Carina Hong on Mathematical Intuition, Formal Proof and AI

Zhang Xiaojun interviews Carina Hong at Facebook House in Silicon Valley. Hong is the founder and CEO of Axiom, which works at the intersection of AI and mathematics. They discuss mathematics, her upbringing and entrepreneurship.

Hong says fundraising often means repeatedly explaining the same idea and answering similar questions. Amid that repetition, an exciting conversation can help a founder find the right investor.

Zhang asks whether she has ever been struck by mathematics. Hong says she often finds beauty in unexpected connections between different fields when reading other people’s work.

She recalls studying elementary number theory at the Ross program, completing problem sets in sequence until reaching quadratic reciprocity. A concise result can have a deep and creative proof behind it, which made a lasting impression.

Asked what mathematics is, Hong describes people agreeing on axioms and building theories from them. In her view, mathematics has qualities of both art and science.

For her, mathematics is not only solving a given problem. Researchers notice patterns in examples, sequences or sets, formulate conjectures and try to prove them. Choosing a question is also part of the creative process.

On whether mathematics is discovered or invented, they acknowledge a longstanding debate. Hong does not give a simple either-or answer; she discusses shared intuition among mathematicians and how proof communicates and tests new ideas.

She cites Ramanujan and Hardy and Littlewood: people from different backgrounds may find different patterns, while rigorous proof lets other mathematicians inspect and accept a result.

She also discusses number-theory work by Yitang Zhang and James Maynard. Different researchers may use different techniques on related results, which others can compare, organize and simplify.

Hong says she once wished for a genius’s intuition but often felt she relied more on persistence and brute force. On geometry problems she found difficult, she used algebraic representations that were more familiar to her.

She points to AlphaGeometry as an example of translating geometric relationships into symbolic form and using computation to seek proofs. Its method differs from hers, but both involve changing the representation of a problem.

At MIT she spent months thinking about a sphere-packing question from a professor without resolving it, reporting her attempts each week. She believes willingness to do difficult, prolonged work can complement other people’s strengths.

Zhang asks whether AI is also a brute-force problem solver. Hong says a system can combine different models: some propose a broad direction, while others search, check details and construct proofs.

She recalls a problem with a concise human solution for which a machine produced a long formal proof. Comparing different human and machine routes can reveal what each is good at.

She distinguishes automated theorem proving, or ATP, from interactive theorem proving, or ITP. Computer scientists and mathematicians were already using programs to help construct and check proofs before modern deep learning.

In Hong’s account, AI can take on some of the work previously done by a person in interactive proving, while a rules-based system checks formal steps. She sees the field as a combination of existing proof tools and AI.

Recalling her childhood in Guangzhou, she remembers local food, a nearby school and occasionally wandering while thinking about a math problem. She enjoyed the freedom to let her mind roam.

She introduces two ideas from a mentor: attention constrained by tasks and deadlines, and attention free to explore. Email and daily obligations require execution but can also consume space for reflection.

Hong believes free attention can help founders and mathematicians discover new directions; measuring only tasks completed can crowd out those opportunities. She does not prescribe a fixed ratio between the two kinds of attention.

Inspiration does not arrive in direct proportion to time spent. She says ideas left by free exploration may connect with a task only later.

She uses three founder types to think about teams: people who set direction, strong executors and persuasive communicators. The categories are a way to reason about teams, which need both complementary skills and common ground.

She sees herself as closer to the direction-setting type and admits she can be extremely optimistic about goals. When Zhang asks about well-known entrepreneurs, Hong offers personal impressions rather than a rigorous classification.

Hong says many early Axiom members came from Facebook, and their familiar ways of working influenced the new company’s culture. She values both shared understanding and complementary strengths.

Returning to her upbringing in Guangzhou, she says she enjoyed history, literature and math competitions. Family ties to Beijing also exposed her to stories about writers and artists.

She says her coach did not see her as the hardest-working student, but she would spend a long time wrestling with a problem that interested her. She distinguishes mechanically spending time from being drawn in by the problem.

In middle school she began exploring more advanced mathematics, including calculus. Unlike competition rankings, she felt exploration need not be a zero-sum game: classmates could pursue questions together.

Competition rules still affected choices. Because she loved number theory, she might start with the hardest final problem even when a scoring strategy would favor first completing the geometry question she found difficult.

The number-theory problem she enjoyed could consume much of an exam. The example showed her that pursuing an interesting question and optimizing a test score can conflict.

Asked whether she is competitive, Hong recalls frequent ranking and reassignment in childhood math training. She felt intense pressure and began deliberately resisting the idea that ranking should be her only goal.

She did not leave exams entirely, but paid less attention to ranking and found friends who also wanted to read mathematics beyond the syllabus. Those peers helped turn curiosity into shared exploration.

She recalls studying a knight’s-tour problem with three to five friends: could they visit every square without repetition and prove a more general statement? They split up small cases and exchanged discoveries.

The experience reminds her of collaborative mathematics: a large problem can be divided into pieces and assembled from many contributions. That differs from a story centered only on one genius proving everything alone.

She and her friends passed notes in class with constructions they had found. The shared pleasure of solving a problem appealed to her more than an individual ranking.

She thinks broader mathematical reading may have indirectly helped her competition work, but later at MIT she also had to learn to focus. She does not think there is one universal formula for learning mathematics well.

At MIT she often viewed her classmates as smarter and felt fortunate to learn with them. This is her subjective experience, not an objective ranking of anyone’s ability.

She initially considered quantitative finance and obtained an internship opportunity. During the pandemic she also applied to Ken Ono’s undergraduate research program, entered the waitlist and was later admitted.

She chose to spend that summer on mathematical research and postponed the finance internship. Looking back, she says she wanted to make the most of an opportunity that could change her direction.

On family, she says her mother worried about her own difficulties with mathematics and encouraged her daughter to start early. Hong sees both that guidance and her own later interest as influences.

When Zhang lists competition honors, Hong says she also had many attempts that fell short of her expectations. Not being selected after intensive preparation complicated her feelings about the gap between honors and personal experience.

She says optimism can mean setting very high goals and therefore often feeling that she has failed. What outsiders see and what she expected of herself do not always match.

She cites MIT’s first-term grading policy, which allowed students to try difficult classes without treating every early grade as a permanent mark. Her East Campus dorm also brought together people who loved building and problem-solving.

Older students advised her to take the hardest classes, even without all the prerequisites. She and several first-years enrolled in doctoral probability and immediately encountered unfamiliar measure theory.

This difficulty differed from an individual competition: several students could admit they were lost and work through the problem sets together. Hong found that collaboration rewarding.

On a forty-point midterm she scored four. She concluded that her analysis background needed work and returned to real-analysis material she had encountered earlier.

Zhang asks what motivated her to keep going. Hong says that when she was younger, a major reward was camaraderie: the group decided to face the challenge together instead of quitting separately.

After the group did poorly on the midterm, they discussed dropping the course together or continuing, and chose to continue. Hong says the feeling of not giving up together was its own reward.

She describes her later attraction to difficult work as a habit that may not always be healthy, and questions the simple equation of a founder’s suffering with business success.

The pandemic sent MIT students away from campus, removing the small group she had studied with daily. She says she had to learn to find some satisfaction in the difficult work itself.

She admires the persistence she saw among MIT classmates while acknowledging that she may not meet her own imagined standard. Their perseverance influenced how she approached long-term work.

Pressure can test relationships and teams as well. She values people who can maintain technical conviction while helping colleagues continue through difficulty.

On leadership, she prefers a service-oriented analogy: on a team’s climb, the leader need not be the person at the front with a megaphone, but may be the one behind passing out water.

For her, advanced mathematics resembles building with blocks: introduce a definition, combine it with existing concepts and discover new theorems and questions. Exploration need not be limited to an exam syllabus.

She wanted to attend MIT from high school and wrote its name on math scratch paper. Films and stories about mathematicians, physicists and astronauts shaped her image of the school.

She chose a double major in mathematics and physics. Mathematics was already a clear choice; physics reflected an interest in quantum topics and the physical connections she heard about in probability research.

Discussing undergraduate awards, she says many came through professors’ nominations and encouragement rather than a single competition. She remembers mentors helping students find research opportunities suited to their interests.

Regarding the Morgan Prize, she emphasizes nomination, recommendations and committee review. She says many peers were equally strong and that recognition also involves some chance.

She cautions that receiving an award does not imply other candidates were less capable. Community support, evaluation and opportunity can all affect who is ultimately recognized.

She continued studying number theory, including modular forms and elliptic curves, and coauthored papers with Ken Ono and collaborators from the summer program. She was still finding the direction she liked most.

For her master’s she went to Oxford to study neuroscience, partly because a family experience made her want to understand the brain. After encountering experimental requirements, she realized she preferred computational research.

The overlap between computational neuroscience and AI attracted her: it let her use mathematics and collaborate with researchers from different backgrounds. She found particular enjoyment in AI questions.

She describes using linear algebra, matrix calculations and differential equations in her master’s research. With her supervisors, she placed AI questions in a neuroscience context for the degree.

She later returned to Stanford for mathematics doctoral study while exploring law. A deferred mathematics opportunity and a Rhodes Scholarship linked those experiences; her longstanding interest in debate also drew her to law.

Hong says she has strong interests across disciplines and clear weaknesses too. She does not equate interdisciplinary learning with being good at everything, but with finding connections among different tools.

Law-school discussions of constitutional interpretation led her to ask whether AI could help with structured text and rules. She was especially interested in precise definitions, not treating model output as an authoritative judgment.

She became interested in differences among ways of interpreting legal texts. The experience made her attentive to how the choice of material and interpretive rules can affect a result even when wording looks precise.

A friend working on formal proofs in Lean showed her that mathematical statements can be written in a form a computer can check. She began asking whether AI that handles structured language could also assist mathematics.

At Verve Coffee in Palo Alto, she repeatedly discussed science and technology with Shubho, who later became a collaborator. She initially went there to read law, drink matcha and watch dogs in the courtyard; the relationship grew gradually.

She hoped AI could help mathematicians with large amounts of standard but tedious work, such as checking possibilities or applying known tools to new problems, leaving people more time for higher-level thought.

She relates the idea to her research experience: some mathematical tools transfer across families of problems, but using them fluently demands extensive time and training.

In law school she enjoyed expanding her perspective through extensive reading, while missing mathematics and science. She often took a shuttle to the café to continue open-ended conversations with Shubho.

Their acquaintance began with a small everyday request to adjust a café window shade. They discovered shared interests in mathematics and science and gradually became friends.

Their conversations continued for over a year and covered mathematics, scientific history and technology. Hong says not rushing into a business relationship gave them time to understand each other’s thinking.

Hong says they only gradually learned the details of each other’s professional backgrounds. She values a relationship formed first through shared interests rather than an immediate career objective.

In autumn 2024 she began seriously considering an AI mathematics company. She and Shubho estimated the required compute on a café napkin and felt an academic setting alone might not support the project.

Hong says she began fundraising before leaving school and waited until she had a work visa. Shubho initially remained at Meta; they did not decide from the first day that they would found the company together.

She says she loved academic life and spent two months trying to talk herself out of founding a company. Her question was not whether the area was fashionable but whether she understood it well enough to build something.

To test the idea she read science history and many AI-for-math papers, sketching system designs on paper. She felt responsible for understanding the technical risks before asking investors for resources.

She even asked about a role at another company in the area: joining an existing effort could have spared her founding one from scratch. Its hiring requirements did not match her background at the time.

Reading introduced her to automated proving and the search for mathematical patterns. Some authors whose work she studied later joined the team, an opportunity she says she deeply values.

Zhang observes that this resembles forming another small group. Hong describes a team including machine-learning and code-generation researchers, mathematicians, and contributors to Lean and its mathematics library.

Lean is a formal language, while Mathlib is a mathematics library built in it. Besides mathematical knowledge, she says, building tools, training models and engineering the system require different expertise.

During the holidays she and Shubho formed a remote reading group. Although neither usually liked long video calls, they often discussed papers for hours and found their thinking both similar and complementary.

She says the early team considered limiting the number of mathematicians, then came to value open-minded experts willing to think about both scale and methodological efficiency. She wants mathematicians to expose system weaknesses.

She encountered mathematical researchers who were skeptical of scaling. She does not regard a mathematics background as an obstacle; she seeks people open to different approaches who can also challenge the system’s results.

Mathematicians can design harder benchmarks that expose failure modes rather than relying only on the team’s existing tests. Hong sees this adversarial evaluation as part of complementary teamwork.

During the holidays, a survey of formal theorem proving helped her connect scattered methods into a larger picture. Checking its references revealed many papers she had not yet read.

She says researchers in Silicon Valley move among academia, industry, advising and startups, bringing different experiences into discussion. She values the work people do together more than titles alone.

They discussed connections among conjecture generation, automated proof and earlier expert systems. Hong wanted to organize these directions into a system that could be tested sustainably when resources allowed.

She places AI mathematics in a longer history, including rule-based systems, early theorem proving, AlphaGeometry and AlphaProof as background for later systems.

She considers AlphaProof’s 2024 International Mathematical Olympiad performance an important milestone and says Axiom’s later Putnam work builds on that sequence of research.

Once fundraising began, investors gradually made offers. She says she was unfamiliar with the process and unwilling to accept terms that would dilute the founding team excessively.

She describes the most tiring part of fundraising as repeating the same explanation and answering similar questions. Occasionally, a conversation with someone who understood the direction made the process exciting.

She recalls speaking with Howard Morgan of B Capital and feeling that he understood the mathematical and technical potential. She values an investor’s long-term understanding and help alongside price.

In pitches she openly said the business model was uncertain and the team first wanted to build the technology. She later realized investors apply their own discount to optimistic pitches, so communicating risk also requires context.

She says some investors did not directly decline but waited to see who would lead. She took this as a lesson in fundraising group dynamics and the importance of a lead willing to decide.

As offers arrived, she continued weighing dilution, valuation and long-term support. She emphasizes that she learned while doing rather than knowing how to structure a financing from the start.

During fundraising and company formation she was still studying and recruiting. After her work visa was approved she left school in the summer; investment terms were followed by legal diligence, office setup and hiring.

She recalls raising about $64 million in the seed round and says the funds had to support models, systems and the team. The figures reflect her account at the time of the interview.

Asked about identity and age, she says she did not perceive a clear advantage or disadvantage from being a Chinese woman, but youth and lack of a large-team technical leadership record could concern deep-tech investors.

She says founders repeatedly make important decisions with limited time and information. Waiting can be valuable but can also cost opportunities; she is still learning to carry that uncertainty.

She recalls often feeling unprepared before important decisions. Experience can help, but real decisions often cannot wait until all information is available.

She compares it to her first zip-line ride: even with a harness, taking the first step felt difficult. Some founder decisions feel similar, she says, though not every risk can be ignored.

Hiring is one example: strong candidates may have several offers, and a small company must make choices with limited resources. Hong says such decisions often lack a fully certain answer.

She describes the later Series A: an existing investor proposed investing early, and the team compared alternatives. She says they chose a lead able to provide long-term support while also including other supporters.

She attributes investor confidence to the team’s rapid construction of infrastructure, models and verification tools. This is her interpretation of the investment decision.

Hong describes company-reported progress on Putnam problems and formal proofs for several research questions. Those claims concern particular evaluations and system setups, not a conclusion that AI has solved mathematical research generally.

Asked why an experienced team accepts her as CEO, she says she wants to create an environment where researchers can focus on a shared problem, again comparing her role to passing water to a climbing team.

She says the company faces more than model training: Lean data is limited, and the formal language and verification tools create engineering challenges. The team must improve data, search, tooling and compute efficiency together.

She gives verification as an example: checking a proof requires more than seeing code run; the statement and assumptions must match the original problem. A formally accepted proof with changed premises may not answer it.

Resource constraints also affect search. Hong says the team compares system designs, trying to control compute cost while paying down infrastructure debt accumulated during rapid progress.

Zhang asks how Ken Ono joined the team. Hong describes her former mentor as an optimistic basketball coach who encourages people and helps identify worthwhile mathematical questions.

She says she previously hesitated to invite senior researchers directly and preferred them to decide after understanding the project. When Shubho offered to join, she was happy because pursuing the idea alone had felt lonely.

Ono later emailed about his career options, and Hong suggested he also consider Axiom. She recalls that they quickly discussed the team and research direction.

She guesses that the team’s mathematical focus and the presence of other mathematical researchers appealed to him, while making clear that this is her interpretation of his motivation.

She sees Ono as a theory builder who connects fields and identifies problems for others to pursue. Alongside his research, he has long mentored young students, including her.

Asked whether AI will replace mathematicians, she imagines people and tools collaborating at different levels of abstraction: mathematicians choose directions and judge value while systems help explore and verify. She presents this as a future vision.

She compares it to changes in programming abstraction: tools let people work at a higher level, but understanding and checking lower-level results still matter. She thinks mathematicians may similarly adjust their roles.

She hopes conjecture and proof systems can form a feedback loop: new questions are tested by a prover, and proofs and failures inform later exploration. Whether such a loop works effectively still needs experimentation.

The team explores turning solved proofs and search experience into later tools or training material. Hong hopes the system can accumulate capability, but that remains a research goal requiring evaluation.

She recalls that after the 2025 Putnam problems became available, the team converted them into formal statements and supplied them to its prover. People participated in transcription and in some problems requiring a concrete answer.

The team considered whether to announce partial results and ultimately reported formal proofs for all twelve problems. She says contest problems and research mathematics have different difficulties and evaluation methods.

The team initially thought people had to supply answers for some problems before formal verification. Later they found an informal model in the system could also supply those answers, she says as a retrospective observation.

The name Axiom comes from the idea of an axiom. Hong likes the image of deriving new results from limited foundations and connects it with definitions and logic in formal proof.

She envisions AI expanding the capacity available for mathematical research, allowing mathematicians to focus more on choosing important questions, offering intuition and allocating effort. This is an optimistic forecast, not an achieved result.

If compute remains limited, she says, judging the importance of questions remains essential. If resources and methods improve substantially, researchers might explore more questions than they can pursue today.

Hong argues that pure and applied mathematics depend on each other: tools from basic research can become useful in science, engineering or other fields much later. She opposes valuing basic mathematics solely by immediate applications.

She sees mathematical proof, programs and real-world experiments as different sources of feedback. Formal verification can check specified logical properties, while applications still depend on whether models, specifications and environments match real needs.

Zhang asks whether AI mathematics will have a ChatGPT-like moment. Hong says a technical demonstration alone is not enough; useful products and workflows are needed to put the capability in people’s hands.

She distinguishes milestones in contest mathematics from research mathematics and notes that natural-language and formal proofs are different outputs. Evaluating a result requires examining the problem, verification and degree of human participation.

She outlines a draft–formal sketch–proof workflow: propose an approach, express its structure formally and fill in unproved parts. A placeholder in the middle is not itself a completed proof.

To fill proof gaps, a system can use traditional rule-based tools as well as neural networks. Hong says inexpensive, reliable deterministic methods should handle the parts they can solve first.

She discusses automation tools in Lean and says existing rule-based methods can solve some steps that look complex. AI’s contribution should be assessed within the full toolchain rather than credited for every step.

Another direction is to explore subtasks in parallel and learn from search trajectories. She describes subagents and tool use as system designs under investigation, not as proven superior to every alternative.

She says the team observed signs that mathematical proof capability transferred to code-verification tasks. Because comparisons depend on benchmarks and implementation details, she treats it as a finding for further research.

In the AI mathematics system she describes, pretrained models, post-training, tools and verifiers work together. Teams may make different choices about search, data and system structure.

She believes a useful system needs conjecture generation as well as a prover. Feedback from a prover can help screen ideas, but a provable conjecture is not necessarily important or mathematically valuable.

Measuring novelty, elegance and significance remains difficult. She mentions rough filtering methods and notes that they may not extend well to advanced research mathematics.

A knowledge base is essential too: much human mathematics has not been written as definitions and theorems directly usable in Lean. A system needs to know what is established and find possible counterexamples to conjectures.

Autoformalization is more than translating words. Decomposing a paper into sufficiently detailed definitions, lemmas and dependencies and then expressing them in machine-checkable form is difficult work in itself.

She describes mathematicians writing proof blueprints for large formalization projects and many contributors completing individual pieces. Automating such a detailed blueprint requires reliable decomposition and reasoning.

Translating formal content back into natural language also requires checking whether meaning changed. She mentions round-trip conversion as one consistency check, but it cannot by itself guarantee a correct translation.

Zhang asks how mathematics and coding differ as ways to carry out a task. Hong says programs produce outputs and proofs can check specified properties; they complement each other, with accurate specifications as a key challenge.

She imagines generating a program while verifying it against a specification, rather than checking only finitely many test cases. But a proof cannot fix an incorrect specification, omitted requirement or missing formal definition.

She illustrates the limit with research problems: if required concepts are absent from the formal library, a system may struggle even to state a problem accurately, let alone prove it.

She thinks transfer from mathematics to other tasks may be slower and less dramatic than progress in a specialized domain. Connections among mathematics, code and hardware verification merit study, but capabilities should not be assumed to improve together.

She uses a sorting program to illustrate specifications: finite tests can help clarify requirements, but passing them alone does not prove correctness for every allowed input.

She mentions chip and software verification as potential applications requiring checks of specified properties. Formal tools may help specialists, she says, but they do not remove the work of defining properties and understanding systems.

For commercialization, the team wants to improve the core system while exploring which verification problems it can and cannot solve. Hong values understanding meaningful failures over collecting superficial successes.

She sees natural language and formal proof as complementary: language can communicate needs or propose an outline, while a formal language helps check some proof steps rigorously.

Different models in the system receive different post-training, with some specialized in generating Lean code. She wants to connect understanding user intent with machine-checkable output.

She hopes verification can reduce hallucinations in mathematical tasks. Formal checking establishes a formal statement under its assumptions; people still need to check whether translation, assumptions and the original question correspond.

In her view, conjecture and verification form an iterative process: generation explores possibilities, and verification rules out paths that fail. Generation methods can also draw on mathematical structure, not only natural language.

The team hopes to try more research areas, especially those with less formalized groundwork. Hong says research-level benchmarks are hard to assemble and mathematicians are needed to propose worthwhile questions.

If an area’s basic definitions are absent from the library, a system may be unable to state a theorem. She considers automatically building and extending the knowledge base a more fundamental and difficult problem than solving one existing exercise.

Automatically generated definitions must also be checked for fidelity to human intent and consistency with the existing system. She lists these as limitations requiring further research.

On AGI, she resists calling a system general merely because it is strong at mathematics. Her analogy is a sector of a circle: a capability may extend to adjacent code verification or physics without covering every human task.

She offers her own notion of specialized superintelligence while acknowledging that a general system might eventually cover the same domains. The classification is her strategic view, not an established industry standard.

She hopes proof tools can become part of broader systems, rather than claiming a mathematical model already possesses intelligence in every domain. The extent of transfer remains to be verified.

She says Axiom wants people with mathematics, AI and compiler backgrounds. Together they can approach a bottleneck from data generation, proof search, software tooling and other perspectives.

Lean data is scarce, making scaling through entirely human-written examples difficult. She discusses model-generated, repaired and categorized examples, requiring both engineering and mathematical judgment.

She calls mathematics a sandbox for the real world: formal problems can provide relatively clear feedback, whereas biological or physical experiments also involve materials, equipment and real environments. The two kinds of research can help each other but verify results differently.

She hopes AI mathematics tools may one day help scientists with theoretical questions, with experimental researchers testing relevant hypotheses in the real world. This is a proposed future collaboration.

Zhang asks whether AI can create promising mathematical questions rather than only verify them. Hong says conjecture is especially difficult and the team has encountered failures; it also needs stronger natural-language-to-formal translation.

She says a good question requires judging difficulty, significance and existing knowledge, not randomly generating statements. She admires Ono’s ability to connect perspectives and formulate questions.

They discuss Ramanujan’s mathematical intuition and his later exchange with other mathematicians to prove and organize results. Hong sees intuition and proof as mutually reinforcing, while much about their origins remains unknown.

Using pretraining and post-training as analogies, they ask whether mathematical intuition comes from accumulated experience, specialized training or both. Hong acknowledges there is no simple answer.

She says the team was not then planning large-scale pretraining from scratch, instead using existing models and post-training, with possible mid-training. Cost and data availability affect that choice.

Large labs and specialized mathematics companies may take different paths. Hong sees both competition and possible collaboration around tools and expertise; her comments about other companies’ internal plans are personal observations.

She sees one of the biggest challenges as balancing execution speed with time to learn. More founder duties leave less time for reading and research, while excessive urgency can produce strategic errors.

A company must be responsible to employees and its early team while pursuing a difficult research goal. She sees commercial sustainability and scientific ambition as a continuing balance.

She compares the project to a moonshot that may succeed or fail. The analogy conveys the uncertainty of high-risk research, not a claim that every business has only two possible outcomes.

If the project does not succeed, she says, neuroscience and human–machine interaction would still interest her. Her attraction to long-term questions does not depend entirely on one company’s outcome.

On Silicon Valley competition, she says intense rivalry can accelerate progress but may also crowd out research that takes longer to validate. She hopes small teams can create room for such work.

She imagines that even if AI someday solves extremely difficult problems, people will still want to understand proofs, compare methods and ask new questions. Curiosity and the mathematical community would not automatically disappear.

She also acknowledges that failure in high-risk research affects investors and wider sources of capital, making responsible investment a question that cannot simply be dismissed.

Against large labs, she sees an opportunity for small teams in focus, execution and a complementary talent mix, while acknowledging the real resource gap. This is her assessment of the competitive position.

Small and large companies differ in resources, talent concentration and organizational structure. She says startups should find questions they can address particularly well rather than pretending the resource gap does not exist.

Asked whether her motivation now comes from the work or the team, Hong says the problem itself supplies the drive, while colleagues provide support and help her stay grounded.

Her long-term ideal is to make stronger reasoning broadly available and verifiable under appropriate conditions. She describes it as a research direction, not a capability current systems already possess.

She imagines that easier-to-use mathematical tools could let more scientists ask and explore questions they previously lacked resources to address. That potential still depends on reliability and practical use.

Hong says her most comfortable role resembles a research intern who can learn and ask imperfect questions. She founded the company to pursue the work, not because she particularly wanted to be a CEO.

She describes a management lesson: what she meant as a hobby project sounded like a high-priority assignment to junior colleagues because she was CEO. She became more attentive to the weight her words carry.

The company named meeting rooms after mathematicians and computing pioneers, prompting lively discussion. The team favored researchers who worked across fields and wanted to recognize contributions from different backgrounds.

She particularly admires Gauss’s number theory and problem-solving. If she could dine with a historical mathematician, she thinks discussing combinatorics and life with Erdős would be interesting.

She values mathematicians’ community, friendships and collaboration and once worried powerful tools might erase those experiences. She came to believe people would still find joy in conjectures, intuition and challenging one another.

She recalls academic celebrations where students and collaborators describe work done with a colleague. Those relationships and traditions are part of mathematics for her.

She distinguishes skillful use of existing proof tools from inventing a new method and suspects the latter remains harder for AI. Her suggested timeline is a personal forecast, not a guarantee.

She recalls running past Stanford’s Memorial Church and thinking about mathematicians’ intellectual legacies and the possibility of expanding discovery. She acknowledges both public purpose and personal ambition in that vision.

Asked how she wants to be remembered, she says labels matter less than experience. Rather than fixing her identity as mathematician or founder, she prefers to remain an apprentice who keeps learning.

She enjoys gradually building a picture of a new field from its literature. Later working with some authors whose papers she had read has been especially meaningful to her.

When people and goals come into conflict, she says leaders should act carefully and examine earlier management choices that may have contributed. Decisions affecting others carry responsibility.

For reading she mentions elementary number theory, Davenport’s analytic number theory and literature including Dream of the Red Chamber. She values the different kinds of understanding mathematics and literature provide.

Zhang imagines AI proving a major conjecture using a new axiom. Hong says mathematicians would need to distinguish the original assumptions from the new axiom and debate the resulting system; formal acceptance does not make the original claim unconditional.

She praises Chinese teams’ AI mathematics work and hopes scientific ideas can circulate. She says it is hard to predict future US–China roles, and researchers choose where to work for individual reasons.

For 2026 she offers personal forecasts about continual learning, multimodal reasoning, agents and verification tools. These are directions she expects to watch, not confirmed outcomes.

She says conversations with prospective colleagues about mathematics and AI often reconnect her with why she began. Finding people with shared interests and fresh perspectives is a joyful part of hiring.

She recommends a range of work on automated proof and mathematical AI and emphasizes combinations of system design, tools and post-training. Connections between older methods and new models often inspire her.

She emphasizes a bet on complete systems, including coordination among models and verification tools, rather than comparing one model in isolation. Ideas such as recursive self-improvement remain her predictions.

Hearing the studio’s name, “Language Is World,” she thinks of mathematicians expressing rigorous reasoning in natural language and formal languages offering another checkable representation. They end on language, logic and continuing exploration.