# Celebratio Mathematica

## Julia Robinson

### The autobiography of Julia Robinson

#### Introduction

It was my sis­ter Ju­lia Robin­son who first sug­ges­ted to me that I wrote the lives of math­em­aticians. She thought that stu­dents would be in­ter­ested in know­ing something about the people whose names are at­tached to the­or­ems and con­cepts in text­books. She her­self, in the nor­mal course of events, would nev­er have con­sidered re­count­ing the story of her own life. As far as she was con­cerned, what she had done math­em­at­ic­ally was all that was sig­ni­fic­ant. However, with her ac­cept­ance in 1982 of a pub­lic role as pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety, she found this po­s­i­tion in­creas­ingly un­ten­able. She also came un­der pres­sure from the so­ci­ety and vari­ous academies for of­fi­cial bio­graph­ic­al ma­ter­i­al. Fi­nally one day she said, “Con­stance, you write something!”

That was late in the spring of 1985 when we were bi­cyc­ling at Pebble Beach. The pre­ced­ing Au­gust, dur­ing the sum­mer meet­ing of the AMS at Eu­gene, she had learned that she had leuk­emia. After lengthy treat­ment by chemo­ther­apy, she had fi­nally won a re­mis­sion from the dis­ease. At Pebble Beach she said that she felt as good as she ever had.

I could nev­er write about Ju­lia without writ­ing more in­tim­ately then she or I would wish, and it took me a while to come up with the solu­tion of writ­ing her “auto­bi­o­graphy.” What I wrote would then be en­tirely what she would want to have writ­ten about her own life. I would be writ­ing in her spir­it, not my own. She was amused by the idea and agree­able, al­though not com­pletely re­con­ciled. Later she happened upon something by the writer Kay Boyle to the ef­fect that the only ex­cuse for writ­ing an auto­bi­o­graphy is to give cred­it where cred­it has not been giv­en. That seemed to her a reas­on­able jus­ti­fic­a­tion, for there were people to whom she very much wanted to give cred­it.

Just a few weeks after we were bi­cyc­ling at Pebble Beach, she learned that her hard-won re­mis­sion had ended. When I star­ted to write, she was back in the hos­pit­al. Al­though she was hope­ful of a second re­mis­sion, she was also real­ist­ic about her chances. Every few days I read aloud to her what I had writ­ten. She listened at­tent­ively and amended or de­leted as ap­pro­pri­ate, some­times just a word. She heard and ap­proved all that which ap­pears be­low — al­though she ob­jec­ted that my ac­count of her life was much too long. Her own life was not. She died on Ju­ly 30, 1985, at the age of sixty-five.

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I was born in St. Louis, Mis­souri, on Decem­ber 8, 1919, the second of two daugh­ters born to Ral­ph Bowers Bow­man and Helen Hall Bow­man. Neither of my par­ents had gone to col­lege, but both had had good sec­ond­ary edu­ca­tions and my moth­er had gone to busi­ness col­lege after gradu­ation from high school. I learned re­cently from her com­mence­ment pro­gram that in high school she had elec­ted to fol­low the sci­entif­ic course rather than the more pop­u­lar lib­er­al arts course.

My moth­er died when I was two, and my fath­er sent my sis­ter, Con­stance, and me with our nurse to Ari­zona, where our grand­moth­er wintered for her health. We lived 12 miles from Phoenix in the middle of the desert, very close to Camel­back Moun­tain. Ours was a tiny com­munity of only three or four fam­il­ies liv­ing un­der quite prim­it­ive con­di­tions.

After my moth­er’s death my fath­er, who was the own­er of a ma­chine tool and equip­ment com­pany, lost in­terest in his busi­ness. He had saved what was an enorm­ous sum in those days; and he was cer­tain that, con­ser­vat­ively in­ves­ted, it would provide an in­come suf­fi­cient to sup­port his fam­ily. When he re­mar­ried, he closed his of­fice and joined us in Ari­zona. My new moth­er had been Edenia Kridel­baugh be­fore her mar­riage. Sub­sequently I shall refer to her as my moth­er, for I al­ways thought of her that way.

We con­tin­ued to live in Ari­zona for sev­er­al years. One of my earli­est memor­ies is of ar­ran­ging pebbles in the shad­ow of a gi­ant saguaro, squint­ing be­cause the sun was so bright. I thought that I have al­ways had a ba­sic lik­ing for the nat­ur­al num­bers. To me they are the one real thing. We can con­ceive of a chem­istry which is dif­fer­ent from ours, or a bio­logy, but we can­not con­ceive of a dif­fer­ent math­em­at­ics of num­bers. What is proved about num­bers will be a fact in any uni­verse.

I was slow to talk and pro­nounced the words so oddly that no one ex­cept Con­stance could un­der­stand me. Since people would ask me a ques­tion and look at Con­stance for the an­swer, she got in­to the habit of speak­ing for me, and she is now. My moth­er, who had taught kinder­garten and first grade be­fore her mar­riage, said that I was the stub­born­nest child she had ever known. I would say that my stub­born­ness has been to a great ex­tent re­spons­ible for whatever suc­cess I have had in math­em­at­ics. But then it is a com­mon trait among math­em­aticians.

Our fam­ily al­ways left Ari­zona dur­ing the sum­mer. Sev­er­al times we went to San Diego; and in 1925, when I was five and Con­stance sev­en, my moth­er, who had been teach­ing Con­stance at home, in­sisted that my fath­er settle some­place where we could go to school. That fall we moved to Point Loma on San Diego Bay.

Ex­cept for the fort and the light­house, which are still there, Point Loma was at the time quite dif­fer­ent from the ex­pens­ive, over­built res­id­en­tial area which it is today. There were about fifty fam­il­ies scattered over the hill, not count­ing the mil­it­ary fam­il­ies at Fort Ro­secrans or the colony of Por­tuguese fish­er­man. Like the desert, it was open to ex­plor­a­tion and fantasy.

The Cab­rillo Ele­ment­ary School which we at­ten­ded was very small with sev­er­al grades com­bined in each classroom. Dur­ing our first few years both Con­stance and I were skipped so that later we were al­ways among the young­est in our classes.

The most ex­cit­ing event of our first years on Point Loma was the birth of our little sis­ter, Bil­lie, on East­er Sunday at 1928. It was fol­lowed by an event which was to have a per­man­ent ef­fect upon my life and ca­reer.

Less than a year after Bil­lie’s birth, when I was nine years old, I came down with scar­let fever. To pre­vent the spread of the dis­ease, es­pe­cially to the new baby, my fath­er took over my care. He washed all my dishes and, whenev­er he entered my room, put on an old dust­er which he had worn when we had an open tour­ing car. The en­tire fam­ily was isol­ated and a con­spicu­ous sign to that ef­fect pos­ted on the front door. When, after a month, the isol­a­tion was lif­ted, the fam­ily cel­eb­rated by go­ing to see “The Ghost Speaks.” I be­lieve it was our first “talk­ie.”

The scar­let fever was fol­lowed by rheum­at­ic fever, which today would be treated ef­fect­ively with peni­cil­lin. My fam­ily moved from Point Loma so that I would not find my­self in a class be­hind my old class­mates when I went back to school, but I did not re­cov­er as soon as ex­pec­ted. Ul­ti­mately I had to spend a year in bed at the home of a prac­tic­al nurse. Dur­ing that year there was noth­ing in the world which I wanted so much as a bi­cycle. My fath­er as­sured me that when I got well I would get one but, child­like, I in­ter­preted this as mean­ing that I was not go­ing to get well.

I have since read that a sol­it­ary child­hood or, what amounts to the same thing, a peri­od of isol­a­tion res­ult­ing from ill­ness is fre­quently noted in the early lives of sci­ent­ists. I am not sure what the sig­ni­fic­ance of this find­ing is. Ob­vi­ously I had to amuse my­self for long peri­ods of time, but I didn’t do so with math­em­at­ics. I am in­clined to think that what I learned dur­ing that year in bed was pa­tience.

By the time I was well enough to go back to school, I had missed more than two years. My par­ents ar­ranged to have me tutored by a re­tired ele­ment­ary school teach­er. In one year, work­ing three morn­ings a week, she and I went through the state syl­lab­uses for the fifth, sixth, sev­enth, and eighth grades. It makes me won­der how much time must be wasted in classrooms. One day she told me that you could nev­er carry the square root of two to a point where the decim­al be­gin to re­peat. She knew that this fact had been proved, al­though she did not know how. I didn’t see how any­one could prove such a thing, and I went home and util­ized my newly ac­quired skills at ex­tract­ing square roots to check it but fi­nally, late in the af­ter­noon, gave up.

In the fall of 1932, a few months be­fore the elec­tion of Frank­lin Roosevelt, I entered the ninth grade at Theodore Roosevelt Ju­ni­or High School. For me it was an al­most Kafka-like ex­per­i­ence. I was a be­gin­ner in the game which every­one else in my class have been play­ing for two years. I made many stu­pid and em­bar­rass­ing mis­takes and ate lunch in a corner as quickly as I could so that no one would no­tice that I was alone. Fi­nally a girl named Vir­gin­ia Bell in­vited me to eat with her and her friends. She be­came my best and only friend as long as I re­mained in San Diego. A few years ago, when I re­turned for a col­loqui­um lec­ture there, I vis­ited her and found that al­though much had happened to us both in the in­ter­im we were still just as con­geni­al as we had been dur­ing our school days.

At Roosevelt I was in­tro­duced to al­gebra by a wo­man math­em­at­ics teach­er. Be­fore gradu­ation she made a vali­ant ef­fort to ex­plain to the class that some­times the best stu­dents in math could not get math hon­ors be­cause they had not re­ceived grades at their pre­vi­ous school.

The math­em­at­ics course at San Diego High School was stand­ard for that time: plane geo­metry in the tenth grade, ad­vanced al­gebra in the el­ev­enth, and tri­go­no­metry and sol­id geo­metry in the twelfth. There were two wo­men math­em­at­ics teach­ers, and I took classes from both of them. After plane geo­metry (which ful­filled the Uni­versity of Cali­for­nia’s en­trance re­quire­ment), I was the only girl still tak­ing math­em­at­ics. I was also the only girl in phys­ics. I was very shy so it may sound strange for me to say that en­ter­ing a room full of boys did not dis­con­cert me. Un­like many shy people I have nev­er giv­en much thought to what oth­er people think about me. I be­lieve this at­ti­tude is a leg­acy from my par­ents. My fath­er con­veyed it by ex­ample, but my moth­er fre­quently ar­tic­u­lated it to us. Nat­ur­ally I was in­ter­ested in some of the boys in my math classes, but they didn’t pay any at­ten­tion to me ex­cept when they had a ques­tion about the home­work. None of them ever seem to be bothered by the fact that a girl was get­ting the best grades.

My high school math­em­at­ics teach­ers were all well qual­i­fied to teach the sub­ject at that level — un­like the high school teach­er my neph­ew later had who al­ways re­ferred to “the com­mu­nic­at­ive laws of arith­met­ic.” There were, however, no en­rich­ment pro­grams in the high schools in the 1930s, no math days at the loc­al col­lege, no well pub­li­cized com­pet­i­tions like the Put­nam. None of my teach­ers en­cour­aged me to do more ad­vanced work. Of course I did try a few of the usu­al things like tri­sect­ing the angle. Once — and this is just about the only piece of per­son­al dir­ec­tion that I re­call — one of my teach­ers, it may have been the head of the de­part­ment, who was my coun­selor, ad­vised me that now that I had learned to solve math prob­lems I should learn to be neat.

We had all been giv­en an in­tel­li­gence test — I think it was the Ot­is — while we were still in ju­ni­or high school. Con­stance had done very well on it but I, be­ing a slower read­er and un­ac­cus­tomed to tak­ing tests, had done poorly. She found out later, when she was her­self a teach­er at the high school, that my I.Q. was re­cor­ded as 98, two points be­low av­er­age. The res­ult was that even after we were in col­lege, Con­stance, who took her classes lightly while de­vot­ing her­self to the school pa­per, was be­ing called in­to the of­fice to find out why she wasn’t do­ing bet­ter while I was be­ing called in to find out why I was able to per­form above abil­ity.

My friend Vir­gin­ia Bell was an art ma­jor — she later be­came an art teach­er and su­per­visor in the San Diego City Schools — and, en­cour­aged by her and by the fact that one semester of art or mu­sic was a re­quire­ment, I took an art course in which I learned something about per­spect­ive and among oth­er things drew an im­press­ively real­ist­ic base­ball. I was a great base­ball fan, keep­ing box scores at games and spend­ing my al­low­ance on The Sport­ing News. In spite of my com­plete lack of mu­sic­al abil­ity or ap­pre­ci­ation, I had a crush on the Met­ro­pol­it­an Op­era’s bari­tone, Lawrence Tib­bett, who starred in sev­er­al movies at that time. When he gave a con­cert in San Diego, my moth­er got tick­ets for us; and my fath­er, an in­vet­er­ate pho­to­graph­er, took a pic­ture for me of the bill­board ad­vert­ising the con­cert. I learned from my fath­er how to shoot both a rifle and a pis­tol and once wrote a pa­per on bar­rel rifling for phys­ics. I men­tioned these things only to show that I was not ab­sorbed en­tirely in math­em­at­ics.

In ret­ro­spect, I see my high school years as very re­laxed com­pared to those of young people today. There was no pres­sure to get in­to a “good” col­lege, and my par­ents were seem­ingly un­con­cerned by the fact that on oc­ca­sion I was in an Eng­lish class which was not col­lege pre­par­at­ory. They were con­cerned, though, that I had only one friend and didn’t seem to know how to make any oth­ers.

Of course, since we were still in the middle of the De­pres­sion, I was al­ways con­scious of eco­nom­ic pres­sures. My fath­ers sav­ings were be­ing eroded more rap­idly than any of us dreamed. He listened every noon to the stock mar­ket re­port, and his mood for the next 24 hours de­pended on wheth­er the mar­ket had gone up or down. We nev­er went without any­thing es­sen­tial, but we had no lux­ur­ies such as trips dur­ing sum­mer va­ca­tions. I re­mem­ber that our next-door neigh­bor, a civil en­gin­eer, lost his job and began to make jig­saw puzzles, which along with Mono­poly had be­come a na­tion­al fad.

When I gradu­ated from high school, I re­ceived awards in math­em­at­ics and the oth­er sci­ences I had taken as well as the Bausch–Lomb medal for all-around ex­cel­lence in sci­ence. My se­lec­tion for this last was not ap­proved by some of the sci­ence teach­ers be­cause I had nev­er taken chem­istry, the sub­ject which to this day I know noth­ing about. After the award as­sembly my moth­er ex­pressed some con­cern about what the fu­ture could hold for such a girl, but my fath­er told her not to worry — I would marry a pro­fess­or. My gradu­ation present was a beau­ti­ful and ex­pens­ive slide rule, which I christened “Slippy.”

It had al­ways been taken for gran­ted that Con­stance and I would go to col­lege. That meant the loc­al state col­lege (now San Diego State Uni­versity). State, as it was called, had been un­til quite re­cently a teach­ers’ col­lege and, be­fore that, a nor­mal school. Very few of my high school class­mates went away to col­lege after gradu­ation, but a num­ber at­ten­ded State for two years and then trans­ferred to UC or UCLA. Those who re­mained took some edu­ca­tion courses and got one of the sev­er­al teach­ing cre­den­tials which were offered. My moth­er had al­ways in­cul­cated in us the idea that a girl should equip her­self to earn a liv­ing. She placed an es­pe­cially high value on a teach­ing cre­den­tial be­cause it qual­i­fied the hold­er to do a very spe­cif­ic thing for which she would be paid.

At State there were only a few PhD’s on the fac­ulty. Neither of the two math­em­at­ics pro­fess­ors had a doc­tor­ate. There were no wo­men teach­ing math­em­at­ics; but I re­mem­ber wo­men, with doc­tor­ates, teach­ing bio­logy and psy­cho­logy.

Nat­ur­ally I elec­ted to ma­jor in math­em­at­ics. The lower di­vi­sion ma­jors fol­lowed the usu­al se­quence of courses in ana­lyt­ic geo­metry and cal­cu­lus. There were 35 or 40 math stu­dents, most of them plan­ning to be en­gin­eers, so there was some com­pet­i­tion. There were also girls who were go­ing to be teach­ers. At that time I had no idea that such a thing as a math­em­atician (as op­posed to a math teach­er) ex­is­ted.

By the be­gin­ning of my sopho­more year all the sav­ings which my fath­er had so con­fid­ently ex­pec­ted to sup­port his re­tire­ment had been wiped out. He took his own life that Septem­ber, leav­ing be­hind only an in­sur­ance policy on which he had bor­rowed to the lim­it and an un­im­proved lot on Point Loma. We moved to a mod­est apart­ment and re­ceived some reg­u­lar fin­an­cial help from our aunt, Lu­cille Hall, an ele­ment­ary school teach­er in St. Louis. In spite of our straightened cir­cum­stances, Con­stance and I con­tin­ued in col­lege. Tu­ition at that time was \$12 a semester. In the up­per di­vi­sion at State the num­ber of math stu­dents dropped pre­cip­it­ously, those who were go­ing to be en­gin­eers hav­ing trans­ferred to oth­er col­leges. Two, and only two, up­per di­vi­sion math­em­at­ics courses were offered each semester. All the math ma­jors had to take them. In a way this was a good sys­tem be­cause we fo­cused on those two in a way we wouldn’t have if there had been a lar­ger num­ber of courses offered. In my ju­ni­or year I took ad­vanced cal­cu­lus, which com­pleted the cal­cu­lus cycle al­though it wasn’t so ad­vanced as Math 104 (real ana­lys­is) at Berke­ley. I also took a course in al­gebra that was the equi­val­ent of Math 8, a lower di­vi­sion course at Berke­ley. There was something called mod­ern geo­metry, which was really very old-fash­ioned (noth­ing nonEuc­lidean). The his­tory of math­em­at­ics was also offered. It was prob­ably in that class that I read E. T. Bell’s Men of Math­em­at­ics, which had just been pub­lished. Math­em­at­ics was by far my fa­vor­ite sub­ject, but I hardly knew what the sub­ject was. The only idea of real math­em­at­ics which I had came from Men of Math­em­at­ics. In it I got my first glimpse of a math­em­atician per se. I can­not over­em­phas­ize the im­port­ance of such books about math­em­at­ics in the in­tel­lec­tu­al life of a stu­dent like my­self com­pletely out of con­tact with re­search math­em­aticians. I learned many in­ter­est­ing things from Bell’s book. I was es­pe­cially ex­cited by some of the the­or­ems of num­ber the­ory — he was a num­ber the­or­ist him­self — and I used to re­count these to Con­stance at night after we went to bed. She soon found that if she wasn’t ready to go to sleep she could keep me awake by ask­ing ques­tions about math­em­at­ics. Neither Con­stance nor I was in­ter­ested in teach­ing ele­ment­ary school or qual­i­fied to get one of the spe­cial cre­den­tials offered in art, mu­sic, or phys­ic­al edu­ca­tion. We settled re­luct­antly on the very lim­ited ju­ni­or high school cre­den­tial. I took some of the re­quired edu­ca­tion courses and found them bor­ing. Also, when Con­stance gradu­ated, I learned that a ju­ni­or high school cre­den­tial did not guar­an­tee a teach­ing job. It was not highly re­garded by school su­per­in­tend­ents, who could get teach­ers with the more com­pre­hens­ive gen­er­al sec­ond­ary cre­den­tial for the same salary. To ob­tain such a cre­den­tial, however, you had to take a post-gradu­ation year on one of the cam­puses of the Uni­versity of Cali­for­nia. When, six months after gradu­ation, Con­stance still had no job, my moth­er, with great cour­age and faith in the fu­ture, dug in­to the fam­ily’s small sav­ings and sent her to Berke­ley. Hap­pily the gamble paid off. Even be­fore Con­stance had fin­ished the course­work for the new cre­den­tial, she was hired as an Eng­lish/Journ­al­ism teach­er and fac­ulty ad­viser of the school pa­per at San Diego High School. I now con­ceived an ab­so­lute pas­sion to go away to school, too — wheth­er to UC or UCLA, I was not par­tic­u­lar — any place where there was a real de­part­ment of math­em­at­ics. A young PhD in as­tro­nomy from Berke­ley, Clif­ford E. Smith, had joined the fac­ulty at State; and al­though I don’t re­mem­ber his en­cour­aging me to go away, he did give me a glimpse of something bey­ond Mr. Liv­ing­ston and Mr. Gleason. I am sure he found the stu­dents at State quite a change from the polit­ic­ally con­scious stu­dents at Berke­ley. One morn­ing he an­nounced that we were ex­cused from turn­ing in our home­work be­cause he knew that we had been up late the night be­fore listen­ing to the ra­dio. We looked be­wilderedly at one an­oth­er, none of us aware that Cham­ber­lain and Hitler had just come to an agree­ment in Mu­nich which would still, al­most 50 years later, sym­bol­ize ap­pease­ment and dis­hon­or. When, after Con­stance had her job, I told the math pro­fess­ors at State that I was go­ing to go some­where else the fol­low­ing year, Mr. Liv­ing­ston, the head of the de­part­ment, tried to dis­suade me. The col­lege was plan­ning to in­aug­ur­ate an hon­ors pro­gram, and I was ob­vi­ously the only math­em­at­ics stu­dent whom he could pro­pose. Mr. Gleason, however, said that I should go and that I should go to Berke­ley rather than UCLA. I ar­rived at Berke­ley most for­tu­it­ously as far as math­em­at­ics was con­cerned, al­though of course I did not real­ize it then. At the be­gin­ning of the 1930s the oth­er sci­ence de­part­ments had per­suaded Pres­id­ent Sproul to bring in someone of re­cog­nized achieve­ment to head the math­em­at­ics de­part­ment and up­grade it. The math­em­atician who had been chosen was Grif­fith C. Evans. He had al­most im­me­di­ately hired Al­fred Foster, Charles Mor­rey, and Hans Lewy. The year be­fore I ar­rived he had brought Jerzy Ney­man from Eng­land. My moth­er ex­pec­ted me to get a gen­er­al sec­ond­ary cre­den­tial, just as Con­stance had; but the ad­viser for math ma­jors plan­ning to go in­to teach­ing dis­cour­aged me. I nev­er un­der­stood why, but Con­stance tells me that al­though there were a num­ber of wo­men teach­ing math­em­at­ics in ju­ni­or and seni­or high schools, as I have in­dic­ated, there was a def­in­ite drive (af­firm­at­ive ac­tion?) to bring more men in­to sec­ond­ary edu­ca­tion and it was thought this could be done most eas­ily in the sci­ences. I took five courses in math­em­at­ics that first year at Berke­ley, in­clud­ing a course in num­ber the­ory taught by Raphael M. Robin­son. The fact that Raphael was teach­ing num­ber the­ory was a stroke of luck — for us. Evans had hired Dick Lehmer as the de­part­ment’s num­ber the­ory spe­cial­ist, but Dick had had to ful­fill a year’s com­mit­ment to Le­high be­fore he could come to Berke­ley and Raphael had been as­signed to teach num­ber the­ory in his place. In the second semester there were only four stu­dents — I was again the only girl — and Raphael began to ask me to go on walks with him. Al­though I had lost some cred­its by trans­fer­ring, I was still able to get my A.B. in a year. I ap­plied for jobs with vari­ous com­pan­ies in San Fran­cisco, but they were not in­ter­ested in my math­em­at­ic­al train­ing — they asked if I could type. (A few years later, after we were in the war, they sud­denly did be­come in­ter­ested in me.) I ap­plied to Evans for a teach­ing as­sist­ant­ship, but he was try­ing to bring stu­dents from oth­er uni­versit­ies to Berke­ley. He told me that the only pos­sible po­s­i­tion for me was at Ore­gon State. Since it was an un­der­gradu­ate de­part­ment and I would not be able to go on with my stud­ies, he ad­vised me not to take it. Ney­man, hear­ing of my plight, quickly ar­ranged for me to get some of the money which had been al­lot­ted for Betty Scott, his half-time lab as­sist­ant. As I re­mem­ber, she wanted a little more time for her stud­ies any­way — she was an as­tro­nomy ma­jor then, now of course a long-time pro­fess­or of stat­ist­ics at Berke­ley — so she took two-thirds of the half and I took the oth­er one-third. I re­mem­ber that Ney­man asked me how much I needed to live on. I said \$32 a month and he got me \$35. I was very happy, really bliss­fully happy, at Berke­ley. In San Diego there had been no one at all like me. If, as Bruno Bettel­heim has said, every­one has his or her own fairy story, mine is the story of the ugly duck­ling. Sud­denly, at Berke­ley, I found that I was really a swan. There were lots of people, stu­dents as well as fac­ulty mem­bers, just as ex­cited as I was about math­em­at­ics. I was elec­ted to the hon­or­ary math­em­at­ics fra­tern­ity, and there was quite a bit of de­part­ment­al so­cial activ­ity in which I was in­cluded. Then there was Raphael. Dur­ing our in­creas­ingly fre­quent walks, he told me about vari­ous in­ter­est­ing things in math­em­at­ics. He is, in my opin­ion, a very good teach­er. He thor­oughly un­der­stands a large part of math­em­at­ics, both clas­sic­al and mod­ern, and has it so well or­gan­ized in his mind that he is able to ex­plain it with ex­cep­tion­al clar­ity. On one of our early walks, he in­tro­duced me to Gödel’s res­ults. I was very im­pressed and ex­cited by the fact that things about num­bers could be proved by sym­bol­ic lo­gic. Without ques­tion what had the greatest math­em­at­ic­al im­pact on me at Berke­ley was the one-to-one teach­ing that I re­ceived from Raphael. Al­though I had done well in math­em­at­ics, my moth­er was con­cerned about my get­ting a real job and earn­ing some real money. Earli­er, I had taken a civil ser­vice ex­am­in­a­tion for Ju­ni­or Stat­ist­i­cian; now I was offered a job as a night clerk in Wash­ing­ton DC at \$1200 a year. My moth­er thought that I should ex­cept it, but Raphael had oth­er ideas. At his in­sist­ence I came back to Berke­ley for a second gradu­ate year and, this time, re­ceived a teach­ing as­sist­ant­ship. I wanted to teach cal­cu­lus, but Ney­man asked Evans for me and so I taught stat­ist­ics (which I found very messy, not beau­ti­ful and clear and true like num­ber the­ory). At the end of the semester, a few weeks after the Ja­pan­ese at­tacked Pearl Har­bor, Raphael and I were mar­ried.

Mina Rees has ob­served that it is hard to name a wo­man math­em­atician who isn’t mar­ried to a man math­em­atician. I think what she says was very true in her gen­er­a­tion and also in mine, al­though no longer true. I doubt that I would have be­come a math­em­atician if it hadn’t been for Raphael. He taught me and has con­tin­ued to teach me, has en­cour­aged me, and has sup­por­ted me in many ways, in­clud­ing fin­an­cially. Through his po­s­i­tion as a pro­fess­or at Berke­ley, he has provided me with ac­cess to pro­fes­sion­al fa­cil­it­ies and so­ci­ety. Al­though he is a much bet­ter and much bright­er math­em­atician than I, his re­search is not so gen­er­ally ap­pre­ci­ated, since he has pur­sued his own in­terests rather than cur­rent fash­ions or flashy prob­lems. He keeps up with mod­ern de­vel­op­ments even now in his 70s, work­ing through the re­cent proof of the Bieberbach con­jec­ture, for ex­ample; but he has al­ways been a rather old fash­ion math­em­atician — as he says, he has liked to work on “neg­lected prob­lems.” I feel that his work is very in­ter­est­ing and should be much bet­ter known, and I am plan­ning to take it as the sub­ject of my Pres­id­en­tial Ad­dress at the AMS meet­ing in New Or­leans this winter.

When we were mar­ried, there was a rule at Berke­ley that mem­bers of the same fam­ily could not teach in the same de­part­ment. Since I already had a one-year con­tract as a teach­ing as­sist­ant, this rule did not im­me­di­ately ap­ply to me. I didn’t really like teach­ing stat­ist­ics, es­pe­cially since Ney­man, con­vinced that Amer­ic­an stu­dents were woe­fully ig­nor­ant of stat­ist­ic­al the­ory, had con­ceived the idea of us­ing both lec­ture and lab for lec­tures and mak­ing the stu­dents do the lab work on their own time. I wrote and asked Evans if I could teach math­em­at­ics in­stead. He did not re­spond, but Ney­man heard about my let­ter and be­came very angry. He stop us­ing me as a T.A. and left me in a kind of limbo for the rest of the aca­dem­ic year, do­ing ab­so­lutely noth­ing for the money I was reg­u­larly be­ing paid. He did not hold a grudge, however. Dur­ing the war he em­ployed me in the stat lab, and my first pa­per came out of the stat lab work. Ac­tu­ally I did not want to pub­lish it be­cause someone else had already proved the same thing, al­though in a dif­fer­ent way; but Ney­man in­sisted. (He al­ways en­cour­aged stu­dents to pub­lish be­fore they got their de­grees.) For many years I avoided him be­cause I found it al­most im­possible to say no to him, but I un­der­stand that when I was pro­posed for mem­ber­ship in the Na­tion­al Academy of Sci­ences he was one of my most en­thu­si­ast­ic and en­er­get­ic sup­port­ers.

Be­cause of the nepot­ism rule I could not teach in the math­em­at­ics de­part­ment the next year, but this fact did not par­tic­u­larly con­cern me. Now that I was mar­ried, I ex­pec­ted and very much wanted to have a fam­ily. Raphael and I bought a house and, al­though I con­tin­ued to audit math courses, I was really more in­ter­ested in shop­ping for fur­niture. When I fi­nally learned that I was preg­nant, I was de­lighted — and very dis­ap­poin­ted when a few months later I lost the baby. Shortly af­ter­wards, vis­it­ing in San Diego, I con­trac­ted vir­al pneu­mo­nia. My moth­er called a doc­tor. His first ques­tion after he ex­amined me was, “how long have you had heart trouble?” It was true that I had al­ways puffed, es­pe­cially climb­ing the stairs to the math classes on the third floor of Wheel­er Hall (only pro­fess­ors were per­mit­ted to use the el­ev­at­or in those days); but no one, in­clud­ing my ob­stet­ri­cian, had ever shown more than a curs­ory in­terest in the con­di­tion of my heart. I be­lieve the doc­tor in San Diego had had rheum­at­ic fever him­self and was thus more fa­mil­i­ar with the res­ult­ing buildup of scar tis­sue in the mitral valve. He ad­vised me that un­der no cir­cum­stances should I be­come preg­nant again and told my moth­er privately that I would prob­ably be dead by forty, since by that time my heart would have broken down com­pletely. What he could not know was that when I was forty-one a sur­geon would be able to go in­to the mitral valve and re­move the scar tis­sue!

For a long time I was deeply de­pressed by the fact that we could not have chil­dren. Fi­nally Raphael re­minded me that there was still math­em­at­ics. He had writ­ten a pa­per about sim­pli­fy­ing defin­i­tions of prim­it­ive re­curs­ive func­tions, and he sug­ges­ted that I do the same thing for gen­er­al re­curs­ive func­tions. I worked very hard on the prob­lem dur­ing the year 1946–47, when we were at Prin­ceton, and pub­lished my res­ults the fol­low­ing year. I can­not hon­estly say that the math­em­at­ic­al prob­lem elim­in­ated the emo­tion­al prob­lem, but it did help to take my mind off it some of the time. When we came back to Berke­ley, I began to work to­ward a PhD with Al­fred Tarski.

Tarski, a Pole, had been caught in the United States, as a vis­it­ing lec­turer at Har­vard, when Ger­many in­vaded Po­land in 1939. Un­be­liev­able as it now seems, a per­man­ent po­s­i­tion had not been found for him between 1939 and 1942, when Evans brought him to Berke­ley. Like Ney­man, Tarski was a tre­mend­ous ad­di­tion to our de­part­ment. In my opin­ion, and that of many oth­er people, he ranks with Gödel as a lo­gi­cian.

Pre­vi­ously, in the sum­mer of 1943, I had audited a sem­in­ar giv­en by Tarski on Gödel’s res­ults. In the sum­mer he had read us a let­ter from Mostowski, who had been his only Pol­ish PhD. Mostowski wanted to know wheth­er it was pos­sible to define ad­di­tion in terms of suc­cessor and mul­ti­plic­a­tion. I played around with the prob­lem and in a couple of days came up with a very com­plic­ated defin­i­tion. It is still rather sur­pris­ing to me that I was able to do this, con­sid­er­ing the low prob­ab­il­ity of a math­em­atician’s go­ing dir­ectly to a defin­i­tion. Tarski was im­mensely pleased and made some re­mark to the fact that my work was so ori­gin­al that it would do for a thes­is. In writ­ing up my res­ults, however, I kept gen­er­al­iz­ing and sim­pli­fy­ing it un­til it be­came es­sen­tially trivi­al. I knew without Tarski’s telling me that it wasn’t enough for a thes­is. Later he sug­ges­ted a prob­lem about re­la­tion al­gebra. I nev­er really got any­where with it or maybe just didn’t work very hard, since I wasn’t par­tic­u­larly in­ter­ested in it.

Tarski had great re­spect for Raphael and of­ten talked with him about prob­lems. One day at lunch at the Men’s Fac­ulty Club (in those days wo­men were not al­lowed in the main din­ing room at lunch), he men­tioned the ques­tion wheth­er one could give a first or­der defin­i­tion of the in­tegers in the field of ra­tion­als. This was not meant as a sug­ges­tion for a thes­is top­ic for me; but when Raphael came home, he told me about it. I found it in­ter­est­ing, and I just began to work on it without say­ing any­thing to Tarski. I think that a great deal of the dif­fi­culty that stu­dents have in pro­du­cing a thes­is goes back to the fact that they are not really in­ter­ested in the prob­lem that they are giv­en, just as I was not in­ter­ested in Tarski’s prob­lem about re­la­tion al­gebra. I con­sider my­self very lucky to have come so early upon a field and a prob­lem that ex­cited me.

In my thes­is, “Defin­ab­il­ity and de­cision prob­lems in arith­met­ic” [1], I showed that the no­tion of an in­teger can be defined arith­met­ic­ally in terms of the no­tion of a ra­tion­al num­ber and the op­er­a­tions of ad­di­tion and mul­ti­plic­a­tion on ra­tion­als. Thus the arith­met­ic of ra­tion­als is ad­equate for the for­mu­la­tion of all prob­lems of ele­ment­ary num­ber the­ory. Since the solu­tion of the de­cision prob­lem was already known to be neg­at­ive for ele­ment­ary num­ber the­ory, it fol­lowed from my res­ults that the solu­tion of the de­cision prob­lem is neg­at­ive for the the­ory of ra­tion­als. When I took my work to Tarski, he was de­lighted. It was then that he told me that he had been con­cerned that the oth­er thing had be­come so simple, al­though it is still in­cluded in my thes­is.

Tarski had al­ways re­cog­nized that the de­cision prob­lem for the the­ory of ar­bit­rary fields would be un­de­cid­able if the in­tegers could be defined in the field of ra­tion­als. That was why he had been in­ter­ested in the prob­lem in the first place. So he ad­ded a sec­tion to my thes­is point­ing out that un­de­cid­ab­il­ity for ar­bit­rary fields fol­lows from my work. I al­ways gave him the cred­it for that res­ult, since he was the one who re­cog­nized it; but he al­ways gave me the cred­it, since he had not been able to es­tab­lish it him­self. Later some­body pro­duced a sim­pler and more dir­ect proof for a dif­fer­ent field, but I don’t be­lieve that any­one has im­proved on my work on defin­ab­il­ity in the ra­tion­al field.

Tarski was a very in­spir­ing teach­er. He had a way of set­ting res­ults in­to a frame­work so that they all fit nicely to­geth­er, and he was al­ways full of prob­lems — he just bubbled over with prob­lems. There are teach­ers whose lec­tures are so well or­gan­ized that they con­vey the im­pres­sion that math­em­at­ics is ab­so­lutely fin­ished. Tarski’s lec­tures were equally well or­gan­ized; but, be­cause of the prob­lems, you knew that there were still things that even you could do which would make for pro­gress. Of­ten, of course, he had prob­lems which he didn’t give to stu­dents be­cause he thought they were too hard; and some­times he was mis­taken about what was an easy prob­lem. Bob Vaught once went to him, ter­ribly de­pressed be­cause he felt that he hadn’t been able to ac­com­plish any­thing in math­em­at­ics. He asked for an easy prob­lem that he was sure to be able to solve, and Tarski gave him this prob­lem — it’s still un­solved! For­tu­nately Bob went on with math­em­at­ics any­way.

In 1948, the same year that I got my PhD, I began to work on the tenth prob­lem on Hil­bert’s fam­ous list: to find an ef­fect­ive meth­od for de­term­in­ing if a giv­en Di­o­phant­ine equa­tion is solv­able in in­tegers. This prob­lem has oc­cu­pied the largest por­tion of my pro­fes­sion­al ca­reer. Again it was Tarski, talk­ing to Raphael, who star­ted me off. He had no­ticed that the num­bers which are not powers of two can be ex­ist­en­tially defined as the solu­tion of a Di­o­phant­ine equa­tion. One simply has to show that the num­ber con­tains an odd factor; for ex­ample, $$z$$ is not a power of 2 if and only if there ex­ist in­tegers $$x$$ and $$y$$ such that $$z=(2x+3)y$$. He wondered wheth­er, pos­sibly us­ing in­duc­tion, one could prove that the powers of 2 can­not be put in the form of a solu­tion of a Di­o­phant­ine equa­tion.

Again Raphael men­tioned the prob­lem to me when he came home. I am sure that Tarski was think­ing about the Tenth Prob­lem, but I wasn’t — in the be­gin­ning. Prob­ably if I had been, I would nev­er have tackled it. I was just think­ing about that spe­cif­ic prob­lem. It was a prob­lem that was not of par­tic­u­lar in­terest in it­self; however, it ap­pealed to me. I like to work on that type of prob­lem. Usu­ally in math­em­at­ics you have an equa­tion and you want to find a solu­tion. Here you were giv­en a solu­tion and you had to find the equa­tion. I liked that. I would have worked on the prob­lem very hard without the con­nec­tion to the Tenth Prob­lem, but soon it be­came clear to me that that was where it came from. I haven’t worked on very many prob­lems, and the ones that I have worked on have been prob­lems that I find in­ter­est­ing even when I re­cog­nize that they would not be so in­ter­est­ing to oth­er people. That is partly be­cause I’ve nev­er been held to get­ting res­ults and pub­lish­ing or per­ish­ing. As Raphael says, the prob­lem of over-pro­duc­tion of math­em­at­ics would be solved if we just changed the or to and.

I wasn’t able to show that the powers of 2 can­not be ex­pressed as the solu­tion of a Di­o­phant­ine equa­tion. In fact, I be­came dis­cour­aged right away, be­cause prov­ing something by in­duc­tion over poly­no­mi­als, as Tarski had sug­ges­ted, is very dif­fi­cult. In­stead I star­ted to work in the oth­er dir­ec­tion, try­ing to prove that powers of 2 like non­powers of 2 could be so ex­pressed. When I couldn’t do that either, I turned to re­lated prob­lems of ex­ist­en­tial defin­ab­il­ity. The rel­ev­ance of my ef­forts to Hil­bert’s prob­lem is clear from the fact that a set of nat­ur­al num­bers is ex­ist­en­tially defin­able if and only if it is the set of val­ues of a para­met­er for which a cer­tain Di­o­phant­ine equa­tion is solv­able. The main res­ult in my pa­per, “Ex­ist­en­tial defin­ab­il­ity in arith­met­ic” [3], was the proof that the re­la­tion $$x=y^2$$ is ex­ist­en­tially defin­able in terms of any re­la­tion of roughly ex­po­nen­tial growth.

Raphael had a sab­bat­ic­al com­ing up in 1949–50. Since I had had vir­tu­ally no teach­ing ex­per­i­ence, I wanted to teach at UCLA that year. As it turned out, Oliv­er Gross was there, and he was in­ter­ested in George Brown’s fic­ti­tious play prob­lem, which had been pro­posed as a means of com­put­ing a strategy for zero-sum games. The idea was that you set up two fic­ti­tious play­ers. The first play­er makes a ran­dom choice of moves, and then the second play­er does the best thing against what the first play­er has done. Then the second play­er takes the av­er­age of the two strategies — in oth­er words, weights the prob­ab­il­it­ies equally — and does the best thing. Then the first play­er weights the choice of the second play­er and so on. The ques­tion was wheth­er, if this pro­ced­ure were con­tin­ued in­def­in­itely, it would con­verge to a solu­tion of the game. A num­ber of people at Rand had tried to prove that it would. Von Neu­mann had even looked at the prob­lem. And Rand was of­fer­ing a \\$200 prize for its solu­tion. In my pa­per, “An it­er­at­ive meth­od of solv­ing a game” [2], I showed that the pro­ced­ure did in­deed con­verge; but I didn’t get the prize, be­cause I was a Rand em­ploy­ee. I was once told by Dav­id Gale that he con­sidered the the­or­em in that pa­per the most im­port­ant the­or­em in ele­ment­ary game the­ory; but I can­not judge, since I nev­er again did any­thing in game the­ory.

Even while em­ployed at Rand, I con­tin­ued to think about prob­lems of ex­ist­en­tial defin­ab­il­ity rel­ev­ant to Hil­bert’s tenth prob­lem. Since there are many clas­sic­al Di­o­phant­ine equa­tions with one para­met­er for which no ef­fect­ive meth­od of de­term­in­ing the solv­ab­il­ity for an ar­bit­rary value of the para­met­er is known, it seemed very un­likely that a de­cision pro­ced­ure could be found. But a neg­at­ive an­swer would be an an­swer, too.

In 1950, at the first post­war In­ter­na­tion­al Con­gress at Har­vard, Mar­tin Dav­is, who had just com­pleted his thes­is un­der Emil Post, presen­ted a 10-minute pa­per on his the­or­em about re­du­cing re­curs­ive enu­mer­able sets to a par­tic­u­lar form, and I presen­ted a 10-minute pa­per on my work on ex­ist­en­tial defin­ab­il­ity. That was the first time I had met Mar­tin. I re­mem­ber that he said he didn’t see how my work could help to solve Hil­bert’s prob­lem, since it was just a series of ex­amples. I said, well, I did what I could.

Dur­ing the 1950s, in an­oth­er field, I ex­per­i­enced a fail­ure which still em­bar­rasses me. (I think our fail­ures should be in­cluded along with our suc­cesses.) There was a lot of money avail­able for math­em­at­ic­al re­search at that time, and Hans Lewy got me in­to some work on hy­dro­dynam­ics that was be­ing done at Stan­ford un­der Al Bowker. It was not my field, and I shouldn’t have taken it on, but I did. Al­though I worked very hard, I was able to prove ab­so­lutely noth­ing. When the year was up, I resigned without even turn­ing in a re­port, I had noth­ing to re­port. Bowker later be­came Chan­cel­lor here at Berke­ley, and I could hardly bring my­self to look him in the face.

After I es­caped from hy­dro­dynam­ics, I read a magazine art­icle about Ad­lai Steven­son, then the gov­ernor of Illinois, which in­ter­ested me very much. I be­came even more in­ter­ested after he was nom­in­ated for pres­id­ent and prom­ised in his ac­cept­ance speech “to talk sense to the Amer­ic­an people.” (This was in the middle of the Mc­Carthy era.) Al­though I did not en­tirely aban­don math­em­at­ics, I spent a lot of time on polit­ics in the next half a dozen years. I was even county man­ager for Alan Cran­ston’s first polit­ic­al cam­paign.

And I con­tin­ued to struggle with the Tenth Prob­lem. In 1961 Mar­tin Dav­is, Hil­ary Put­nam, and I pub­lished a joint pa­per, “The un­de­cid­ab­il­ity of ex­po­nen­tial Di­o­phant­ine equa­tions” [4], which used ideas from the pa­pers Mar­tin and I had presen­ted at the In­ter­na­tion­al Con­gress along with vari­ous new res­ults. The pa­per con­tains what is some­times re­ferred to as the Robin­son hy­po­thes­is (or, as Mar­tin calls it “J.R.”) to the ef­fect that if there were some Di­o­phant­ine re­la­tion that grew faster than an ex­po­nen­tial but not too ter­ribly fast — less than some func­tion that could be ex­pressed in ex­po­nen­tials — then we would be able to define ex­po­nen­ti­ation. It would fol­low from the defin­i­tion that ex­po­nen­tial Di­o­phant­ine equa­tions would be equi­val­ent to Di­o­phant­ine equa­tions and that, there­fore, the solu­tion to Hil­bert’s tenth prob­lem would be neg­at­ive. At the time many people told Mar­tin that this ap­proach was mis­guided, to say the least. They were more po­lite to me.

By the time the joint pa­per was pub­lished, my heart had broken down, just as the doc­tor in San Diego had pre­dicted; and I had to have the open-heart sur­gery which I men­tioned earli­er. One month after the op­er­a­tion I bought my first bi­cycle. It has been fol­lowed by half a dozen in­creas­ingly bet­ter bikes and many cyc­ling trips in this coun­try and in Hol­land. Raphael some­times com­plains that while oth­er men’s wives buy fur coats and dia­mond brace­lets, his wife buys bi­cycles.

Throughout the 1960s, while pub­lish­ing a few pa­pers on oth­er things, I kept work­ing on the Tenth Prob­lem; but I was get­ting rather dis­cour­aged. For a while I ceased to be­lieve in the Robin­son hy­po­thes­is, al­though Raphael in­sisted that it was true but just too dif­fi­cult to prove. I even worked in the op­pos­ite dir­ec­tion, try­ing to show that there was a pos­it­ive solu­tion to Hil­bert’s prob­lem; but I nev­er pub­lished any of that work. It was the cus­tom in our fam­ily to have a get-to­geth­er for each fam­ily mem­ber’s birth­day; and when it came time for me to blow out the candles on my cake, I al­ways wished, year after year, that the Tenth Prob­lem would be solved — not that I would solve it, but just that it would be solved. I felt that I couldn’t bear to die without know­ing the an­swer.

Fi­nally — on Feb­ru­ary 15, 1970 — Mar­tin tele­phoned me from New York to say that John Cocke had just re­turned from Mo­scow with the re­port that a 22-year-old math­em­atician in Len­in­grad had proved that the re­la­tion $$n=F_{2m}$$, where $$F_{2m}$$ is a Fibon­acci num­ber, is Di­o­phant­ine. This was all that we needed. It fol­lowed that the solu­tion to Hil­bert’s tenth prob­lem is neg­at­ive — a gen­er­al meth­od for de­term­in­ing wheth­er a giv­en Di­o­phant­ine equa­tion has a solu­tion in in­tegers does not ex­ist.

Mar­tin did not know the name of the math­em­atician or the meth­od he had used. I was so ex­cited by the news that I wanted to call Len­in­grad right away to find out if it were really true. Raphael and oth­er people here said no, hold on — the world had gone for sev­enty years without know­ing the solu­tion to the tenth prob­lem, surely I could wait a few more weeks! I wasn’t so sure. For­tu­nately I didn’t have to wait that long. Three days later John Mc­Carthy called from Stan­ford to say that in Nov­os­ibirsk he had heard a talk by Ceitin on the proof, which was the work of a math­em­atician named Yuri Mati­jasevic. John had taken notes on Ceitin’s talk. While he was do­ing so, he had felt that he un­der­stood the proof; but by the time he got back to Stan­ford he found that he couldn’t make much sense of his notes. He offered to send them to me if I wanted to see them. Of course I wanted to, very much.

When I re­ceived the notes, I sent a copy to Mar­tin even be­fore I went over them my­self. He told me later that he was al­ways glad that I had let him go through them on his own. It was the next best thing to solv­ing the prob­lem.

It was quite im­me­di­ately clear what Mati­jasevic had done. By us­ing the Fibon­acci num­bers, a series which had been known to math­em­aticians since the be­gin­ning of the thir­teenth cen­tury, he had been able to con­struct a func­tion that met the re­quire­ments of the Robin­son hy­po­thes­is. There was noth­ing in his proof which would not be in­cluded in a course in ele­ment­ary num­ber the­ory!

Just one week after I had first heard the news from Mar­tin, I was able to write to Mati­jasevic:

“…[N]ow I know it is true, it is beau­ti­ful, it is won­der­ful.”

“If you are really 22 [he was], I am es­pe­cially pleased to think that when I first made the con­jec­ture you were a baby and I just had to wait for you to grow up!”

That year when I went to blow out the candles on my cake, I stopped in mid-breath, sud­denly real­iz­ing that the wish I had made for so many years had ac­tu­ally come true.

I have been told that some people think that I was blind not to see the solu­tion my­self when I was so close to it. On the oth­er hand, no one else saw it either. There are lots of things, just ly­ing on the beach as it were, that we don’t see un­til someone else picks one of them up. Then we all see that one.

In 1971 Raphael and I vis­ited Len­in­grad and be­came ac­quain­ted with Mati­jasevic and his wife, Nina, a phys­i­cist. At that time, in con­nec­tion with the solu­tion of Hil­bert’s prob­lem and the role played in it by the Robin­son hy­po­thes­is, Lin­nik told me that I was the second most fam­ous Robin­son in the So­viet Uni­on, the first be­ing Robin­son Cru­soe. Yuri and I have since writ­ten two pa­pers to­geth­er; and, after the 1974 De Kalb sym­posi­um on the Hil­bert prob­lems, Mar­tin, Yuri, and I col­lab­or­ated on a pa­per en­titled “Pos­it­ive as­pects of a neg­at­ive solu­tion” [5].

I have writ­ten so in­com­pletely and non­tech­nic­ally about my more than twenty years of work on the Tenth Prob­lem be­cause Mar­tin, who con­trib­uted as much as I to its ul­ti­mate solu­tion, has pub­lished sev­er­al ex­cel­lent pa­pers telling the whole story. These in­clude both a pop­u­lar ac­count in Sci­entif­ic Amer­ic­an and a tech­nic­al one in The Amer­ic­an Math­em­at­ic­al Monthly.

When any one of Hil­bert’s prob­lems is solved or even some pro­gress made to­ward a solu­tion, every­body who has had any part in the work gets a great deal of at­ten­tion. In 1975, for in­stance, I be­came the first wo­man math­em­atician to be elec­ted to the Na­tion­al Academy of Sci­ences, al­though there are oth­er wo­men math­em­aticians who in my opin­ion are more de­serving of the hon­or.

When the Uni­versity press of­fice re­ceived the news, someone there called the math­em­at­ics de­part­ment to find out just who Ju­lia Robin­son was. “Why, that’s Pro­fess­or Robin­son’s wife.” “Well,” replied the caller, “Pro­fess­or Robin­son’s wife has just been elec­ted to the Na­tion­al Academy of Sci­ences.” Up to that time I had not been an of­fi­cial mem­ber of the Uni­versity’s math­em­at­ics fac­ulty, al­though from time to time I had taught a class at the re­quest of the de­part­ment chair­man. In fair­ness to the Uni­versity, I should ex­plain that be­cause of my health, even after the heart op­er­a­tion, I would not have been able to carry a full-time teach­ing load. As soon as I was elec­ted to the Academy, however, the Uni­versity offered me a full pro­fess­or­ship with the duty of teach­ing one-fourth time — which I ac­cep­ted.

In 1982 I was nom­in­ated for the pres­id­ency of the Amer­ic­an Math­em­at­ic­al So­ci­ety. I real­ized that I had been chosen be­cause I was a wo­man and be­cause I had the seal of ap­prov­al, as it were, of the Na­tion­al Academy. After dis­cus­sion with Raphael, who thought I should de­cline and save my en­ergy for math­em­at­ics, and oth­er mem­bers of my fam­ily, who differed with him, I de­cided that as a wo­man and a math­em­atician I had no al­tern­at­ive but to ex­cept. I have al­ways tried to do everything I could to en­cour­age tal­en­ted wo­men to be­come re­search math­em­aticians. I found my ser­vice as pres­id­ent of the So­ci­ety tax­ing but very, very sat­is­fy­ing.

Oth­er hon­ors, in­clud­ing elec­tion to the Amer­ic­an Academy of Arts and Sci­ences, an hon­or­ary de­gree from Smith Col­lege, and a gen­er­ous grant from the Ma­cAr­thur Found­a­tion, have come with dis­con­cert­ing speed. Even more gen­er­al no­tice has been taken of me. Vogue and The Vil­lage Voice have in­quired after my opin­ions, and The Ladies’ Home Journ­al has in­cluded me in a list of the 100 most out­stand­ing wo­men in Amer­ica.

All this at­ten­tion has been grat­i­fy­ing but also em­bar­rass­ing. What I really am is a math­em­atician. Rather than be­ing re­membered as the first wo­man this or that, I would prefer to be re­membered, as a math­em­atician should, simply for the the­or­ems I have proved and the prob­lems I have solved.

### Works

[1] J. Robin­son: “Defin­ab­il­ity and de­cision prob­lems in arith­met­ic,” J. Symb. Lo­gic 14 : 2 (June 1949), pp. 98–​114. A ver­sion of the au­thor’s 1948 PhD thes­is. MR 31446 Zbl 0034.​00801 article

[2] J. Robin­son: “An it­er­at­ive meth­od of solv­ing a game,” Ann. Math. (2) 54 : 2 (September 1951), pp. 296–​301. MR 43430 Zbl 0045.​08203 article

[3] J. Robin­son: “Ex­ist­en­tial defin­ab­il­ity in arith­met­ic,” Trans. Am. Math. Soc. 72 : 3 (1952), pp. 437–​449. MR 48374 Zbl 0047.​24802 article

[4] M. Dav­is, H. Put­nam, and J. Robin­son: “The de­cision prob­lem for ex­po­nen­tial di­o­phant­ine equa­tions,” Ann. Math. (2) 74 : 3 (November 1961), pp. 425–​436. MR 133227 Zbl 0111.​01003 article

[5] M. Dav­is, Y. Mati­jasevič, and J. Robin­son: “Hil­bert’s tenth prob­lem: Di­o­phant­ine equa­tions: Pos­it­ive as­pects of a neg­at­ive solu­tion,” pp. 323–​378 in Math­em­at­ic­al de­vel­op­ments arising from Hil­bert prob­lems (DeKalb, IL, 13–17 May 1974), Part 2. Edi­ted by F. E. Browder. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 28. 1976. With a loose-leaf er­rat­um. MR 432534 Zbl 0346.​02026 incollection