Something unspeakable conscionable happened. My wife, Elise Cawley, was recovering from bosom room and had conscionable attended virtually a ceremony for 1 of our children erstwhile she had a freak, immense cardiovascular event—and died instantly. We had been together for 36 years. The image supra was taken conscionable hours earlier she died.
In each the penning and nationalist speaking I person done, I person chosen, arsenic a matter of privacy, to opportunity small astir my family. But now that Elise is gone I cannot restrain myself from telling the world thing astir the singular personification pinch whom I shared the past 36 years of my life.
It was September 17, 1990, and I was successful New York City. The arena I had been attending vanished a small early, truthful I decided to driblet successful connected a friend of mine. And there, sitting stylishly connected the floor, was Elise, a somewhat bashful but evidently superb young axenic mathematician. It took maine a mates of weeks to telephone her. But from that infinitesimal connected we talked fundamentally each time for 36 years—until the time she died a week ago.
Somehow successful the daze of what has happened it feels arsenic if I conscionable met Elise, and now she is gone. But really location were 36 awesome years successful between, successful which my life was lit up by Elise’s intellect, emotion and energy. She was profoundly thematic, capable to get, pinch singular ease, to the principle of things. Truth, beauty and our family and 4 children were her awesome themes. She ever told maine that truth and beauty were yet the aforesaid thing, and that 1 time I would understand that. What I could spot is that she herself loved to create beauty—whether successful mathematics, interior design, architecture aliases individual style. She was a forceful intellect, benignant and sweet, but persistent and often feisty successful arguing for what she thought was true.
Despite her heavy knowledge and capacity successful absurd mathematics, she was astatine immoderate level fundamentally a humanist, reasoning astir the world successful quality terms. She decried barren modernism and was drawn to the quality connections of classicism. In caller years she thought progressively astir the foundations of mathematics, taking a Platonic position of truth and lamenting the twentieth-century modulation to a much formalistic approach.
There was ever a definite lively spontaneity to Elise, mixed pinch a thrust towards the highest standards of intelligence and artistic rigor. People’s first impressions of Elise tended to beryllium of her individual energy, her lively style and her keen intellect. But arsenic they sewage to cognize her, they would besides travel to spot really overmuch she cared astir the group astir her and really overmuch loving thought and effort she would put into things she did for them. Whether it was a gift aliases the interior creation of a space, Elise would use her productivity and spell backmost and distant until it was conscionable right.
Our 4 children were a defining portion of Elise’s life, and she was immensely proud of each of them (as americium I!). She had her ain unsocial narration pinch each of our children that helped them each create successful their ain way. She besides built america a awesome home, afloat of warmth, architectural beauty and imaginative design. She took awesome pleasance successful perfecting each detail, maintaining singular wide coherence, pinch dashes of the unexpected.
Elise was a very good mathematician, apical formation successful method mastery but, much importantly, capable to thematically propulsion together expansive conceptual arcs. She was ever drawn to elegance, often pinch an absurd geometrical bent, and by the clip I met her she had already established herself pinch results that proceed to beryllium cited today. Later successful life Elise would mention to herself arsenic a “retired mathematician”, but if exposed to her benignant of math, she would instantly prosecute pinch awesome enthusiasm.
In each my years pinch Elise we ne'er straight worked together connected intelligence projects. Perhaps we were some excessively beardown willed, and pinch her speedy mind, it did not return agelong for her to get impatient pinch the differences successful our styles of thinking. Still, I would often show her astir activity I was doing. And it was singular really effortlessly she would spot deeper themes, which she would past explicate backmost to me, pinch varying degrees of patience.
She liked my conception of computational irreducibility, and I deliberation was pleased that the efforts successful subject connected which I had spent truthful galore of our years together had led to a spot that highlighted the limitations of subject and of scientism, and aligned good pinch her humanistic worldview. When I began to shape ideas astir observers and the ruliad, she was acold up of maine successful seeing their philosophical and metaphysical implications.
For years, the foundations of mathematics were thing of a sore constituent betwixt america (and our children were highly amused that 1 of the astir vigorous arguments they ever saw betwixt america was astir the metaphysical characteristic of the conception of a circle). Elise maintained that earthy axiomatic formalization cannot beryllium the existent principle of mathematics and that mathematics is really thing overmuch much human. And finally, conscionable a fewer years ago, by a agelong and circuitous route, I came to recognize that—despite my obstinate insistence to the contrary—she’d been correct astir this each along. But past she made different assertions too, that she thought were rather significant. Like that the basal abstractions from which we build mathematics arsenic we cognize it are the conception of constituent (which she viewed arsenic balanced to space, continuity and infinity), and the conception of number. She besides asserted that physics differs from mathematics chiefly successful its preamble of the conception of time.
While Elise could beryllium a very original thinker, she besides believed successful the worth of existing contented and existing ways of doing things—and was perpetually telling maine that I shouldn’t effort to fig retired perfectly everything (including astir mundane life) from first principles. Being pinch Elise was ever thing of an adventure. There was spontaneity (“no plan; let’s play it by ear”), yet besides precision and perfection. And location were the forcefully delivered bursts of insight, not conscionable astir mathematics and abstraction, but besides astir the quality information and the measurement the world works. Elise would opportunity that location were group of action, and location were philosophers. She saw herself much arsenic the latter. She had beardown opinions astir really things should beryllium successful the world. But she was overmuch much willing successful figuring retired what should beryllium than successful what she saw arsenic the grind of trying to make it really happen.
Elise was a personification who had some awesome assurance and awesome humility. While she was ever convinced that she was correct successful things she thought (and successful truth usually was), she was ne'er 1 to advertise her capabilities. Still, if ever a speech turned to things she knew aliases cared about, she wouldn’t restrain herself from making what was often a profoundly insightful contribution.
I ever thought Elise and I were an outstanding match—similar successful galore ways, yet besides complementary. We some weighted thematic reasoning (though successful galore domains she was amended astatine it than me), and we shared an appreciation for aesthetics and activity good done. But for illustration our ways of interacting pinch group were somewhat different. My children opportunity I person only 1 mode of interaction: afloat on. Elise was astatine immoderate level much introverted and would ideate herself to beryllium shy—though erstwhile engaged she would go highly talkative and animated. And erstwhile it was conscionable Elise and maine connected our own, we ever seemed to person things to talk about, successful truth an infinite number of things.
Elise was calved successful 1961 successful Urbana, IL—ironically not acold from the office of our company—when her begetter was a physics postgraduate student astatine the University of Illinois. The 2nd of 4 children, she grew up mostly successful Columbia, MD, arsenic a apical student, peculiarly recognized for her mathematics and her thematic essays. As she often mentioned to our children, successful 6th people her coach characterized her penning arsenic “the cat’s pajamas”—and for a while she imagined increasing up to beryllium a writer. In precocious schoolhouse she had the formative acquisition of going to the Hampshire summertime mathematics program, wherever for the first clip she met different group who were intensely willing successful math.
She went to MIT for college, falling successful pinch a group that included respective later salient mathematicians. She ever told maine that what really ignited her liking successful conceptual axenic mathematics was an epiphany she had successful a class she took astir topology. At MIT, she supported herself by moving successful the thesis bindery, utilizing her calligraphic skills to explanation theses. She besides made up connection puzzles for a connection acquisition study and had a summertime occupation moving connected algorithms astatine an early reside nickname company. A family situation took her backmost to Maryland, wherever she vanished degrees successful some mathematics and physics astatine the University of Maryland. She besides had an internship moving connected a PET scanner astatine NIH, volunteered astatine immoderate hospitals and considered going to aesculapian school. But successful the extremity she decided connected postgraduate school.
She couldn’t make her mind up betwixt physics and mathematics but ended up applying successful physics. One of her physics professors had said she was the champion student he’d ever seen but would beryllium astir suited to very theoretical physics. She had her prime betwixt Harvard and Berkeley. And successful her ever-typical manner she waited until the past minute, picking Berkeley because she was told she’d beryllium capable to move to mathematics there.
After an aggravated “think connected your feet” question and reply process, she received a Hertz Foundation fellowship, which generously supported her postgraduate studies. Before moreover arriving astatine Berkeley she’d settled connected math, and having impressed group pinch her elegant solution to a mini unfastened problem, she joined a group moving connected geometrical approaches to dynamical systems. After 4 years successful postgraduate schoolhouse she completed her PhD thesis connected “Smooth Markov Partitions and Toral Automorphisms”. It was quintessential Elise. An elegant thematic thought implemented pinch cleanable method proficiency.
It made her a hotshot young mathematician, sought aft by galore universities. She ended up pinch 2 jobs: a tenure-track professorship astatine Stony Brook and an NSF postdoc sponsored by the salient mathematician Dennis Sullivan. She chose to defer the professorship and return the postdoc for a year, partially astatine CUNY successful New York City and partially astatine IHES adjacent Paris.
While astatine IHES, Elise lived successful the very halfway of Paris, only steps from the Jardin du Luxembourg, successful an unused workplace owned by an creator who was the sister of different mathematician. It was a play of aggravated mathematical activity for Elise astir which she was very enthusiastic. And her thematic and artistic sensibilities drew her to the study of Teichmüller spaces, which are spaces of imaginable geometrical objects, aliases successful a consciousness spaces of imaginable spaces. It was besides astatine this clip that she embarked connected what would beryllium a semipermanent liking successful the alleged thermodynamic formalism, aliases Gibbs theory.
With connections to mathematical physics, Gibbs mentation provides a measurement to talk astir infinite collections of infinite structures, and their development, for illustration done time. (Ironically enough—as Elise would many times mention—concepts specified arsenic transversals that look successful Gibbs mentation are now straight applicable to my ain activity connected infrageometry and the foundations of physics.)
Rather untypically for a mathematician, Elise was ever notable for her unique individual style—often an mentation of existent fashion, but pinch her ain spunky and colorful touches. As 1 of my daughters tells it, Elise’s liking successful style began to grow pinch the backing she received from her Hertz fellowship and developed further during her clip successful New York City and Paris.
Upon returning from Paris, Elise was astir to commencement astatine Stony Brook, but while waiting for her flat to beryllium ready, was staying pinch her long-time friend Lisa Goldberg successful New York City. And that’s how, connected September 17, 1990, Elise and I first met.
Lisa’s flat was an elegant one, but I was not rather truthful elegant that day. I had been astatine a tech manufacture arena wherever I had received a alternatively bulky award, which was successful my overgarment pouch weighing it down. Elise was sitting connected the floor, pinch her bangs flopped crossed her face, successful a airs that I thought mightiness beryllium yoga. We talked conscionable a bit, but it was enough.
The adjacent time I went backmost to Champaign, IL, wherever I was based astatine the time. It had been 2 and a half years since we’d released Mathematica 1.0 and our institution was increasing rapidly. I had started my profession young, truthful moreover though I was only 2 years older than Elise (she was adjacent to 29 and I had conscionable turned 31), I had already done rather a bit, some successful academia and the tech industry.
Early versions of Mathematica came pinch a book, that I had to write. And successful September 1990 I was rushing to decorativeness the 2nd version of that book, to travel Mathematica 2.0. Two weeks aft I returned to Champaign, I did finish, though promptly sewage sick pinch a precocious fever. And that was erstwhile I yet called Elise.
Soon I was taking trips to Stony Brook, and she to Champaign. And erstwhile isolated we were talking by telephone for hours each day. Lisa Goldberg made a constituent of telling me, “She’s a very good mathematician, you know”. Elise had met different personification a small earlier, and Lisa had dismissed them arsenic unsuitable. But—as I conscionable now learned from 1 of my children—when Elise asked Lisa astir maine she instantly responded pinch enthusiasm.
One notable travel was the consequence of a telephone I sewage from Elise wherever she explained that she’d mixed up interaction lens solution and hydrogen peroxide and now had to spot some her eyes for a fewer days. I instantly sewage connected the adjacent flight. And while the only nutrient I could navigator astatine that clip (and still today) was an omelette, she viewed this “rescue” arsenic an enactment of chivalry that—as she told our children—was what definitively sold her connected me.
On Elise’s 29th day successful December 1990 I sent immoderate flowers. She responded by email, now bittersweet:
Hi there. Some astonishing flowers conscionable arrived. I deliberation I tin make to92. I’m heading disconnected to aerobics — coming is the astonishing Margaret(who plays awesome music). I has immoderate bully mathematics speech withcaroline s. today. And sewage a small spot of existent activity done.
I’ll beryllium backmost astir 9pm.
elise
The very adjacent email I received from her was astir a bug successful the Mathematica Residue function.
My time occupation was (and still is) tech CEO. But what made maine primitively create our exertion was that I wanted to usage it myself—to do science. By the outpouring of 1991 I was getting disappointment that I could inject caller ideas into our institution faster than it could sorb them. So I decided I should return thing of a sabbatical and activity connected subject for a while. Meanwhile, Elise still had clip near connected her NSF postdoc, that she could return anywhere. And truthful it was that we decided to get a location together successful the hills supra Oakland, CA, and she returned to Berkeley.
Before moving into the location that she recovered for us, she came pinch maine connected an 18-city circuit of Europe+Russia to beforehand Mathematica 2.0. After that, we settled into a bully routine. She would spell disconnected each time to do math. I would enactment location to beryllium a distant CEO, and activity connected science. And from clip to clip she’d pitchy disconnected to Texas, Montana, France aliases wherever to springiness talks.
By precocious 1992 we were reasoning astir adjacent steps. Elise was adamant that she couldn’t unrecorded successful Champaign-Urbana (despite having been calved there). But she thought the thought of surviving successful the Chicago area was interesting. Meanwhile, she was highly successful request arsenic a mathematician, and location were aggregate opportunities for her there.
Elise took charge, and explored galore different locations and houses astir Chicago, yet picking a location successful Hinsdale, IL. We moved location successful the mediate of 1993, and Elise took up a position astatine the University of Chicago. It was a bully house, but Elise thought it could beryllium nicer, and group astir renovating it to person top-of-the-line interior design. She started moving pinch a designer who she discovered by reference magazines, and learned that her artistic and geometric sensibilities translated good into imaginative interior design. Elise was peculiarly keen connected integrating lively colors and unexpected elements into accepted creation themes.
Meanwhile, astatine the University of Chicago, Elise was school a course astir Gibbs theory. She wrote extended notes which she planned yet to move into a book. Over the years, group asked for the book galore times, and Elise had precocious started talking astir yet finishing it. Ironically enough, our girl Catherine, now herself a mathematician, has ended up moving successful somewhat related areas.
Elise interacted a batch pinch Bob Zimmer, who was past president of the mathematics section (and would later go president of the University of Chicago). Together they devised the conception of a caller activity for the mathematics department: a master master’s grade successful financial mathematics, fundamentally aimed astatine quants, and taught by mathematics professors. Though Elise was ne'er excessively willing successful the messiness of existent marketplace data, she liked the axenic mathematics of marketplace models, and helped create a program astir it. The master’s grade ended up being highly successful and continues to this day.
In the autumn of 1994 Elise and I married. And then, successful December 1995, arsenic Elise would later picture it, “the world overnight had a caller center”: our first child, Alexander, was born. The adjacent fewer years were dominated by the presence of children, pinch Catherine being calved successful 1997 and Christopher successful 1998—leaving Elise, arsenic she put it, pinch “three nether three”.
With our family growing—and our book postulation reaching complete 5000 volumes—we were outgrowing our location successful Hinsdale, and started looking for a caller home. At first, Elise recovered existent property successful Lake Forest, IL. But erstwhile the woody for it fell done we started reasoning much broadly and decided that since the Boston area was the spot wherever together we knew the astir people, that was wherever we should go. But which municipality successful particular? Elise’s #1 first criterion was that it should already person a Starbucks. From the database of specified towns, she past started looking astatine USGS aerial photographs (or what would now beryllium outer images), and soon settled connected Concord, MA. But uncovering nary suitable existing location to bargain there, she group astir designing a location to build.
It was a analyzable process. The location had to accommodate what was by past a room of astir 10,000 books, arsenic good arsenic abstraction for my remote-CEO agency and for our 3 children. Elise had been scouring architecture books, and interviewed respective top-of-the-line architects earlier settling connected 1 to activity with. With her mathematical and artistic sensibilities she easy absorbed principles of architecture and soon developed her ain intuition for it. Sometimes she’d bring successful superior math—like number mentation to creation a staircase pinch aligned squiggly banisters, aliases circle packing to laic retired an Italian-inspired tiling based connected circles and Sierpinski patterns. She started disconnected making sketches, but soon learned the latest CAD tools. And successful the extremity her ideas defined overmuch of the creation of the house. (At the beginning, I had tried making immoderate “suggestions” astir the plans, but quickly realized that this was an Elise project, and I should enactment retired of it.)
It took respective years to build the location (with Elise regularly walking to Boston to oversee the project) but successful the outpouring of 2002 the task was finished—coincidentally astatine fundamentally the aforesaid clip arsenic my 10-year task of penning A New Kind of Science. Other than successful CAD drawings I’d only seen the location once, early successful its construction, truthful erstwhile we drove from Hinsdale and arrived astatine the location I was successful for a surprise. It was overmuch bigger than I expected! And erstwhile we went wrong I could spot that it was a masterpiece, filled pinch personality: beautiful, elegant, creative—quintessential Elise.
And past location was the interior design. Bold and colorful, yet classic. Each room pinch a chopped character, gracefully flowing into the next. Over the years, Elise revised and updated the interior creation of the location galore times. She was often to beryllium seen sketching connected chart insubstantial caller imaginable designs based connected caller ideas. She kept the style fresh, perpetually breathing caller life into the house—even if it meant that our children would remark that each clip they showed up the furnishings seemed to person been rearranged. And 24 years aft I first saw the house, I still find myself wowed by it.
By 2003, our oldest was encouraging america to person different child, noting, among different things, that the symmetry of the location had fixed it 4 children’s bedrooms. And truthful it was that successful the autumn of 2004 our 4th child, Elizabeth, was born.
In her earlier years, Elise had ever said that she “couldn’t ideate her life not doing math”. But partially done me, and, much importantly done our children, her world had been broadened, and her perspectives had shifted. She would later picture her life arsenic having respective chapters, and this was a section astir children.
Through her children showing liking successful math, she ended up coaching immoderate middle-school MathCounts mathematics title teams. She wasn’t a instrumentality of the measurement mathematics was typically taught successful schools, complaining that the beauty of mathematics was being mislaid successful the effort to make mathematics look “applicable”, and noting that “most of mathematics successful modern textbooks is not really mathematics astatine all”. In an email to maine successful 2010 Elise spiritedly went further:
What has happened to beauty successful math? The beauty derivesfrom the simplicity and elegance. That has been mislaid successful theproliferation of extraneous terminology, meant to make things “moreconceptual”, from early endless excursions pinch “place value” to absurdvariations connected algorithms, to gummy descriptions of everything usingcontortions of language, alternatively than the connection of mathematics itself.
Elise did nevertheless do immoderate applications of mathematics herself. During the pandemic, for example, she developed the thought that infection was not a binary phenomenon, but that alternatively each personification had a perpetually changing viral load and immunity, creating a “viral field” astatine the organization level. Elise was ever up to day connected world affairs, and had a heavy liking successful knowing their thematic arcs astatine work.
Elise loved the small-town ambiance of Concord, MA, and enjoyed the emotion of being successful a spot “where everyone knows your name”. She was a regular astatine section cafes and workout classes, bringing her liveliness wherever she went. She had a circle of friends pinch galore different backgrounds, often met done their children aliases simply done many times moving into them astatine Starbucks. She took awesome pleasance successful applying her knowledge and reasoning to thief her friends successful each sorts of ways. Whether it was doing investigation connected aesculapian issues, solving interior creation problems, aliases simply utilizing her keen penetration and judgement to supply life advice, she would reliably spell supra and beyond.
Our family had a definite routine, pinch meal each time astatine astir 6pm. Every Friday night—following a contented from Elise’s ain family increasing up—we would spell retired to a movie (and, yes, that meant we saw galore questionable movies). Before our children were aged enough, it was conscionable Elise and me; later it included various contingents of children too. Elise and I would talk aft each movie, pinch her often being rather appalled by my deficiency of knowing of what seemed to her for illustration the movie’s evident thematic elements. (Elise besides gave maine a difficult clip astir my nonaccomplishment to publication fiction, claiming that galore ideas, peculiarly astir quality nature, are champion communicated successful fiction.)
A twelve years agone 2 of our children were astatine the Stanford Online High School, and Elise was recruited arsenic an inaugural personnel of the school’s Community Advisory Group. Originally this was conscionable expected to beryllium for a year. But a decade later she was still there, a highly weighted personnel of the group. She spent sizeable effort reasoning astir the wide strategy and issues of the organization, and developed galore ideas and opinions. Despite this, she’d often show america that she didn’t deliberation she’d extremity up saying thing astatine a fixed meeting. But pinch awesome consistency it would later transpire that really she had been the astir talkative and engaged personification there.
In the early 2000s, the Hertz Foundation, from which Elise had received her postgraduate schoolhouse fellowship, started reaching retired to her, and she enjoyed engaging pinch the emerging Hertz community, and gathering fellows from a wide scope of fields. In 2018 she was besides recruited to the committee of the Hertz Foundation. And present again she became a cardinal contributor, often expecting not to opportunity anything, but past ending up arsenic 1 of the astir vocal group there.
By 2023, our 3 older children had each graduated from college, but our youngest, Elizabeth, was conscionable starting astatine Yale. Elizabeth has ever been progressive successful a awesome galore activities, and Elise took awesome pleasance successful attending each imaginable concert, sporting aliases different event—and besides for illustration hosting Elizabeth’s full a cappella group for a retreat astatine our house.
A spot much than a decade agone Elise besides discovered a emotion for the Southwest and for hiking. And pinch her relative Jason—with whom she was ever very close—living successful the Phoenix, AZ, area, we started spending clip location each winter.
With Elizabeth disconnected successful assemblage we were yet quiet nesters, and Elise was fresh for a caller section successful her life. She considered returning to wherever she’d near disconnected successful Gibbs mentation 30 years ago, being told by an aged workfellow that her activity location was still very current. She besides considered getting much profoundly progressive successful the accuracy of mathematics and was connected the brink of penning a portion astir it. She was besides rather engaged successful reasoning astir the intent and guidance of higher education, and the value of free look successful the hunt for truth.
In immoderate ways Elise and I were becoming “the aged joined couple”, pinch her admonishing maine astir my messiness successful eating crystal pick cones aliases her desire that I move connected self-driving to debar her being subjected to my ain substandard quality driving.
Elise had ever been a fresh and patient person, and was besides very medically knowledgeable. So erstwhile she started noticing jaw symptom erstwhile hiking successful Colorado and Arizona, she was concerned. Tests astatine first showed thing alarming, though, arsenic she already knew, she had a mini congenital bosom rumor that was gradually worsening. But conscionable a fewer weeks agone her symptoms worsened and much invasive tests revealed that she needed urgent unfastened bosom surgery. She had an outstanding squad of apical doctors, the analyzable room went very well, and she was soon continuing her betterment from home.
Meanwhile location was a long-planned ceremony for 1 of our children that Elise hoped to attend. But though it was not imaginable for her to beryllium location successful person, we arranged for her to be virtually. It was a awesome event, and Elise could beryllium seen via video telephone beaming done each of it. But then, soon after, disaster struck, and she collapsed, the unfortunate of a monolithic cardiovascular event. My only solace successful this calamity is that the extremity came instantly, aft a time filled pinch thing but joy.
There is truthful overmuch that Elise was looking guardant to. The imminent presence of our first grandchild. Elizabeth’s graduation from college. The adjacent section of her life. But Elise will not beryllium present for immoderate of these.
Elise had nary thought the extremity was near. And moreover though she expected more, she had already had galore chapters successful her life, and galore achievements of which she was proud. Elise had a beautiful life, afloat of things she weighted greatly, particularly her children. That she is gone is simply a calamity for america all; she will beryllium profoundly missed.
Thank you, Elise, for each those awesome years.
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