Celebratio Mathematica

Many of us who had close per­son­al and pro­fes­sion­al con­tact with Mary El­len Rud­in re­ceived with deep sor­row the news that she died on March 18 in the eighty-ninth year of her life. In this age of the Wiki­pe­dia and nu­mer­ous oth­er eas­ily avail­able pub­lic sources of in­form­a­tion, I don’t think it’s ne­ces­sary for me to give a de­tailed ac­count of her great sci­entif­ic achieve­ments, most of which were done in the field of gen­er­al and set-the­or­et­ic to­po­logy. In­stead, I take this op­por­tun­ity to re­call a few per­son­al memor­ies about her.

The first of these con­cerns a pa­per of hers in which she presen­ted an ex­ample of a first-count­able and CCC reg­u­lar space that is not sep­ar­able and which, as a stu­dent, I presen­ted in our to­po­logy sem­in­ar. I still re­mem­ber how proud it made me that I could un­der­stand, and make more or less clear to the audi­ence, her very com­plic­ated con­struc­tion. I only much later found out the ex­plan­a­tion of the rather non­stand­ard nota­tion and ter­min­o­logy she used (and which made her tech­nic­ally very com­plic­ated in­geni­ous con­struc­tion even harder to un­der­stand): She was brought up in the (in)fam­ous Moore school in Texas, where stu­dents were for­bid­den to study math books; they had to dis­cov­er everything on their own. I re­call a story I heard from Paul Er­dős, a good friend of the Rud­ins, that il­lus­trates this. On one of his vis­its with them he was sur­prised to find out that she did not know what a Hil­bert space was. This was some­time in the 1950s, and, of course, she later be­came much more fa­mil­i­ar with and well versed in what was go­ing on in her field.

Our first meet­ing in per­son took place at the IMU Con­gress in Nice in the sum­mer of 1970. To­geth­er with my friend and col­lab­or­at­or An­drás Hajn­al we were eager to meet her, and this happened right after she ar­rived in Nice. Her first sen­tence to us was “I just proved that there is a Dowker space;” i.e., a nor­mal space whose product with the unit in­ter­val is not nor­mal. To ap­pre­ci­ate the weight of this sen­tence, one should know that this meant she solved the most im­port­ant open prob­lem of gen­er­al to­po­logy of the 1960s.

The next year I made a short, ba­sic­ally per­son­al, vis­it to North Amer­ica, and she in­vited me to Madis­on to give a talk there. That was the first of many oc­ca­sions when she, as a caring host, treated me so well, both math­em­at­ic­ally and so­cially. Of course, she in­vited me to their beau­ti­ful house de­signed by Frank Lloyd Wright, cooked a great meal for me, and showed me around town. I was glad to be able to re­turn some of her fa­vors in the sum­mer of 1973 when she came to Hun­gary, to­geth­er with her two then-teen­age daugh­ters, for a to­po­logy con­fer­ence.

She was the ar­chi­tect of ar­ran­ging a vis­it­ing po­s­i­tion for me at the Uni­versity of Wis­con­sin–Madis­on for the aca­dem­ic year 1974–75. This was not a trivi­al thing in those Cold War times. One res­ult of this vis­it was our joint pa­per [1] with Ken Kun­en, which is a very fre­quently cited pa­per in the field of set-the­or­et­ic to­po­logy. This vis­it was fol­lowed by many more vis­its to Madis­on, most of them or­gan­ized by her. But I’d like to men­tion an­oth­er trip of mine to the US in which she played a sub­stan­tial role.

This took place in 1983 when my friend En­dre Sze­merédi had been dia­gnosed with a ser­i­ous case of can­cer while on a vis­it in the US. Of course, after hav­ing found this out, I turned to Mary El­len to ask if she could ar­range a vis­it to Madis­on for me so that I could see my ail­ing friend. It turned out that this was not pos­sible be­cause of some fin­an­cial prob­lems at UW Madis­on. Still, she man­aged to con­vince the head of an­oth­er math de­part­ment in the US — as I later found out, not without some arm twist­ing — to in­vite me, thus mak­ing it pos­sible for me to vis­it my friend right after he had a very ser­i­ous op­er­a­tion. This story has a very happy end­ing: My friend has com­pletely re­covered, and, as is well known, in 2012 he was awar­ded the Abel Prize.

I was for­tu­nate to be present at Mary El­len’s re­tire­ment meet­ing in Madis­on in 1991, where I could wit­ness her ef­forts try­ing to help Bor­is Sha­pirovskii, an­oth­er great math­em­atician fight­ing can­cer, un­for­tu­nately in his case with no suc­cess.

I was very happy and proud when in 1995, mainly thanks to the strong re­com­mend­a­tion of An­drás Hajn­al, she was elec­ted to be an hon­or­ary mem­ber of the Hun­gari­an Academy of Sci­ences. Moreover, the next year she and her hus­band, Wal­ter, after vis­it­ing Prague and Vi­enna, Wal­ter’s ho­met­own, man­aged to come to Bud­apest so that she could de­liv­er her ac­cept­ance ad­dress at the academy. A high point of this trip was that my fam­ily had the good for­tune to host a meal in our home for the Rud­ins, the She­lahs, the Hajn­als, and Paul Er­dős, who, sadly, died just a few weeks later.

I last saw Mary El­len in per­son in 2009 at the Kun­en Fest, Ken Kun­en’s re­tire­ment cel­eb­ra­tion. Al­though quite fra­gile phys­ic­ally, she was as cheer­ful as ever. And the last email I got from her was sent in Novem­ber of 2010, con­grat­u­lat­ing us on the oc­ca­sion of the birth of our grand­son.