Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

The Jacobi identity (which forces the heights of a triangle to cross at one point) is an experimental fact in the same way as that the Earth is round (that is, homeomorphic to a ball). But it can be discovered with less expense.

In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course, in total ignorance of any other sciences. They first began teaching their ugly scholastic pseudo-mathematics to their students, then to schoolchildren (forgetting Hardy’s warning that ugly mathematics has no permanent place under the Sun).

Since scholastic mathematics that is cut off from physics is fit neither for teaching nor for application in any other science, the result was the universal hate towards mathematicians - both on the part of the poor schoolchildren (some of whom in the meantime became ministers) and of the users.

Another French pupil (quite rational, in my opinion) defined mathematics as follows: “there is a square, but that still has to be proved”.

How could this happen in France, which gave the world Lagrange and Laplace, Cauchy and Poincar´e, Leray and Thom? It seems to me that a reasonable explanation was given by I.G. Petrovskii, who taught me in 1966: genuine mathematicians do not gang up, but the weak need gangs in order to survive.

By the way, I shall remind you of a warning of L. Pasteur: there never have been and never will be any “applied sciences”, there are only applications of sciences (quite useful ones!).

I was treating Petrovskii’s words with some doubt, but now I am being more and more convinced of how right he was. A considerable part of the super-abstract activity comes down simply to industrialising shameless grabbing of discoveries from discoverers and then systematically assigning them to epigons-generalizers. Similarly to the fact that 🬍🬖🬱🬴🬤🬻 does not carry Columbus’s name, mathematical results are almost never called by the names of their discoverers.

Prof. M. Berry once formulated the following two principles:

• The Arnold Principle. If a notion bears a personal name, then this name is not the name of the discoverer.

• The Berry Principle. The Arnold Principle is applicable to itself.

The de-geometrisation of mathematical education and the divorce from physics sever these ties. For example, not only students but also modern algebro-geometers on the whole do not know about the Jacobi fact mentioned here: an elliptic integral of first kind expresses the time of motion along an elliptic phase curve in the corresponding Hamiltonian system. Rephrasing the famous words on the electron and atom, it can be said that a hypocycloid is as inexhaustible as an ideal in a polynomial ring. But teaching ideals to students who have never seen a hypocycloid is as ridiculous as teaching addition of fractions to children who have never cut (at least mentally) a cake or an apple into equal parts. No wonder that the children will prefer to add a numerator to a numerator and a denominator to a denominator.

From my French friends I heard that the tendency towards super-abstract generalizations is their traditional national trait. I do not entirely disagree that this might be a question of a hereditary disease, but I would like to underline the fact that I borrowed the cake-and-apple example from Poincar´e. The scheme of construction of a mathematical theory is exactly the same as that in any other natural science. First we consider some objects and make some observations in special cases. Then we try and find the limits of application of our observations, look for counter-examples which would prevent unjustified extension of our observations onto a too wide range of events (example: the number of partitions of consecutive odd numbers 1, 3, 5, 7, 9 into an odd number of natural summands gives the sequence 1, 2, 4, 8, 16, but then comes 29).

As a result we formulate the empirical discovery that we made (for example, the Fermat conjecture or Poincar´e conjecture) as clearly as possible. After this there comes the difficult period of checking as to how reliable are the conclusions.

At this point a special technique has been developed in mathematics. This technique, when applied to the real world, is sometimes useful, but can sometimes also lead to self-deception. This technique is called modelling. When constructing a model, the following idealization is made: certain facts which are only known with a certain degree of probability or with a certain degree of accuracy, are considered to be “absolutely” correct and are accepted as “axioms”. The sense of this “absoluteness” lies precisely in the fact that we allow ourselves to use these “facts” according to the rules of formal logic, in the process declaring as “theorems” all that we can derive from them.

A small change in axioms (of which we cannot be completely sure) is capable, generally speaking, of leading to completely different conclusions than those that are obtained from theorems which have been deduced from the accepted axioms. The longer and fancier is the chain of deductions (“proofs”), the less reliable is the final result. Complex models are rarely useful (unless for those writing their dissertations).

The mathematical technique of modelling consists of ignoring this trouble nd speaking about your deductive model in such a way as if it coincided with reality. The fact that this path, which is obviously incorrect from the point of view of natural science, often leads to useful results in physics is called “the inconceivable effectiveness of mathematics in natural sciences” (or “the Wigner principle”).

Every working mathematician knows that if one does not control oneself (best of all by examples), then after some ten pages half of all the signs in formulae will be wrong and twos will find their way from denominators into numerators.

The technology of combatting such errors is the same external control by experiments or observations as in any experimental science and it should be taught from the very beginning to all juniors in schools.

Attempts to create “pure” deductive-axiomatic mathematics have led to the rejection of the scheme used in physics (observation - model - investigation of the model - conclusions - testing by observations) and its substitution by the scheme: definition - theorem - proof. It is impossible to understand an unmotivated definition but this does not stop the criminal algebraists-axiomatisators. For example, they would readily define the product of natural numbers by means of the long multiplication rule. With this the commutativity of multiplication becomes difficult to prove but it is still possible to deduce it as a theorem from the axioms. It is then possible to force poor students to learn this theorem and its proof (with the aim of raising the standing of both the science and the persons teaching it). It is obvious that such definitions and such proofs can only harm the teaching and practical work.

The determinant of a matrix is an (oriented) volume of the parallelepiped whose edges are its columns. If the students are told this secret (which is carefully hidden in the purified algebraic education), then the whole theory of determinants becomes a clear chapter of the theory of poly-linear forms. If determinants are defined otherwise, then any sensible person will forever hate all the determinants, Jacobians and the implicit function theorem.

If mathematicians do not come to their senses, then the consumers who preserved a need in a modern, in the best meaning of the word, mathematical theory as well as the immunity (characteristic of any sensible person) to the useless axiomatic chatter will in the end turn down the services of the undereducated scholastics in both the schools and the universities.

PARC was an interesting place, to say the least, and there were three labs, there was CSL, where I was. That was a lab that was working in Mesa. Mesa was a very C, C+±like compiled language and everything that was done in the lab was done in Mesa. There was another lab in the other third of the building that was done in-- where everything was done in LISP, Interlisp and there was a third lab, where everything was done in Smalltalk and there was a bit of competition between those labs. There were some talks where all the labs would come and listen to whatever was presented. But by and large, the three labs were independent and competing. It’s a little bit crazy to think that in '84, '85, I had access to an email system that had fonts, text with fonts, that had images, attachments, and the other two labs also had access to a system that did that. But it was three different systems and in the entire universe, that was the only place that had such a system, right? And of course, there’s Metcalfe’s Law, which is the square of the interest of a system is the square of the number of users, right, for a network system and this was really silly, to have three labs duplicating all the effort and the worst thing is that those systems were not compatible. So there were three mail systems with fonts and attachments that were incompatible in the building of Xerox PARC in Palo Alto.

So PARC probably peaked before I arrived there and there were some big names, many of the older generations who had left just prior to me arriving there. So it was a place in the decline. But it was still way ahead of any other place in the world, really. It invented technology in so many domains, VLSI, networking, personal computers, the list goes on and on, and so there was so much to learn there. So I stayed four years, but I really learned a lot there. I left unhappy because I was very frustrated because it was a great place, but for 40 people and doing all this work that we were doing for just the benefit of 40 people was very frustrating. So I wanted to have what I do be used by others.

[Hsu: So PARC just recently merged with SRI. So given that maybe could you reflect a little bit on PARC’s legacy and its contributions?]

Serlet: Oh, it has many, many forms. I think it touched all the fundamental, all the basics of computer science. So in many ways, it is an example of what happens when you get a great group of individuals and you give them a lot of freedom and all that. But it’s also an example of total failure of transforming that to a success that benefits many other people. The main benefit of PARC has been visitors like Steve Jobs coming and learning from PARC, having trained all the scientists and then the scientists move elsewhere. So it gave me a sense that research is not a way to do things in computer science, and I think it’s different in, for example, physics. In physics, you want academic research, right? In computer science, it’s also a team effort and PARC was not so great at team efforts. There was a lot of individual personalities who wanted to publish fundamentally as a main goal. So many, many years later, when I started at Apple, my boss, Avie Tevanian, given my research background, asked me to investigate the Apple research and I was not so excited with what I saw. So, yeah.

[Hsu: What was that first meeting with Steve Jobs like? Serlet:]

Oh, so that was an interview. So Steve interviewed me. I had interviewed with the rest of the team, and that was in October '88 and that was before the announcement of the NeXT computer, the Cube, that was unveiled just a few weeks later. So Steve brought me in front of the Cube and he said, let me show you something and he goes to a terminal, a Unix terminal, which I was shocked, okay, that it wasn’t like all [graphical] user interface based and all that stuff and he launched a music player from the terminal and he said, listen to this and he played classical music. I hate classical music. I didn’t tell him. But his demo was a flop with me, and then to grab the classical music, and starting with a Unix terminal, which for me was going backwards right, in history, because I had been working on a VAX at INRIA, doing Unix in the early '80s. But I let that slip and I did join NeXT.

[Hsu: How much continuity, in terms of your experience, was there going from PARC to NeXT? Serlet:] Well, the things I learned at PARC, I think, were very applicable. API, hash tables, immutability. But there was no codebase continuity. It was just what I learned, which is one of the things that’s a little sad about Xerox PARC, is all those people learning all that stuff, but could not apply it unless they left.

So one thing that we had at NeXT was the Mach operating system. It was developed at CMU by Avie and others and Avie had convinced Steve Jobs to base NeXTSTEP on the Mach operating system, which we did, and Mach was very elegant. It was all based on message passing and so you would, nowadays, we call that microservices architecture, you would tell the service, okay, please do this. And it was labeled as an object-oriented operating system. That was a little bit of marketing, but more than anything. But we had an object-oriented language, which was Objective-C. So with my colleague Lee Boynton, we thought, well we can probably automatically map the message of the language to the messages of the operating system, and that became Distributed Objects and that was great. It lent itself to great demos. In the end, I think it was not that useful, but it was great for demos.

[Hsu: Talk about the Workspace Manager. Serlet:]

Yes. So the Workspace Manager in NeXTSTEP was the equivalent of the Finder on the Macintosh. So this is a place where you go to access all your files and there was a first version that was done in ’88 and Steve was not totally satisfied with it and Jean-Marie said, well, there’s a few ideas on how to do that, how to do a browser and all that, and some of those ideas were coming from the work he did on Interface Builder. So Steve said, let’s redo the Workspace Manager and Jean-Marie, you do it. So that’s when, with Lee Boynton, the three of us worked for a year on the Workspace Manager and it was a very exciting time. I was living in Palo Alto and I typically was working all night long and I would meet my wife at the cafe at 7:00 a.m., I was on my way to bed. She was on her way to work and we had this rhythm of working at night for about a year. We would usually have breakfast with Jean-Marie and Lee at Denny’s around 3:00 a.m. just to get a little boost of energy to keep going, and we did a lot of work. Just the three of us did pretty much the Workspace Manager from scratch in about a year. But it was really hard work. But I loved it. We all loved it.

I was in France for just a year. Towards the end, Bud Tribble and Leo Hourvitz, the folks managing the software team, thought it was not a good idea to have in France the people doing Interface Builder, doing Workspace Manager, doing Project Builder, and doing Mail, which we had started doing at that point.

[Hsu: So basically, is that prior to OpenStep, there was no Foundation framework? Serlet:] Correct. The AppKit had both UI and non-UI and we thought that from a layering perspective, it was important to separate what’s non-UI from what’s UI. Because for example, you can develop services that are non-UI that can leverage this space.

OpenStep was just doing some cleanup of the version one of NeXTSTEP. It was necessary cleanup. There were things that were done, it’s called now technical debt, that were done quickly, and we needed to just clean up the code and have a more solid foundation, so to speak. So that was a technical project, really, not based on any business and Bud Tribble had left NeXT at some point and went to Sun, and Bud Tribble said, well, maybe Sun should use OpenStep and so then there was this alliance deal between NeXT and Sun and that was, ultimately, that didn’t go anywhere. Sun didn’t do much with it. But that’s when it happened.

NeXT, I think, had six or seven pivots. NeXT never really worked from a business perspective. It was a great place to do work that was at the leading edge of technology in a number of ways, but we never found this juicy niche. We had a few false starts, okay, where we thought it was working, and then after a few quarters, no, no. So we do another pivot and so the company pivoted many times. It started as the company doing a computer for education. I think, in Steve Jobs ’s mind, it was another Apple, right, kind of done right. But that was a good entry point. But it was way too expensive for education, education cannot afford such a computer. So then it became the interpersonal computing, all based on Mail. We had a great mail system, again, with fonts and attachment. That was probably one of the first commercial systems with fonts and attachment. For me, it was déjà vu, because it was like four or five years after… More than that, it was six or seven years after using such a thing at Xerox. But it was new for the industry and that got some traction, but not really. Then we let go of the hardware, and for a while, we had PCs. We had Windows machines, OpenStep for Windows and it’s only towards 1995 with the internet starting to work, right. So the first [web] browser was, of course, developed on NeXTSTEP and we had this database product, DatabaseKit or something like that. That got some traction, because people in enterprises were able to take the SQL database and produce a web interface for that and so we did a version two. I hired a young engineer from Oracle, whose name is Craig Federighi, to really contribute on that project and he quickly became the thought leader on that project. That became EOF, Enterprise Object Framework and then we had WebObjects, which was on top of that, led by Nicolas Popp, and the combination of EOF and WebObjects was really fantastic for the time, because it let people create dynamic websites based on information that’s stored in the database and it was very easy to do and we had really great customers, notably Dell. Dell was selling 100% of their computers using WebObjects and so that was towards 1997 and we were very excited. Finally, after all those pivots, we had found one that worked, and we were starting to do the work to go public and then we got acquired by Apple.

[Hsu: Talk about the culture of NeXT. Serlet:]

So it was a culture trying to do great things, leading-edge things, and I think this is really important in any company to try to push the envelope, and so the folks that we hired were folks that were interested by that side of things. Now, as always with a startup, you also expect, hope, that one day you’ll have a big exit and all that. But for some people, this is a very, very minor thing. They just want to do great work and benefit users. So the people who were mostly interested in the big exit left over the years. At each pivot, we would shed a few of those people and the core of the team that was left was really trying to push the envelope and make things progress and do great products and that was, I think, the strength of the team at NeXT.

[Hsu: So Swift now has basically extensions on… Basically, with the equivalent of categories on protocols, but I heard that this was actually proposed at NeXT.]

[Serlet:] Well, yes. Yes, the extensions were done at NeXT. Yes, I hacked the new compiler frontend to add them. Yes.

[Hsu: But I heard that adding protocols to categories was something that would have been done then, but due to the Sun relationship.]

[Serlet:] Yeah, I think we stopped doing it at some point because it was complexifying things. Having to change a compiler was not a good thing and we did it some other way. But the concept was in the air.

[Hsu: We talked about shifting to management. So over time, you mentioned your team got bigger and so did your responsibilities grow as well?]

[Serlet:] Yes, yes and so that was another time where I had two mentors. I had our HR person called Caroline Morse and she really taught me the ropes about management, and management is first and foremost caring about the people and she was a great HR person who cared about the people and she taught me that side of things and to pay attention to signals and all this. So she was really a great influence and frankly, my transition happened very smoothly and that was thanks to her, the people side of things and then at the same time, I learned also the ropes for project management and that was from Charlie Kleissner, who at some point became the head of software at NeXT and Charlie, being Germanic from origin, knows how to do a very strict process and he had some great techniques for how to manage a project very systematically and to make sure that the project just keeps progressing all the way to shipping. So I learned that from Charlie. So that’s really the triptych, right? It’s a technical side, which I had. People side, which I got from Caroline, and the project side from Charlie.

[An email in reply to:]

My neighbor who works at Adobe came over the other day and I started showing him photos of the lab and he said, “Wait, you know Bret Victor?” He started saying that he follows you/the lab on Twitter but doesn’t fully understand what’s going on. He said, being cautious but trying to be honest, that he detected a kind of aloofness in the “I’m not quite sure what they’re doing” vibe he was getting. Knowing the lab as I do, it’s clear to me that this is a case of interpreting something brilliant/new/hard-to-understand as a better-than-thou (i.e. “we don’t need to explain this—it would be too over your head to understand”). But there’s a chicken-and-egg problem here. I think that people’s desire to understand isn’t entirely innocent. I think they want to understand it by way of containing/limiting what the lab is doing into something they already know/understand, which for most people wouldn’t be the lab. Yeah.

I’m really uncomfortable with the Dynamicland twitter myself. I’ve always waited to show things until I could explain them fully. But there’s no time to make a good explanation, and it might not even be possible at this point, and regardless it’s way too premature – we don’t have something worth explaining yet.

So we’re showing things that look like teasers, but really, I don’t want to tease anyone, I just want to be funded.

I think your larger point is right – the last few years I’ve been accused of being secretive because I wasn’t showing anything, and now I’m accused of being coy because I am showing something… but before all this, when I put my entire energy into explaining as well as I could with the talks and essays, I was accused of being self-promotional, and of being withholding because I didn’t release source code! I think my conclusion is that no good at all comes out of paying attention to public opinion, and I just need to keep doing what I think is best for the world in the long run.

There’s also a weird sense of entitlement on the part of many people (why do I owe anyone anything in the first place?), and there’s also something weird about how many people now view everything that happens in the world as part of an entertainment program targeted at them. (Like, now that we’ve started a Dynamicland twitter feed, we need to keep the “fresh content” coming or the “audience” will get upset. How did we get into the entertainment business? We’re not even a business!)