This 24-Year-Old Founder Raised $64M to Build World’s First AI Mathematician | Axiom, Carina Hong
If an AI Mathematician can reason and prove on its own, how will the future change? Carina is a mathematician and the Founder and CEO of Axiom. She started the company at 24, and Axiom is building an AI Mathematician with a $64
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Intro
- 00:00Math is full of hardship. Math research
- 00:02is a process of almost a monk praying in
- 00:06the temple [music] day after day. Keep
- 00:08pushing harder and harder. The dopamine
- 00:10hits feeling is a little bit like Quinc
- 00:12Gambit feels natural, effortless. You
- 00:15can look at how far [music] you have
- 00:17come in the competition. So usually the
- 00:20clock is ticking.
- 00:22I think that feeling is just really
- 00:24amazing. It's exhilarating. If you have
- 00:27a hedge fund being able to afford the
- 00:29quant researchers typically paid at 14
- 00:32million each year starting but that AI
- 00:35mathematician um at $5 each hour and
- 00:38then you are able to suddenly afford to
- 00:40tackle a market of total trading volume
- 00:42of say 8 million because that market
- 00:45likely has not been deeply studied and
- 00:48previously it was not considered a
- 00:50target. We are entering an era of mass
- 00:53intelligence and an AI mathematician is
- 00:56a crucial part of this future.
- 01:07Hi, I'm Karina, founder and CEO of
- 01:09Axiom. I was a mathematician for most of
- 01:11my life. I did math and physics double
- 01:14major at MIT where I plunged into the
- 01:17ocean of mathematics. worked on very
- 01:19interesting research projects that
- 01:21settled some open conjectures and then I
- 01:23was a rose scholar at Oxford pursuing
- 01:25degree of neuroscience and that year I
- 01:27also stumbled into AI at the UCL Gatsby
- 01:30[music] institute which is basically the
- 01:32home of deep mind after that I was at
- 01:34Stanford as a Hennessy scholar pursuing
- 01:36a joint JD PhD then dropped out to Dar
- 01:40axium and we are building an AI
- 01:41mathematician that is the first model
- 01:44that will eventually evolve to be a
- 01:46self-improving super intelligent
- 01:48reasoner To build an AI mathematician,
- 01:50you need three pillars. AI, programming
- 01:52languages, and mathematics. Because of
- 01:54this vision, we assemble a world-class
- 01:57team of experts from each of these three
- 01:59pillars coming together. So, it's a very
- 02:01interdisciplinary approach. Axiom
- 02:03[music]
- 02:03was fortunate to raise seed round of $64
- 02:06million. Investors value us at 300
- 02:09million valuation. I'm 24 years old.
- 02:15My background is in combinatorics and
Why Math Will Save the World
- 02:17number theory. It's about patterns.
- 02:19Patterns [music] everywhere in sets and
- 02:21numbers. There are correspondences that
- 02:24are unexpected. I love just everything
- 02:26number theorist. Uh obviously golf.
- 02:29[music] Reading about golf's life was
- 02:30also very inspiring. All these aha
- 02:33moments, all the long nights when he was
- 02:36pushing for an Eureka moment. Um just
- 02:38fantastic. [music] I think it's the
- 02:40crown draw of mathematics. Um, as GS put
- 02:43it, it's [music] quite beautiful and it
- 02:45feels simless compared to other fields
- 02:48of math. [music] So, it's a lot of
- 02:50symbolic expressions. The symbols, they
- 02:53actually look beautiful on the sketch
- 02:55paper. I just remember I want to be a
- 02:57number theorist. In the history, every
- 03:00mathematical tool after its invention
- 03:02has [music] led to terrific
- 03:03breakthroughs not just in fundamental
- 03:06science but also in real world
- 03:07applications. [music]
- 03:08For example, the invention of abacus
- 03:10that has led to the bloom of trade and
- 03:12commerce. Think about integrals and
- 03:14calculus that led to mechanics and
- 03:16thermodynamics. The rest is history.
- 03:18It's the industrial revolution. If you
- 03:20think about babbage engine or the
- 03:22difference engine that is a math tool to
- 03:24calculate log table faster that is the
- 03:27prototype of computer. So
- 03:29aromathematical tool kind of sparks
- 03:31[music] the flywheel in real world
- 03:33applications and in turn requires more
- 03:36computational tools. So [music] there is
- 03:38this theory of Javon's paradox which is
- 03:40when the price of a tool becomes elastic
- 03:44[music] you will then have unexpected
- 03:45use cases and applications hence
- 03:47requiring more tools and making these
- 03:49tools in turn more valuable by building
- 03:52an AI goals at your fingertip. [music]
- 03:54We think there will be so many
- 03:55magnitudes of use cases and markets
- 03:58being [music] unlocked
- 04:00and pragmatically if you think about the
- 04:02time span of a mass invention to say the
- 04:05real world application that has in fact
- 04:08spent centuries. AI compress this
- 04:10timeline. If you think about AI
- 04:12mathematicians working together with
- 04:14applied scientists which by the way
- 04:17human mathematicians seldom work with
- 04:19applied scientists. Now AI
- 04:21mathematicians can go on to these
- 04:23applied [music] fields and solve the
- 04:25complex system that have never been
- 04:27theoretically understood. And we think
- 04:30that's incredibly powerful and will
- 04:31shorten the century long time span to to
- 04:36much shorter.
Problem Solver to Theory Builder
- 04:41I grew up loving math. Every time you
- 04:43solve a math problem, you will get that
- 04:45instant reinforcement of um this is the
- 04:48thing that you love doing, you want to
- 04:49continue doing it, you get this little
- 04:51dopamine hit every time you solve an
- 04:54Olympic math question. I think it's an
- 04:57elementary school at fourth grade. It
- 04:59was about 1,000 really bright kids being
- 05:02assembled into 24 classrooms and try to
- 05:05compete um after each exam. It was a
- 05:09little bit stressful just because you
- 05:11know after each exam you are being sort
- 05:13of ranked and then it's a whole system
- 05:15and only the ones that perform
- 05:17outstandingly can go to um the next
- 05:20level but also it was just eyeopening. I
- 05:23was able to read the proof of quadratic
- 05:26reciprocity. I was able to look at the
- 05:29names of the mathematicians that I've
- 05:31never known or never heard of. And there
- 05:33are some French and German
- 05:35mathematicians. So you kind of wonder,
- 05:38you know, what it's like to visit the
- 05:40French and German research institute. It
- 05:42feels like intellectually exploring the
- 05:45world and that felt really motivating to
- 05:48try harder, do more exercises and to do
- 05:51really well in the exams. I remember the
- 05:53elementary school math Olympia problems
- 05:55are made to be quite fun and interesting
- 05:57formulated actually in a real world
- 05:59scenario, right? like two trucks going
- 06:02across each other and um how long each
- 06:04truck is and how long does it take for
- 06:06them to pass each other. Convert that to
- 06:08mathematical formulation to equations
- 06:11that feels trackable and you can solve
- 06:14without paying much attention to what
- 06:17the real world problem is. I think that
- 06:18process was quite magical to me. Right?
- 06:20And then you solve it and you plug that
- 06:22back in. What does that tell you in the
- 06:25real world scenario? I think that's very
- 06:28beautiful process and it's mathematical
- 06:30thinking that it's very transferable to
- 06:32other fields.
- 06:35At one point I do think that I got
- 06:37introduced to research math and that was
- 06:39eye opening. I think that research math
- 06:42is a lot more delay gratification.
- 06:44Research problems is really hard and it
- 06:46takes you a long time to figure it out.
- 06:49You don't have that dopamine hits
- 06:50anymore. I mean, if you're a mass
- 06:51Olympia student, you can solve a dozen
- 06:54problems each day and feel good about
- 06:55yourself. A dozen months has passed, you
- 06:57have done nothing. That's usually the
- 06:59status of research math if you encounter
- 07:02a bottleneck in the problem. So, I
- 07:04wanted to be a better mathematician. Um,
- 07:06kind of changing from a problem solver
- 07:08to a theory builder. And for that, I owe
- 07:11um to a lot to my mentors that teach me
- 07:14how to do research, how to be patient,
- 07:16how to look around the corners and look
- 07:18for unexpected connections. um from
- 07:20another field to the current problem.
- 07:22That was why I got into research and
- 07:24continued um the fruitful collaboration
- 07:27with um professor Ono and other
- 07:29collaborators. [music]
- 07:30The feeling that you can develop new
Why Taste is Important in the AI Era
- 07:33mathematical theories [music]
- 07:35based on how the flow of past theories
- 07:38go is quite fascinating. You will
- 07:41[music] invent definitions in the
- 07:43natural way. You will link these
- 07:45definitions together to formulate
- 07:47[music] interesting conjectures. And you
- 07:49know what does um natural mean? What
- 07:51does interesting mean? And then after
- 07:53you formulate that conjecture, you prove
- 07:55it in an elegant way. What does elegance
- 07:57mean? These are questions about taste.
- 07:59And I felt like by learning so many
- 08:02[music]
- 08:02um branches of math, I started to form
- 08:05my taste about math. And I think in an
- 08:09era where AI is prevalent and can do a
- 08:12lot, taste becomes quite important. It
- 08:15distinguishes between a good scientist
- 08:17and a mediocre one. I [music] think we
- 08:19want to try to understand the problem of
- 08:22taste and intuition [music]
- 08:24better um using modern-day machine
- 08:26learning techniques and that of course
- 08:28will be a very difficult [music]
- 08:30technical challenge. But it's something
- 08:32that our team is incredibly excited
- 08:34about.
The Hardest Problems Are the Strategy
- 08:40at the Ross uh mathematics program
- 08:42actually when I was 15. It was a
- 08:44beautiful summer where the professors
- 08:46will teach us how to think deeply about
- 08:49simple things. I remember first day
- 08:51they're like can you prove that zero
- 08:53multiplied by everything is zero. I'm
- 08:54like well this is obvious like why would
- 08:56you want me to prove that? In fact you
- 08:58are asked to derive that statement
- 09:01strictly from a set of five axioms such
- 09:04as zero plus everything is that thing
- 09:06itself. one multiplied by everything is
- 09:08that thing itself etc. That way of
- 09:11acimatic and deductive reasoning really
- 09:14was inspiring to me. Thought that was
- 09:17just first of all a bit crazy that a
- 09:19bunch of us stuck for more than 24 hours
- 09:21on um that simple problem set but also
- 09:24it teaches me reason strictly rigorously
- 09:28um to get to the final destination.
- 09:31Axium the name of our company actually
- 09:33comes with this inspiration. We want to
- 09:36build out the knowledge graph and expand
- 09:38the frontier of mathematics through
- 09:40deductive logic and we are using the
- 09:43programming language of proofs lean for
- 09:46that. I think that there are so many
- 09:49components [music] just like math right
- 09:51one think very deeply about simple
- 09:53things a very short concise mission
- 09:57statement AI mathematician requires
- 10:00various techniques joining together for
- 10:02example my colleague Hugh Leather and
- 10:05his team have been working on applying
- 10:07deep learning to code generation since
- 10:10very early since like 2017
- 10:13chart have been pioneering the field of
- 10:15AI for mass discovery using transformer
- 10:18to solve symbolic integration in 2019
- 10:21and they show that it work better than
- 10:23computer algebra. CTO Shoen Gupta have
- 10:27worked in fair for many years and
- 10:29Facebook AI research pioneered work such
- 10:32as large reinforcement learning models
- 10:34like open go. We believe in solving the
- 10:37hardest problem is the best way to win
- 10:40and I think this mission [music] in
- 10:42itself is incredibly attractive to
- 10:45talents. I love the fast-paced
- 10:47environment of startups. I love
- 10:49executing. I love executing with the
- 10:51team. I love unblocking others. I love
- 10:54asking for help. You have the sort of
- 10:56very instant reward signal. It's similar
- 10:59to the childhood Karina trying to solve
- 11:02the ma math problems. Just being in the
- 11:04moment, being immersed in how research
- 11:07engineering is done on day-to-day basis
- 11:09is just a once in a-lifetime experience.
Math is the Sandbox of Reality
- 11:16Mass really is the fundamental of lots
- 11:19of branches of sciences [music]
- 11:21and it's also the sandbox for reality
- 11:23where you can try to put a lot of the
- 11:26real world objects into mathematical
- 11:28variables and then formulate the problem
- 11:31in a purely theoretical way. So I
- 11:33thought understanding math will allow me
- 11:35to generalize to other domains. And
- 11:38indeed in machine learning we found the
- 11:40transferability of mass reasoning to be
- 11:42quite striking. So a model that does
- 11:45really well on math can likely do better
- 11:47in coding. We find this sort of
- 11:50surprising phenomena of math concepts
- 11:53[music]
- 11:53being unexpectedly
- 11:56present in a lot of the applied
- 11:58scientific [music] fields. And if you
- 12:01have a real world problem, you can try
- 12:03to understand that theoretically through
- 12:06solving it mathematically. I think by
- 12:08math is the sandbox of reality. There's
- 12:11another [music] meaning which is if you
- 12:13think about modern machine learning
- 12:15models, they want to gather real world
- 12:19data for them to try to experiment,
- 12:22generate new knowledge from spatial
- 12:25reasoning data. Math is a digital
- 12:28version of that. We can solve reasoning
- 12:32by being in the digital world without
- 12:35relying on the real world [music] data.
- 12:37So yeah, it is the playground for trying
- 12:40out what we understand about about
- 12:43reality and the universe. Math is full
- 12:46of hardships. Like I think like mass
- 12:48research is a process of almost like a
- 12:52monk praying in the temple day after
- 12:56day. You just hope that the storm that
- 12:58you are looking at will have a flower
- 13:00grow out of it. I think the feeling of
- 13:03being stuck [music] can feel quite
- 13:05depressing just because you don't really
- 13:07know where [music] your work and the
- 13:09math ends and where you know your life
- 13:11begins. You kind of blur [snorts] your
- 13:13identity [music] um with your work. I
- 13:16think that's a struggle a lot of
- 13:17mathematicians do face. I think that
- 13:20with AI um hopefully AI mathematicians
- 13:23will make the process a lot more
- 13:25enjoyable. The ideal state is obviously
- 13:27one has a spec a lema that one wants to
- 13:29prove [music] and instead of the human
- 13:32banging the head on the wall um [music]
- 13:34for days and sometimes weeks months the
- 13:37AI mathematician can help prove it and
- 13:41the human mathematician will just guide
- 13:43the collaboration to the next lema makes
- 13:46the journey a lot more exhilarating. I
- 13:48do think that's part of the vision more
- 13:50like a collaborative endgame that we are
- 13:53imagining rather than say replacing
- 13:56humans. Five or 10 years is hard to
- 13:58imagine but uh we fully believe that
- 14:00this is a fundamental technology that
- 14:03will turn us into a generational
- 14:05company.
- 14:13Thank
- 14:14you. Thank you.