what went on in these meetings?” His answer: “I have spies.” Later it became clear to me that Hasler Whitney was giving him a detailed

report. Through Stan, I got to know the Whitneys and we became good friends.

At the IAS Stan had a good friend, Sue Walker (now Sue Walker Toledo). She was Whitney’s

assistant in a math education project, and in that capacity had an office (it was, I think,

Gödel’s old office). Stan often slept there. I would go there in the morning and the office

would be a shambles: coke cans, remains of sandwiches, cigarette butts all over the place.

We spent a lot of time in Sue’s apartment. Stan’s daughter Susan (then about 17) was staying

with Sue; Susan had befriended a young woman who was pathologically shy (who typically

sat in a corner with her hair over her eyes), and Stan was trying to help her; also Domingo

Toledo (whom she later married) was often there. I remember once when Stan became

uncontrollable, Susan shut him down by saying, firmly, “You will not disrupt this

domesticity.”

I met Sue Walker through Stan at the month-long conference on intuitionism and proof

theory at Buffalo University, summer of 1958, and we became good friends. You say in your

memoir, “Uncharacteristically [Stan] met Ayn Rand, complimented her work, but was unable

to engage her further than that.” I wonder in what venue? Wikipedia says that throughout

the 1969s and 1970s she gave talks at various universities.

https://en.wikipedia.org/wiki/A yn_Rand

(http://homepages.math.uic.edu/~jbaldwin/pub/howonbour.pdf)

In any case, I’ll bet Stan sought her out because of Sue Walker, who was much taken by Ayn

Rand’s Objectivist philosophy and talked about it a lot at the Buffalo meeting.

There were various episodes with Stan at the Buffalo meeting. Here is one of them (I am

excerpting it from my reminiscences for Smullyan’s 90th birthday). One evening, Stan

wanted us to hear his son, Peter (who was then 9 or 10), play the organ. We got into the

concert hall. This involved somebody climbing in the window to get the door open, as I

recall. Peter played nicely. This was backstage. Then Raymond spotted a grand piano on the

stage. We took seats in the auditorium (there were eight or ten of us) and Raymond played

Schubert’s A-Major Sonata: a massive forty-minute piece. About halfway through, the

janitor appeared.

“What are you doing here?”

WE: “Listening to Schubert’s A-Major Sonata.”

HE: “You can’t do that!”

WE: “Sure we can. We’re professors.”

He left. Then all the lights went out. The janitor had, no doubt, pulled the master switch.

That did not faze Raymond; he played the second half of the A-Major Sonata in the dark. A

magical performance.

But I am flying off of the original topic (Weil, etc.), so I’ll end here.

Best,

Bill

#### Stan at the IAS

Subject: Stan, IAS

From: Howard, William A.

To: robtully

Date: Saturday, 20 August 2016, 5:35

Dear Rob,

Here are a few more stories from 1972-1973 at the IAS. Stan was impressed by the

following remark by Kaysen in response to a reporter’s question as to how he could

expect to run an institution when significant faculty members were against him.

Kaysen’s reply: “They can be replaced.”

Stan loved that remark as exemplifying the managerial mind. Not suitable for the IAS

or a university, of course. A School of Social Sciences was installed at the IAS; but

Kaysen was gone by 1976, and, since then, the directors have been genuine scholars:

a historian, one straight physicist, two mathematical physicists, and one straight

mathematician. So far, no social scientist. In fact, the social science operation is

relatively small: 20 visiting members, as opposed to 50 or 60 in mathematics. As far

as I can see (mainly by following the IAS Newsletter), the IAS is still much as I knew it

in 1972-1973.

The faculty and visiting members of the IAS lead privileged lives. Stan’s daughter,

Susan, was much impressed by this. She always referred to the place as The

Institsnoot for Advantaged Studies.

Here is an episode that sticks in my mind. One day, Stan said to me, “You have often

said that you are curious as to what schizophrenics are like. Well, now you have the

opportunity to meet one. There is a topologist, John Nash, who hangs out in

Firestone Library; they have given him an office there. A genuine paranoid

schizophrenic. Let’s go see him.”

Me: “No, No.”

Stan: “He won’t hurt you. He is harmless.”

Me: “No, no, no.”

I was afraid that I would be contaminated. (The schizophrenic is inhabited by a

demon. Watch out!)

When Sylvia Nasar published her brilliant book (A Beautiful Mind) in 1998, I

immediately knew who she was talking about.

By 1974 Gödel’s health was deteriorating (enlarged prostate, catheterization, in and

out of hospitals; see Dawson’s biography of Gödel), but Stan must still have seen him

quite a lot. Siobhan Roberts, in her biography of Conway, “Genius at Play”, p. 212,

mentions that Gödel made a list of the topics he discussed with Stan in 1974: Nixon,

McGovern, hippies protesting the middle class, drug addicts, Vietnam, riots and the

decay of the U.S., Cohen and Dedekind, Coxeter and modern geometry, Nash and

games, Chomsky and the “linguistic aspect of math ed”. Very impressive.

Best,

Bill