 My dear Thibaut, my dear Zalida Thibaut of the last city, dear friends of this week, we celebrate the shit that we are making. It is such a pleasure to speak in this occasion and to, despite the fact that we've been told to come here and praise Thibaut, and I am certainly not here to bury him, because I know that it was just continuing, as if nothing had happened, this is just a random bureaucratic moment. So, let me begin a little, just a little bit about reminiscent of, I first met Thibaut when he was, well before he came to the institute indeed, I was asked to praise him as if for the possible position at the, as a professorship to which, of course, I was enthusiastic, and I told to ask him because I knew he was talking about it. So, fortunately, I was saved by the fact that he was all for the job. And, we have had some very active collaborations, both published, the most, in a way the most public that we had was 300 years after the French had published their, now, C'est Club BD. They got the bright idea of doing a second edition, somewhat akin to the Britannica, and I was asked, I've been asked to do the Relativity section, which I did, but then came a second edition, and there I felt it was clear it would be greatly enhanced if we could collaborate. So, we did, and we wrote what was a really great article, and probably it was dealt without policy as good as edictives of the Britannica. So, that put us, I guess, on some sort of French map. And then we collaborated, that is published, collaborated and talked about many, many things over the decades. As I said, we were really on two topics, both of which were, as is natural, to both of us, off the beaten track. One of them was about how masses hire spin theories and their possible geometry, as embodied by spin three. And it was kind of amusing to see how far you could go down Einstein's alley with this, you know, weird and really unphysical, but interesting film, which people to this very day were worried about. So, we wrote several papers on that, and then other physics papers, which again, as I said, went up in this straight standard stuff at the time, but they were sort of interesting. This was about a rather non-symmetric gravitational theories and their problems. And of course, Schrodinger and Einstein had both proposed such theories in their late days as possible candidates. So, we shot them down very well. Since then, people's work has gone. As we can see by the list of resonant collaborators, people who do not take the fools kindly, and therefore, you can judge his standing just by that alone, but he's collaborated with people in high energy physics, mathematical physics, and of course, relativity. And he's had a large, I can say, school of coworkers on technical problems in which they pushed the post Newtonian limits of relativity higher or higher, which is not as easy as it sounds and involves frightfully difficult calculations, which only a master can do. And people was, of course, up to that task, is. And so that has been the keynote of his work at least, as well as, of course, having the duty to make you, who running the IHES, which he has done and doing there, the right publicity for them as necessary and so on. So, since I'm supposed to speak about physics, let me stick to relativity while we're up, since that was really the whole point. Let me stick to physics and mention that I will, I will summarize a little bit the work of ADM that is relevant on the way, Mr. and myself. And in particular, I've come back to that problem, one of the problems posed by that, which is a positivity of energy, energies rather than gravity. The first problem, the basic one in defining an energy field, is it just about as old as general relativity itself? I was first attacked by no less hours, and then we never, and David Hilbert. And the only problem was they were my tissues, I hate to say it here, but they missed them. They precisely, those two people missed the point, because they were too general. They failed to realize that they could only define energy and with respect to a Poirier symmetry rather than full general covariance. And so, we realized, we, how to keep calling it ADM, we realized that what you had to do was, first of all, that was clear that energy should not even be defined for solutions in the theory that are not asymptotically flat, because asymptotically, flat means Poirier invariant. So, it's the only chance for defining an energy. Secondly, that is to say, where the second, very second theorems, and it's the same local variants are broken out too. And there's first, which is a local constant, the parabola invariant, as I said in the Poirier group. And it's not quite the end of the line, because then of course, there are the asymptotically factors associated with the Poirier group. But there's also the deep fact that the total energy of a system is like the total charge in Maxwell-Yagmills, that is to say, it is an integral of the, basically of the Poisson equation, form, therefore, to be formulated as a sphere, as an integral of this sphere and its spatial infinity. And that's very interesting, because the two quite separate ideas mesh completely in that, on the one hand, you are looking at only possible candidate solutions, as asymptotically flat points. And so to speak, by miraculous coincidence, those solutions are both able to lead, they lead to a finite Poisson source for the equation, for the, basically, the energy density. But it really is the energy density in general relativity by the equivalence principle. There's only a total energy, so that can be defined at infinity. And many, many years later, Abbott and I attacked the problem of doing the same for cosmological gravity. Did this sitter or run the sitter with a cosmological constant? That turned out to be quite another bag, because of course, asymptotically, you no longer have the Poirier group, you have the rotations, or metabolic rotations of the sitter and the anti-sitter, and therefore have to, there are those killing vectors. But there's no such, there's clearly no, man, the rotations, there's no energy as such. However, you could differentiate five quantities, or rather four quantities, from the generators of the five, of the four dimensional rotations. And they, they constitute the best of the nearest thing you have to the four, the energy four vector in the normal Einstein. And this is precisely what we worked out. And we're able to show that it was a reasonably well-defined equivalent, although not exactly, of course, as it is, and in the one day, zero case, but enough to make, since actually, we now know that unfortunately, the mathematics you very much prefer is both theory and supergravity, which I'll come to in a minute, prefers anti-sitter, but the Lord, as Einstein calls him, seems to prefer this sitter, for which we are eternally ungrateful and unhappy. But we have to live with it, since that's how the world seems to be the world we live in, choose it. So, as everybody knows, in the city of gravity, all of us are living inside, inside the event horizon, inside the event horizon of the universe, and that event horizon that we live inside of is where energy can be defined, that that's important. So, that is all cleared up. But of course, there's more to energy than its definition, although that was a really heavy lifting part. The other part of energy is whether it, as for all physical systems, is positive, and we finish this so greedy, it should be both positive and have zero energy, only for vacuum and its flat space in the medical case solutions. And that turned out to be an amazingly difficult, you would think, problem. I mean, in Yang-Mills and in Einstein and Maxwell, it is a trivial fact that the Yang-Mills and the Einstein fields have positive energy, because they're just integrals of v squared plus v squared, and certainly the sum of squares is not as positive as you can get, but zero, of course, means no fields. So, how do you prove that here? Is it true? Never mind, I approve it. So, first of all, is it true? And people tried, but the problem was that the definition of energy is a highly nonlinear object, and it's just impossible. So, for a few special symmetric solutions, it was possible to show it, and there were some variational arguments, but for many years, there was nothing else. Then suddenly, this, so this went on, the attempts went on from, I would say, the late fifties on. And remember, Luther and the poor, Hilbert were back in the, around 1918. So, you can see the time gap. So, the supergravity was this, in 1976. And the beauty of supergravity is, of course, in part that unifies gravity with a Fermi-Alexbin 3-2-2, but for the present purpose, it is an amazing gift from God, because it immediately tells you that, again, first solutions of infinity, the energy of supergravity is manifestly positive, just like from Maxwell. It's simply the sum of product of the Fermi-Alex charge and its Hermitian conjugate business, because it feels in my aroma. So, the energy is, not only is it positive, not negative, but also when it vanishes, which means when the supercharge vanishes, then space is flat, and there are no spins we have, so that's perfect. And this is all, of course, a quantum theory, because it has Fermi-Alexbin quantum, whereas classical general relativity is not available. But, of course, it is a special case, so all you have to do is take the limit of h bar equals zero, and then you set, look at the set of diagrams with no external spinners, as was covered earlier, we'll actually do that. The energy is still cute, it's still positive, and that's it. This proof, although it's good enough for all of us physicists, was then replaced by, or at least to add it to it, was the real high heavy lifting proof of Schoen and Yale by mathematical means, which I must confess I've never followed in through a lot speaking of, it was the real, to me again, it's generally, you know, positive as these sorts, but I still prefer to say that the energy is a perfect manifest square, but anyway, and then there was another proof given by Whitton thereafter, which kind of a hybrid in which he used our supergravity idea, but without the supergravity. So, the fact that, the fact that generativity obeys the older physical requirements and that is to say energy exists only when it should and when it does, it is only, its positivity is assured that it's vanishing means nothing's vacuuming. Now, the other thing that I want to talk about is that the definition of energy that we made was on the basis of recasting Einstein's initial term geometric formulation, which of course was the greatest feat ever since the big job that he did was to destruct and destroy, of course, but to provide the open and modern definition as a field theory, a classical field theory, and this was made possible you never know where these things come from, but the beauty of mathematics and physics by Jacobi, the great German mathematician of late 19th century, who discovered or invented whatever it is, the Jacobi action principle. And that is something which was far more deeper than I believe he knew, but of course no one else had done it and it has a real place in life. So, Jacobi said, hey, everybody writes the action principle in terms of integral dt, say for point particles or d4x system, but I can also write in general, in other words, any theory, any action to be written generally covariantly by replacing the time with a covariant time that is a time that is undefined except generally covariant and the price of adding an extra degree of freedom, and at the same time, adding an extra constraint. And the constraint basically is that the Hamiltonian comes in, but when you put down the action without the solve of the constraint, it's a zero Hamiltonian. They rate with one extra degree of freedom and that is a really super deep fact. And of course, for him it was artificial because it was the part with the Newtonian time system, but for general relativity that was it, that was God's own thing. So the action that we discovered was precisely what Jacobi would have given, that is to say zero Hamiltonian for extra degrees of freedom, which really contributed for constraints, energy momentum constraints. And then everything else, you can then exploit all the deep facts of possible field theory or the quarter field theory in order to understand general relativity in a non-geometrical way. For example, you can finally have a perfect definition and existence proof of gravitational wave, which is Einstein always was unsure about, but again going back and forth here, there's no question. You can, having a classical field theory means it's all set to be quantized. Of course, the problem, the final gravity, another problem, the formal ones of setting up the quantization, they are the problems in the calculations after the quantization. And that is of course the primary aim of so much research. And I would say that so much brand unification of our general relativity, the rest of everything, that would be of course super great. But it will be illusory in the sense that what will work will be none of the above, usually when the revelations come. And that's where the revelations and in physics as well as anywhere else, they are revelations because they come from left field and cannot be reduced from existing conditions. So, and I don't know how long it will take if ever to have a consistent theory, but then again I remind you that 1924 Niels Bohr said he didn't know how long it would take to have some kind of final quantum mechanics available. And that only took him a while. We've been waiting for a long time to let us know. I should probably, however, not go on with technicalities for you because I've already overdone it so far, but you'll have to, those of you who are not physicists, must forgive me because that was my remit. Let's just review about physics and not the praise people, if you will remember. So, at the risk of being censured for re-praising people anyway, let me just briefly say that he is the very model of a really first-class physicist, who I have really and many, many others who had the privilege of collaborating on a wide range of important problems. As you can see from the other speakers of this symposium, I mean they range, people like Sasha Palyaakov and Ed Whitton and Gabriella Venenciano, just to name three, and not to mention people like Anna Juanalo, whom he has maintained a long scientific relation with, and not to mention the many, many people who are launched and benefited from his mentorship in their career. He has been an ornament to IHES, he has been an ornament to our profession, and I am only too happy to have contributed this appraisal as well as a little reminiscence about real physics or real relativity. If he has been a very benefit to anyone.