From black holes to AI in mathematics: AI Innovation in Mathematics and Health with Yaron Hadad

Nitay (00:02.87)
It's great to have you with us today. Thank you for joining us. Why don't we start with giving us a big background of your kind of work experience in life.

Yaron Hadad (00:12.198)
Thanks guys. It's pleasure to be here. I love your podcast. So yeah, so in terms of my background, I worked as a software developer in the industry from the age of 13, roughly. And eventually I switched careers a little bit and studied math and physics. I got my PhD on general relativity.

I also worked on a problem related to electrodynamics for a while. I did my PhD on black holes and gravitational waves. And a little bit after that, I decided to come back to Earth. And I started a company called Neutrino. Neutrino developed a way to quantify and predict how food affects people from a health perspective by using both wearable and medical devices.

and harnessing AI and different biomedical models in order to analyze them. In Neutrino, I led, among other things, all the technology work. And the company got acquired about five, six years ago by Metronic. For those of you who don't know, Metronic is the biggest medical device manufacturer in the world. It's a huge company, about 100,000 people.

After the acquisition, I led AI and data strategy for Metronic for about three years, including the work that Metronic has done on the artificial pancreas project, which was the first class three medical device, as far as I know in history, to be using AI for therapy, which is a very big deal. If you want, we can double click on it later. And I was involved as well in the last few years

in starting different companies. I was involved in co-founding four different ventures in different industries.

Nitay (02:14.904)
Clearly one episode is not gonna do this justice, but let's try it, because that's quite impressive background. I'm curious to start from the beginning, because it's definitely rare that we get somebody that has worked on black holes and gravitational waves. So tell us a bit about that. What were you researching? What's the cutting edge of that world?

Yaron Hadad (02:30.818)
Awesome. Yeah, so first of all, it's a fascinating world and in many ways I still miss it. I still get to do a little bit of research in academia, but not as much as I used to back in the day. So I feel like I have this sleep personality, Jeroen, who wants to be a researcher in academia and Jeroen who's an entrepreneur.

Back then I worked on different problems at the underlying kind of like the basis of all of it was a mathematical study of Einstein's equation. So for those of you who don't know Einstein's equation, in general relativity describes the relationship between space and time and the geometry of space and time and the distribution of energy and mass in the universe. Now this is a

crazy complicated equations. It's a highly coupled, very nonlinear partial differential equation. And there aren't too many known solutions to that equation. And my advisor is Vladimir Zakharov, found together with another Russian researcher, Belinsky, a way to solve Einstein's equation in the 70s.

and I basically extended their work as part of my PhD and also used it to study things related to black holes and gravitational waves. So I hope I'm not getting too technical here, but so please stop me if I do. But I'll just give you maybe one example. This ended up being the last chapter of my dissertation. So back then, and this has changed since,

No one has actually found experimental evidence for gravitational waves, right? So a few years back finally there was experimental evidence, but at the time there wasn't any experimental evidence for gravitational waves and a lot of people spent a lot of money and a lot of time to try and find it. Okay, probably hundreds of millions of dollars and different people started hypothesizing why can't we find, why can't we discover, why can't we observe gravitational waves and

Yaron Hadad (04:53.058)
My advisor had this neat idea to potentially try and explain that by saying, you know, maybe gravitational waves are not very stable. So as they get closer to our planet, to Earth, they somehow dissipate. And until they get here, they become so weak that it's impossible to, you know, with today's technology to actually measure them. So I spent about a year of my life trying to prove that they are unstable.

But at the end, we actually ended up proving that gravitational waves are a very stable wave phenomenon, which is good because if I prove that, had I proved that they're unstable and then they observe them, it means my dissertation was wrong. But it was correct. Like we were able to prove that they're actually very stable. So in particular, the types of gravitational waves that really maintain a lot of things about their behavior. And that's one of the things that we were able to prove.

basically back then in the dissertation and funny enough gravitational waves were discovered about three four months after after that if I remember correctly. So that's an example of one of the things that I worked on. I also found one new solution for Einstein's equation that describes something, a weird object that is somewhat like a black hole but it's actually more cylindrical in nature and studied some of its behavior as far as we know it's not something that was observed.

til today so far yeah so

Kostas (06:24.234)
Yaron, okay, I have a question and it might be a little bit naive, but I'd love to hear and learn a little bit more about that. So you started talking about the Einstein equations and you said something about there aren't that many solutions to these equations, right? And my naive question here is what does that even mean? Like, we don't know how many solutions are out there for these equations.

And why is that the case? If this is the case, right? I don't know, like I think most people going through, you know, like the math that you learn at school is that you have an equation and the equation has some solutions, or maybe you can, maybe you can prove that it doesn't have like solutions, right? But when you hear like a researcher saying, we don't...

like we don't know how many solutions or there aren't that many solutions like that's very intriguing. So tell us a little bit more about that. It sounds like very, very interesting.

Yaron Hadad (07:25.99)
Sure. That is super interesting. It's one of my favorite things about mathematical physics in general. So Einstein's equations and the majority of the equations, not all of them, but probably the majority of the equations in physics are typically differential equations. So these are equations that describe dynamics between dynamics in systems. And typically, it's dynamics between derivatives of different functions.

So in the case of Einstein's equation, this is an equation. It's almost like this equation is like a recipe, or something that encompasses a lot of the information related to the behavior of the universe as far as we know, at least at the macro scale. The thing is, as you can imagine, one can decide to study different cases, different scenarios.

And those equations, in order to solve them, you typically need to make some kind of an assumption about the scenario that you want to study. So for example, I want to study what's going to happen next to a star. A star is, for the most part, spherical. So maybe an assumption that I'm going to put is some kind of a boundary condition, or even a symmetry that I'm trying to solve the equation in the case that it's very spherical.

Or you can say, I want to study the early universe. So I'm going to make some kind of an assumption on how things were many billions of years ago. All those kind of assumptions can be plugged in to the equations in order to try and solve them under that specific condition. Now, in general, in some cases, relatively very few cases, we know how to solve this kind of differential equations generally. So you can write a formula.

that perfectly solves the equation in all cases. And then you just plug in your assumption, and it will give you a prediction of everything that is going to happen. But in most cases, and generally in the case, definitely in the case of nonlinear equations, like Einstein's equation, we don't know how to do it generally. So we need to study it on a case by case basis. And I can tell you that a big portion of my time, I'm sharing here a trade secret.

Yaron Hadad (09:45.166)
A big portion of my time in my dissertation was, my advisor came up with an idea, hey, here's an interesting assumption. Let's study this assumption. I would have to go back home or to my office. spent sometimes, I would say the average was probably 15 hours, 20 hours to simplify the equations to a form that we can actually study and then go back to him and have a discussion about it every single time. So one of the things I did, and that's a trade secret here.

is I developed a piece of software that I could take the assumptions, plug it in. I would go boulder in and rock climbing and come back afterwards. And I will get everything simplified to a point where I can print it out and have a discussion with them about it. So yeah, so generally, are some general ways of addressing differential equations. But for the most part, it's not like, you know,

like a linear equation that you learn in middle school that has one solution and is really easy to solve. It depends on the initial conditions, can depend on the boundary conditions. I hope that makes sense.

Nitay (10:56.59)
And you touched on something there. So welcome back to the trade secret. Definitely. That sounds very interesting. You touched on something there. I was curious about kind of for our audience, how is theoretical physics done? Right? Like, like, we imagining like, you know, your own sitting, furiously with a notebook and a chalkboard, right? Because you're not going to a particle accelerator. It's all theoretical. But then you mentioned kind of using a computer to do some of the algorithmic part for you. So what is like the tools of the trade and what is how is it done these days?

Yaron Hadad (11:22.97)
Yeah, that's a good question. So probably going to generalize, but you know, I have to. But I think that generally the tools that are available for scientists are for the most part pretty embarrassing compared to what you see in the industry. Also in terms of their penetration to be used by the scientific community.

There are some exceptions to this, like tools like Matlab and Mathematica and others that are incredible. Wolfram Alpha, Wolfram, by the way, was an advisor to my first company, Neutrino, is phenomenal. There are some exceptions, but for the most part, researchers don't use tools as much as probably they should, I think.

Generally in terms of the day-to-day a lot of it involves with you know sitting in your office and either reading papers of work that other people have done or trying to you know study a set of equations and try to either solve them simplify them project them and Show them in a different way. So it's typically very tedious work. I think that with the right tool set

researchers I would say can probably enhance their productivity pretty significantly and that's one of the things that I was trying to do a couple of times with different projects that I've done in the past. One, if that's okay, I'll double click on that one. One project was something that is called the Ramanujan machine that was done in collaboration with

Professor Ido Kaminer's group at the Technion, where we basically build a tool that helps mathematicians discover new potential conjectures in number theory and facilitate that work. We can elaborate on that if you'd like. And a second thing is an open source tool that I developed in the past called SciHive. It's not publicly available anymore, unfortunately, but it's

Yaron Hadad (13:39.706)
basically a tool for collaborated work on scientific projects for researchers.

Nitay (13:46.707)
And what does that mean to find new conjectures and how does a machine do that? Right now we're kind of stepping into the AI realm a little bit, so that sounds super interesting.

Yaron Hadad (13:54.786)
Awesome. Yeah. This is a project I really love and I'm very passionate about, especially because so many people... Before Ido and I wanted to pursue this, so many people said it's not going to work, which is like one of those things you're like, have to show them this has to work. So the remuneration... Okay. So I'll take a couple of steps backwards.

You know, right now, a lot of people talk about how AI can be used for science. And in many ways, one of the, you know, some people don't treat it as pure science, it's mathematics, but it's really the foundations that a lot of science is based on. It's something that is like, you know, it's probably the one of the most abstract fields and hardest ones to study sometimes. Now, mathematicians, if I overgeneralize do

Typically two main things from a research perspective. One is trying to come up with conjectures. What is some kind of a fundamental truth that has to do with the field that I'm studying that might be correct? this as a, you know, a famous example is Fermat's last theorem. If anyone has read the book, where people knew this

about it might be true. Most likely it's true, but no one was able to prove it until a couple of decades ago. So that's conjecturing. That's coming up with the truth without even proving them. Just things that might be correct about the world. know, finding structure, finding patterns and so on. And then the second thing is proving, you know, if you have a conjecture, how do you show that it's true? Okay.

Now naturally again, I really overgeneralized, but I did it for the sake of simplicity here. And in the world of mathematics, there's been a lot of works related to what is called automatic theorem proving, which is basically building algorithms either from the world of AI or outside of the world of AI that can take a statement and try to write step by step what you need to do in order to prove it. This is something that's been studied for years.

Yaron Hadad (16:18.822)
we, with the Ramanujan machine decided to take a completely different, approach and we focused much more on conjectures. You know, can AI and generally can algorithms help us guide the future of research? What things might be more interesting to study than other others? Now, historically, the way it was done is you had, you know, some of those really famous names, famous mathematicians, or even famous scientists that had this

almost this sporadic breakthrough due to their ingenuity, intuition. know, Gauss comes up with some kind of a formula that he believes is correct. He puts it out there and then people try to prove it. And I think one of the most famous cases is actually Ramanujan himself. That's why we ended up calling this work the Ramanujan machine, who was an Indian mathematician who was a hobbyist at the beginning from a very poor background.

who said that different formulas in number theory were given to him during when he was dreaming by a goddess. And he used to wake up and come up with this brilliant, sometimes insanely complex, mathematical formulas. And for many, many years, people were able to prove the majority of them. So the majority of them, as far as we know, maybe even

all of them were correct. And what we wanted to do is instead of having to wait for a few decades for some genius to wake up from a dream and come up with conjectures, we wanted to create a more methodological way of coming up with conjectures in mathematics. And we decided to focus first on number theory. And basically, we developed a

Back in the day, in the first paper that we published on it, it was published in Nature about four years ago, I think. We developed three different algorithms from the world, at least one of them is from the world of AI, but different algorithms that can study patterns in numbers and come up with really, really beautiful formulas to describe famous numbers in mathematics.

Yaron Hadad (18:40.132)
So pi and e and the golden ratio and all of these very fundamental important constants. we, to date, already in the first paper, we found hundreds of formulas, dozens of which were known before and were discovered independently before by a lot of famous mathematicians, including Gauss and Ramanujan and Euler. But the important thing is that the algorithm didn't know that they were known before.

The algorithm came up with them by itself. And for us, those were just sanity checks. But we also came up, the algorithm came up with a lot of other formulas that were unknown. And maybe just one more comment about this. One of the things I thought it would be so inspiring to actually use that to open opportunities to younger generation and people that are not professional mathematicians to

to try and get them into math and excite them about mathematics. for me, math and physics really changed my life. And I really wanted to share that love. one of the things that we've done, so we created this open source project. There is a website. It's www.ramanujanmachine.com. Ramanujan is R-A-M-A.

N U G A And the code is open source. Anyone can take the code and run it. Today, it's even easier to run. You don't even need to know how to run code, technically. It's a Boeing project. And then you can let your computer run and find formulas. You can put certain assumptions on the kind of formulas you want to find. If your computer finds a formula, that conjecture, if it's unknown from before, is going to be named after you.

So you can have a Nittai's conjecture, for example. If you build a new algorithm, we'll implement it, put it into our system, and it will also be named after you. And if you can prove one of those conjectures, then you'll have a new formula named after you. So then you can have the Costus pi formula, for example. And you know, that was just amazing to see how powerful our communities

Yaron Hadad (21:07.035)
work collaboratively with AI in a sense, with algorithms. All of a sudden, there are like over 10,000 people that were supporting this project in different capacities. The youngest person that we had that actually proved a formula was, I believe, a 15-year-old girl from Israel that actually proved a new formula, wrote a paper about it, someone who never wrote a paper and wasn't a professional mathematician.

and you just see the opportunity of bringing science to the masses, how much knowledge it can create and how exciting it can get.

Kostas (21:48.007)
This is amazing. How was this whole work perceived from the scientific community? Because you mentioned, okay, like a 15 years old kid there, community of like 10,000 people, like open sourcing. I'm sure a lot of these people are just amateur people who found, you know, like...

a safe space for them to explore mathematics without the pressure of being at school and having to prove something and actually find the beauty in all that stuff and be creative. But how was the scientific community? Because I'm sure you had mixed reactions to that as usually happens.

with this very traditional and very kind of rigid systems for creating knowledge that we have as humans.

Yaron Hadad (22:46.52)
Yeah, I love that question. So you're right. mean, we got very conflicting feelings about this from the professional academic community. There were many, researchers that absolutely loved it. I'm starting with the good in many ways, that absolutely loved it and promoted it and mentioned it.

both online and some of them even in their work. Some of them started writing papers based on that, which was really, really cool. I'm trying to prove some of our conjectures, including really like top tier researchers and mathematicians. However, naturally, there was also some conflict. So we did get some, you know, you want to call it almost like a

fight, I don't know if that's the right way to describe it, but we did get some resistance, let's say, by some of the more traditional mathematical community. I think part of that is because of the way we approached it. I felt, and I think our extended team actually felt, like the right thing to do would be to promote this in all channels. This is not just the work that we want to share with professional mathematicians.

This is for everybody. Kind of like the goal is to lower the bar of getting into it and get more people excited about mathematics, about science, about algorithms and about what you can do when you put all these things together with creative people. yeah, that got a lot of resistance. I used Twitter to promote the work. I started creating animated GIFs of formulas and promoting them. And we actually, there was specifically even a...

couple of researchers that decided to turn this into a head on battle in many ways, writing blog posts about why it's a fraud and why there were sentences like Silicon Valley is trying to penetrate mathematics with marketing or weird sentences like that. And that conspiracy and those conflicts.

Kostas (24:59.338)
You

Yaron Hadad (25:09.88)
Ironically, like at the beginning, it wasn't easy for me to see it because I was really passionate about the project and it came from, from all of us, it came from a very sincere place of trying to build something that allows to do mathematics differently, faster, using a crowd of individuals and not just, you know, professional mathematicians necessarily and so on. So it came from a very sincere place of trying to do things differently in a novel way.

So at first it was a little hard for me to see all the backlash. But ironically, think that all in all it was for the good of science because I think that a lot of that intense debate online is what made the work so successful eventually and what made so many people get attracted to it and wanting to explore this further. So it was covered.

from a PR perspective in so many places without us even trying to do anything about it. in Wants to be a Millionaire, on YouTube you can probably find a few hundreds of videos that people created about the work and so on. But yeah, it wasn't an easy one.

Nitay (26:19.104)
That's amazing. I was going to say that them attacking the project was probably what made it popular. as they say, kind of there's no bad PR as the saying goes. And I love the dating myself a little bit, the kind of set it at home nature of it. Like anybody can grab the project, run it for a while and find some things that get their name. What, tell us a bit about, friend, maybe a couple of minutes of like, so how does it work? Like you mentioned, you know,

Kostas (26:20.201)
Yeah, there are...

Yaron Hadad (26:27.92)
Yeah.

Nitay (26:48.994)
Gauss and Euler and whatever, like you don't have any of these things built in. How does it find these conjectures and what knowledge does it have and how does it evolve?

Yaron Hadad (26:57.476)
Yeah. Yeah, so today there are, so how does that work has multiple answers. It really depends on which one of the algorithms we're talking about because there are different algorithms that we developed. So by the way, today there is, as I said, like a Boeing infrastructure that anyone can run. There are the different algorithms that actually do the actual conjecturing.

And the way we approached, maybe I'll mention just one of the algorithms, otherwise it might be too long of an answer. But just as an example, one of the approaches for one of the algorithms that proved to be one of the most successful ones is based in an algorithm called MITM, so Meet in the Middle. And basically, idea was to take

You know, an equation has two sides, the left-hand side and the right-hand side. And for that equation to hold, the two need to match. So what we do, we look for one side of the equation that has, you know, different patterns related to a constant of choice that you choose. So when you run the algorithm, you can say, you know, I wake up today, today's Tuesday, I want to find a new formula for pi. So you can say, I want a formula for pi.

And I want that formula to meet certain constraints. So what the algorithm does, it starts generating a lot of combinations for that left-hand side and approximating them up to a certain number of decimals that you get to choose. But it also takes the right-hand side and it tries to find different patterns that may fit the formula for pi that you wanted.

We only look for formulas that have this infinite nature to them. It's called continued fractions. So basically, if one of you have seen, it's really hard to describe formulas in, know, when people listen to it, it will be so hard to catch, but I'll do it anyways. But for example, there is a very famous formula for the golden ratio that you can write it as 1 plus 1 divided by 1 plus 1 divided by 1 plus 1, et cetera.

Yaron Hadad (29:23.078)
and it's recurring forever for you to converge to the golden ratio. our earlier algorithms were only looking for those kind of formulas, and they basically tried to match different patterns on the right-hand side to the pattern of the constant that you look for on the left-hand side. But what it is that they do, they don't start testing things up to a very high number of decimals. You basically create hash tables of the different size, and you try to match them.

And as you find signal, we like to say, as it clicks, as two terms on the left and on the right seem to be matching, we start diving deeper and calculate more and more decimals until it's getting validated to a very high number of decimals. And once you have a match, that means you found a conjecture, basically. Maybe one last comment related to this. So.

the new couple of papers that one was published, another one that will come out, because that project ran on such scale. mean, hundreds of people ran the algorithms on their computers. And we found so many formulas in the later iterations of it, probably in the last year. Now, I don't know the exact number, but it's probably over 10,000 different formulas that were found. We actually...

had a couple of the students that were working on the project were looking at the formulas and they're like, whoa, there is like interesting patterns between different types of formulas here. And they were actually able to find a mathematical structure that generalizes formulas for pi, for e, for the golden ratio, and for a lot of other very, very famous constants in mathematics, all under one mathematical structure. So right now we have a whole

very mathematical project that is taking place in order to study that structure. Because it seems like it generalizes probably every known formula of that type for those constants, by the way, and beyond, including very famous formulas from Gauss and Ramanujan and Euler. Yeah, so I know it's a little technical, but it's already showing that it has a lot of fruits in the world of mathematics.

Kostas (31:42.824)
Yeah, that's amazing. Yaron, before we move forward, one last question about the haters that helped also with turning this into a viral project. So we should thank them for that. What was the scientific criticism? Because, okay, like people might not like the way that things happen in terms of who gets access to things or what the process is and like all that stuff.

That can be valid too, right? Like the scientific community has their own ways. They have a reason that they have it. When it gets challenged, of course there's going to be resistance. That's like human nature. But there has to be also some like scientific debate about it. Like if someone says, this is fraud, they have to say something. Why it's fraud? Like what's the problem with it? What's wrong with the algorithm or what is wrong with...

whatever let's say conjectures or formulas come out of that. So what were like the most valid let's say that you've heard from their side?

Yaron Hadad (32:49.592)
Absolutely. So I think the most valid point against what we did, which is a point that we spent a lot of time on, think it's really hitting the nail on the head in many ways, is the following. The algorithm found a lot of different formulas. Some of those formulas were formulas that were known in the literature.

others were not known in the literature to the extent that we can tell. So here are two interesting questions related to them. One, are they really unknown in the literature or did someone already find them before? Okay, that's like a search engine problem for a formula search engine problem. A second question is, let's say it's a new formula that wasn't known in the literature, is it interesting in any way or is it like completely trivial?

Is it, you know, it might be, you can take a known formula, multiply it by two on both sides and you get a new formula in a sense. But at the end, there is nothing fundamentally new about it. so some of the, rejection that we got by a couple of folks in the mathematics community was about, about that point. They cherry picked a couple of formulas from the, I don't know, 700 formulas and said, Hey, you know, I can prove this.

in one line. This is not interesting at all. And it's true that some of those formulas were not interesting mathematically because you could prove them very quickly and very easily. And they're almost trivial in that sense. But I do think that it beats some of the, you know, it misses some of the point. The point is the algorithm did not know this. Okay. That's one thing. The algorithm doesn't

try to quantify how complex it is to prove something. It just tries to find conjectures that appear to be true. And in that sense, they're completely valid formulas. But I do think the point was interesting because at the end, the potential impact of this is really a function of how meaningful and non-trivial and novel these formulas are. And back then, like at the beginning, it wasn't completely obvious.

Yaron Hadad (35:14.97)
But I can tell you a few years after right now, and I think that's one of the reasons Nature decided to publish this paper, is because there are so many formulas that were unknown, including some formulas there that were still until this point are not proven. So in general, definitely opened a new realm and a new way of thinking about the way we do this. And I also, as far as I know, that this new mathematical structure that we found, I mean, this generalizes work.

Kostas (35:28.297)
Mm-hmm.

Yaron Hadad (35:44.378)
that has been done in the last probably roughly 300 years by so many famous mathematicians. So I think that the merits of this approach at this point becomes obvious, but back in the day it wasn't.

Kostas (35:49.812)
Yeah.

Kostas (35:57.862)
Yeah. One last question from me and then like I'll let Nitai like take the mic and ask his questions. Do you think that if you didn't choose number theory as the fields to implement that things would be a little bit easier because number theory is kind of this special thing in mathematics and in human intellect that we are really proud and we...

sure like mathematicians consider it as like, you know, like it's like the pure form of mathematics of like reasoning about numbers and like probably like mathematics in their purest form in a way. So I'm trying to add a little bit like the human factor in that. That's why I'm asking that and especially because you are coming from physics, right? And you know, like

You were talking at the beginning about like partial differential equations, for example. It's like a standard thing where like, okay, we know we don't have general solutions for that. So we have to work with approximates many times. And many times we come up with assumptions, we get a solution, but the solution actually is like either trivial or it doesn't matter, right? Or we cannot move forward in that. And I think like physicists in a way are like more comfortable with that than...

pure mathematicians that live in the realm of this platonic world of number theory. So do you think that if it was a different field, if it was, let's say, you use it in the PDEs fields, you would have a little bit of a different reaction at the end?

Yaron Hadad (37:39.256)
Yeah, so the reason I'm smiling is because I'm trying to drag my colleagues, Edo and others, to work specifically on ODs and PDs, but that's a longer conversation. But I do think that the choice of field or the choice of subfield really affects how easy it is to get the community to accept it. Today, you can see AI being

leverage and use for scientific discovery in a lot of different fields, material sciences, chemistry, some places in physics as well, and so on. But it is worthwhile saying there was a very specific reason why we chose number theory after all. Initially, we wanted to do it for physics. We wanted to build an engine that finds formulas that, say, can compute the fine structure constant.

you know, find a pattern in it that maybe no one knows about or, you know, find relationships between masses of particles. Maybe there is a hidden structure there that physicists don't know about. That was the initial goal. And the reason we didn't take that route is because physics is physics. So in physics, unlike in number theory, you know, if I know a formula up to seven digits, if I want to get two more digits for that formula,

I will need to probably build something in hundreds of millions or billions of dollars to do an experiment. Well, in number theory, it's really nice, but you can technically calculate numerically anything you want to as many decimals as you want. So in that sense, it's much easier to generate like a ground truth, not in the sense of pure AI ground truth, but in the sense that it's very easy to know if something is valid or invalid.

where in physics you can find a formula that fits the error range, but is it correct or incorrect? Now, if I may elaborate, I do have this side project that I've been doing for the last few years and I haven't published it. Here I took another famous scientist. It's called the Planck machine. I should actually post it on archive probably soon. I've been wanting to do it for the last year. And it's...

Yaron Hadad (40:00.568)
analogous idea to what we've done with the Ramanujan machine, but it actually does it for constants in physics. The problem is that, again, if you do it for constants in physics, you run even my computer with this algorithm on it, after 24 hours you get 10,000 formulas, because you can find so many formulas that fit the error bars that we have at the moment in physics. So one of the things we did there that is slightly differently, we invented this beauty concept

And we asked computer only to highlight equations that are beautiful enough. And we defined beauty as simplicity, which might be a wrong assumption. But we had somehow to find a way to distill the formulas that you get. I can share with you afterwards. I have a 300-page PDF on my computer with formulas that how do you know what's useful or not?

But that algorithm was able to find very famous formulas, Bohr's radius, Compton wavelength, et cetera. But it also was able to find a lot of other formulas related to masses of particles, for example, that as far as I know are unknown in the literature. Now, the reason I still haven't published it is because I was trying to find a better way of validating it than that.

God's I don't have one.

Nitay (41:25.87)
I love this, the plank machine that you talked about, because I think one of the things we've seen with AI in general is it's much, much harder to make AI produce something simple than it is to produce something complex. You people often forget pretty much every AI, LLM, et cetera, training machine there is, you've got these billions of parameters and so on. There's always some part of the loss function that's trying to reduce the complexity of the parameters themselves. There's always something that says the smaller the parameters, the less parameters.

do a bunch of dropout, do a bunch of whatever I can to make the solution as simple as possible. And so one question I have before we move on, kind of tying a lot of what you've said here, we've talked a bunch about generalization and making things that are kind of flexible and able to conform to a bunch of different areas and adapt. What is like?

I guess I would ask it as what is Yavon's grand theory of the universe? What I mean by that is, physicists for a long time have been really studying the world looking for this one grand unifying principle, right? The four forces, quarks, maybe the world is actually run by strings, all these different ideas. If you fast forward 100 years, where do you think we will be from like a physics understanding of the world?

Yaron Hadad (42:49.798)
Where we will be or how far we will be from...

Nitay (42:54.422)
Where will it be in terms of understanding the fundamental nature of physics and what the laws that govern our world? What do you think we're trending towards?

Yaron Hadad (43:04.814)
Yeah, interesting. Yeah, I think we'll be closer, but I think we'll be very far still. I'm trying to think how we will start answering this question, because you can unfold it in so many different ways.

Yaron Hadad (43:26.768)
So, I think that physics as a general trend has been going in a more abstract way, I think, than it did in the past a little bit, and the mathematics that we need in order to understand the most modern physics today is much more complicated and complex.

than the mathematics that was used in the past in previous theories. And it's OK. I think it's almost a natural process. But I do think that if I had to guess in the next decades, there's going to be a combination of multiple things that would happen. I hope, I very much hope, that we'll find more anomalies related to the theories that we have at the moment.

Today there are some anomalies related to the universe as a whole. You can talk about things like dark matter, dark energy. Generally everything that has the word dark related to it in physics is typically something we really don't understand. If I had to guess, as the precision of the tools that we have gets better, as the scale at which we do things get better, as we live...

and travel in space more, we'll start discovering more anomalies. That's also a hope. It's not just a prediction, but I think it will be more exciting that way. So let's say I hope it happens. But I also think there will be a lot of opportunities for unification. I personally, and I know this is not necessarily a popular opinion, but I think that in many ways, the

The way the scientific community explained certain fundamental phenomena related to particle physics is through complexity. Like today, particle physics, there's like a zoo of particles. You have the standard model. You can make certain predictions about it. And we have Lagrangian that describes it and formulas and so on. But the way we did it is by introducing more more and more complexity into our theories.

Yaron Hadad (45:50.278)
And this is exactly where I hope there'll be breakthroughs in simplification. One of my favorite things related to it, I know there is this dream of grand unified theory that you mentioned. And today, one of the things that stand in the way of the community finding that is basically uniting general relativity and quantum mechanics, right? Or quantum field theory.

And we're not there. We have one research project that we do also with the dough related to it. And one of the reasons is that the two theories, general relativity and quantum field theory, the standard model are just so vastly different mathematically. They're really different. And I think that one of the things that historically happened in this kind of situations where you have, where you're trying to move forward.

in these kind of situations is a lot of it has to do with giving up, know, forfeiting certain assumptions that everybody has. And if I had to guess, there is probably at least one or two assumptions that everybody is taking for granted in the physics community and potentially even much beyond that are not allowing us to put those things together, if I had to guess. And I do hope that as time goes by, there'll be more experimental data.

We'll start implementing new tools from the world of AI also to help us understand it. We may be able to find which assumptions we're making that is potentially wrong in order to come to a new theory. I don't know if this is exactly answering your question, but I decided to take it in this specific route.

Nitay (47:40.45)
Yeah, no, that's super interesting. A physics rewrite, if you will. That's fascinating. Very cool. No, this is really interesting stuff. OK, so let's move on a little bit. So as you said yourself, you kind of came down to Earth after doing all this cool physics, number theory, conjectures, and so forth. So tell us a bit about the neutrino and what you built there.

Yaron Hadad (47:44.366)
I wouldn't. Long due.

Yaron Hadad (48:09.798)
Awesome, sure. So maybe if it's okay, I'll share very briefly my history with nutrition because it really helps explain what the trino actually build and why. But I used to suffer from different health related problems when I was younger for many, many years. Anything from migraines, I was very overweight, could not even move much. And eventually I found out that it might be related to the food I'm

Okay. And I went through this very long journey from the ages of 16 to 19, 20, roughly, where I used to do this N equals one experimentations on myself based on what I studied in the literature. So I read back then, I think about 200 different nutrition books over that period of time.

And I was obsessed about nutrition. Once I discovered that the food I'm eating can actually be the thing that is making me feel worse, I was fascinated by it. The problem with nutrition, and this is what Neutrino in a nutshell was working on solving, is that nutrition is really freaking complicated. I hope I can use this word here. Nutrition is really complex. It's exactly the kind of places where you think

AI can give humanity an edge all of a sudden because we're pretty bad at analyzing complex systems. Nutrition is complex and you can cherry pick two random books from a nutrition bookshelf in any store and most likely they're going to give you lot of recommendations that contradict one another. Okay, almost certainly actually. You know, you should be a fruterian, you should do a keto, low carb, you should be a vegan, you should eat a Mediterranean diet and so on.

And maybe just like another random piece of information, but in nutrition, there is over 10,000 papers published every year, only in English. And I think there is the number of diets in the space is about 800 different diets. It's a very confusing space. And I did a lot of experimentation on myself. I basically tried 24 diets in those three and a half years, each one for one to four months.

Yaron Hadad (50:36.07)
and measured and tracked what things did to me. And in many ways, Neutrino was trying to take the same process, the same journey that I went through and make it as short as like a couple of days instead of you having, or like let's say two, three days instead of you having to spend years of your life trying to understand which foods are better for you. So fundamentally, the basic question that we were trying to answer is what should I eat? Okay. Very, very simple question that I think a lot of people can connect to.

Now, in order to do it technologically, we invented a concept called foodprint. So foodprint is like the digital signature of how food affects your bodies. And in order to find the footprint of a person, we had to overlap two types of data. The first is information about foods. That's something that when we started the company, I was hoping we could license, but we couldn't find a good enough database.

But we basically build this autonomous system that goes and analyzes food information, both on recipes, packaged foods, menus of restaurants. And if you want, can dive deeper into that, but we build a lot of IP and a lot of technological assets around that piece. And the second part is information about individual biomarkers.

And we build this very rich infrastructure that can collect information continuously from a wide range of data services, health tests, wearable devices, and medical devices. I think before the acquisition, there was 420 different data sources related to a person's body that neutrino could connect with. My favorite one was a CGM, a continuous glucose monitor.

And basically what people did when they used Neutrino, they went through this very simple process where you put a device out of different ones that we worked with on yourself, capture pictures of what you're eating for a couple of days. And then we will give you a complete mapping, a complete analysis of your body and how different foods affected from a health perspective. So that's in a nutshell. Long answer.

Kostas (53:01.076)
So, Jarom, you said you were collecting data from like probably 400 different sources. You have your favorite, you mentioned it already. So from your experience, how you drank the sources in terms of, let's say like the importance for understanding like yourself and how you interact.

with food, which are the more important ones. And most importantly, where do you think there's space for new devices or new techniques to come in so we can measure more and more interesting data for that stuff?

Yaron Hadad (53:46.864)
I love this question because I think that the space right now is just so, it's still lacking in many different ways. And there are a lot of opportunities to build new companies here. yeah, so first of all, and very unfortunately, you see a lot of nutrition companies that are trying to place a bet on a specific data source. Neutrino took a much more...

general kind of like a universalist approach because different devices are more important and can measure things that are more important for different individuals depending on your health goals and depending on your background and medical needs. Unfortunately, still today there is no, you know, one device to rule them all that I can say everybody should use this device and it will tell you everything you need about your health. It doesn't exist, okay?

maybe in 10, 20 years from today, hopefully, but at the moment it doesn't exist. You know, I personally, my favorite one, you know, if I had to choose a single biomarker I could measure for myself, I would probably choose insulin for different reasons. We don't have today a continuous way of measuring insulin, unfortunately. It's a pretty difficult molecule to measure, but the closest thing,

is glucose, and that's one of the reasons why I was so excited about continuous glucose monitors. The best thing about glucose that is not always true for other devices, so for example, you can measure your weight. The thing is, I just have this protein shake, or I can eat a meal. I won't see much happening to my weight, either of them, roughly the weight of the meal, adding to it. But generally, if you look at most devices,

there is a certain latency between the events of what it is that you're eating or what you're doing and its effect on your body. And the cool thing about a continuous glucose monitor is that usually within 15 minutes, you'll already start seeing the result of you eating something on your glucose level. So it's almost, it's not instantaneous, but almost instantaneous. And it correlates.

Yaron Hadad (56:04.778)
And it's very much directly related to the behavior of insulin in the body, which is, you know, the principal regulator of fat storage. It's related to insulin sensitivity and to diabetes management. In many ways, it's also related to other diseases related to the brain, cardiovascular. So that's, that I would say is probably my favorite one. And, but generally in terms of important would really depend on what it is that you're trying to optimize for. Right. So someone with the.

Kostas (56:33.499)
Mm-hmm.

Yaron Hadad (56:35.002)
I don't know, high blood pressure, should try and get a continuous blood pressure monitor naturally. Yeah. So I, you know, maybe one last comment related to the last part of your question. I think there will be a lot of very interesting, there are already a lot of very interesting opportunities to build continuous devices that measure post-predial responses. So there are different things that happen in the body immediately after you eat a meal. Okay.

Kostas (56:39.678)
Mm-hmm.

Yaron Hadad (57:05.254)
that you can potentially track. Unfortunately, there aren't a lot of devices that track those biomarkers, but you you could measure, we already mentioned glucose, blood pressure, fatty acids, amino acids, lactic acid, ketones. There is a lot of things that if you knew exactly what happens, you can really start to extract very powerful insights about a person's health.

Kostas (57:29.674)
Okay. And let's say you get one of these glucose, like continuous glucose devices, measuring devices. And what I find like very interesting and kind of like challenging also, to be honest, is that you have a very simple metric, right? Like at the end of the day, you put this thing like on your skin, starts like measuring gives you like, I don't know, like one dimensional like data.

But what this thing gets affected by, by like a very complex thing. Like let's say I eat a donut, right? Like a donut, like in order like to build it has, I don't know how many different ingredients in there, right? So sure, I eat the donut. I have a feeling that like probably the sugar is like doing something there because it has sugar. But going from these, how to say that, like very complicated.

that I put in my body, which has gone through a lot of processing also, right? Like it's not, I'm trying like raw sugar or just protein or just fat. It's a much more complicated like compound that I'm putting there. How do I connect these two? And okay, obviously you dedicate yourself building a whole company around that, but I'd like to hear from you how you think before you...

formulate these into software and all these things. How do you connect them? To me, it feels like it's very... The complexity can be too much and reducing it, it's not an easy task.

Yaron Hadad (59:12.47)
Yeah, you're completely right here again. Yes, I mean when we initially started, the answers to some of these questions was not completely obvious from the very beginning. We were hoping that we'll be able to just use a few basic pieces of information about food in order to predict really well what's going to happen. So basically the macronutrients.

To some extent, you can, but you won't get the same level of precision naturally. And that's one of the reasons we ended up building what I described before as the first type of data that we leverage in the system, which is the food-related data. So we built this autonomous food analysis system that analyzes food from different sources. And foods were mapped into an ontology.

So at the end, had a lot of different layers of data on the food, anything from micronutrients, micronutrients, ingredients, the way it was cooked, the way it was processed, and also a very precise way of handling with imprecision, because imprecision is inherent in nutrition. Nutrition, fundamentally, there are a lot of things that are not measured accurately, and we can talk about that.

And we had to find a way to address that in a scientific way. So the system was designed from the very beginning. It was architect to support unknowns, right? Uncertainties. Now, once we had this foot ontology, we basically developed a set of algorithms that are trying to find patterns between information in the foot ontology and what happens in a person's body. The problem is, and

it's even amplified more with glucose is that it's not just about food. It's much more holistic. I hate this word, but it's true. The body, there are many things that are affecting the way we process food. So specifically with glucose, let's say the three of us are going to eat an apple, even the same apple or the same bar, we're going to see different responses.

Nitay (01:01:31.758)
you

Yaron Hadad (01:01:34.8)
But not only there's going to be interpersonal variability between each one of us process food differently because we have different metabolism, different physiology, et cetera. Also, if I will eat an apple separately at two different occasions, the responses might be somewhat different. Okay. So there is also intrapersonal variability. It depends in the conditions in which the person consumes the food. So that took us to a path that we found out.

You know, it's not just about food. I wanted to start a nutrition company, but dang, you know, to start a nutrition company, you need to start doing a lot of other things. so generally, maybe as an example, but like glucose is affected by food, is affected by physical activity and exercise and movement. It's affected by stress. It's affected by sleep, you know, so a lack of sleep for one night can really amplify the responses that you typically get.

It's affected by menstrual cycle for women and a couple of other things And we had to build an algorithm that takes all these things into account together. So a big portion of the company Spent a lot of efforts in identifying all the different features that actually need to be integrated into the algorithm for the algorithm to even be able to find the patterns and Okay here maybe maybe here's something that really surprised me

We tried to take an AI first approach for everything because we really believed in it. was early days, but we really believed in it. But we found out that with the existing data that we had at the time, and we had more data than any other company in the world as far as I know, AI could actually not make those predictions well enough in all cases. So one of the things that we actually eventually built was a biomethematical model. So a model of equations, right? We started the discussion talking about differential equations.

I guess we'll finish it with as well, but we developed a set of a couple differential equations based on work from the literature that was done that describes the physiology or the physics of glucose absorption and how it interacts with insulin in the body. And the place where we use the AI specifically for glucose was instead of using AI to try and predict the whole glucose curve,

Yaron Hadad (01:04:04.314)
which is a problem that is very, let's say, it's pretty under-determined in the sense that there is so many inputs, and the output is also relatively complex. It's a continuous function. So instead of that, we had a differential equation. The set of differential equations, those we could solve. But the solution would just depend on a few parameters. You don't need to know the exact.

form of the function. So all the AI needed to do was to predict a few parameters. So basically we used physics or mathematics in order to simplify the problem. And we used AI to actually make the predictions. And that's what ended up being the most successful route in order to solve that. But the approach was slightly different depending on the biomarker that we studied.

Nitay (01:05:01.634)
That's really fascinating. Perhaps one last question to close us out. You mentioned a lot about the lagging time in the signals. You mentioned clearly some very sophisticated algorithms. You mentioned kind of the lack of standardization, many different devices and so forth. What is like if you had to place a bet on just one, what would be the future thing that would help the nutrition ecosystem the most out of these three? Where is the biggest gap?

Yaron Hadad (01:05:26.406)
Can you repeat what are the three options here?

Nitay (01:05:29.548)
So either we need a better signal, better way to get glucose signal, better way to get insulin, et cetera, or some better algorithm, the differential equations you built, or some more standards in the space. Because it sounds like you guys were kind dealing with the mess of all three things. I'm curious which one is holding back the space the most and where you would like to see nutrition as a field to get to in the future in terms of solving it.

Yaron Hadad (01:05:55.524)
Yeah, interesting. So I think that from a software perspective, know, what Metronik owns today from Neutrino addresses the majority, obviously, it's never all, but the majority of the concerns around the algorithms, and obviously, things can be improved, etc. But I would say that's not the key bottleneck in that space. If I had to guess, it's, you know, it's a person, it's a...

It's an opinion, but I would say that the quality of the sources of data about an individual body is still the main bottleneck. So what other devices could one build that measure biomarkers from the body, ideally passively, ideally continuously, and ideally non-invasively, right? So CGMs today are invasive. They have a little needle.

It's not a big deal, but it's still not for everybody. So I think if I had to say that will have the biggest impact on the world of nutrition is if there were better devices.

Nitay (01:07:06.766)
That makes a of sense. Cool. Well, this has been really fantastic. have pages of notes. I feel like I learned so much on this episode. So thank you again for joining us. We'll have to definitely do it again soon, continue the conversation. And appreciate it. It's great.

Yaron Hadad (01:07:13.766)
Thank you.

Yaron Hadad (01:07:21.848)
I would love that. Thank you so much, guys. Great questions. yeah, I'm looking forward to hearing what your audience thinks about all of this and if there are any follow-up questions in the future. Appreciate it.