Four Biological Conjectures: Strange and Marvelous Challenges for Biological AI

A biologist proposes a set of "Biological Conjectures" — hard, Fermat-style open problems intended to draw frontier AI labs into biological research, following a July 2026 claim by mathematician Levent Alpöge that he used Claude Fable to disprove the Jacobian conjecture. The first conjecture challenges researchers to reconstruct the variable lab reagent Matrigel from first principles, arguing that lot-to-lot inconsistency may contribute to biology's replication crisis.

The best conjectures are written in the margins. In 1637, Pierre de Fermat set the most iconic intellectual thirst trap in the history of mathematics when he scribbled a note in his copy Diophantus’s Arithmetica . There are no positive integers that satisfy aⁿ + bⁿ = cⁿ for n greater than 2, he teased, “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” I’m not a mathematician, but I like math enough to feel a certain frisson when I read Fermat’s Last Theorem. It’s a call to adventure. It sets before you a goal that is easy to understand, yet unreachable until you first push back the frontier of human knowledge. Something about it was compelling enough to hold the attention of the math community for 350 years a proof was finally published in 1994 . Recently, the internet has rediscovered the appeal of a good conjecture. On July 20, 2026, the mathematician Levent Alpöge posted a short message on X saying the Jacobian conjecture is false and that he had used Claude Fable to determine the solution. Since then, we’ve seen a mini gold rush in AI-guided conjecture-hunting. It turns out that math has a substantial backlog of unclaimed prizes that are well matched to the capabilities of frontier AI in 2026. These problems are like catnip for the neolabs as they relentlessly seek out ever-more-challenging benchmarks to test their agents against. My fellow biologists, I want this for us. Biology deserves more of the attention, and the resources, currently being dedicated to advancing AI capabilities. A good set of Biological Conjectures, calibrated to intellectually thirst trap the Members of the Technical Staff over at Ant or OAI, might be just the thing. But before we start scribbling in the margins, a minute to prepare your mind. This isn’t your typical list of open questions in biology. We’re not asking you to cure all diseases, although some of these might advance that goal indirectly. We’re not here to build a virtual cell, to design a target-specific drug, to find the causal mechanism of a disease, or any of the other high-profile applications of AI for medical research that you already knew were important. Fermat’s Last Theorem was legendary, in part, because it called from the margins of mathematics. For 350 years, it stood apart from the waves of progress directed at other goals. There were entire centuries when it was considered a disreputable problem, not something that serious researchers should prioritize. But that weirdness is exactly what makes a good conjecture generative. It calls people away from the mainstream and leads them to domains they might not have otherwise explored. We believe that AI changes the scope of biological inquiry. It transforms impossible problems into merely hard problems. It elevates problems that live at the edge of the AI frontier. It challenges Bio-AI teams to entertain stranger possibilities. And so we present the Biological Conjectures. Solve one and be a legend. Conjecture 1: We can reconstruct Matrigel from first principles Matrigel is a common lab reagent in cell biology. It’s basically a protein slurry secreted by mouse tumor cells and sold commercially in 10 mL vials. Biologists use it for growing mammalian cells in culture. It provides a physical scaffold for cells to grow on and supplies various growth factors that signal them to replicate and behave normally. The problem is that composition of Matrigel varies lot-to-lot and this variation propagates directly to experimental results. If you want to perform a set of experiments under constant conditions, the size of the dataset you can generate is limited by how much Matrigel you can get in one batch. Different batches of Matrigel may or may not vary in ways that matter for your experimental outcome. We’ll never know for sure how much Matrigel is contributing to the replication crisis https://en.wikipedia.org/wiki/Replication crisis as long as it remains chemically undefined. We conjecture that Matrigel can be replaced with a fully defined synthetic alternative. It isn’t a magic potion after all, it’s just a bunch of biological molecules mixed together. But the admixture is abnormally complex: laminin, collagen, entactin, heparan sulfate proteoglycans, growth factors, proteases, and God knows what else is in there. Designing a replacement https://www.nature.com/articles/s41578-020-0199-8 would mean teasing apart perhaps 100 molecular ingredients, confirming their biological importance, then developing a manufacturing strategy to produce each component through chemical synthesis or precision fermentation. Matrigel is the right challenge for frontier Bio-AI in 2026 because it is more complex than studying single cells, less complex than modeling whole organisms. If we can’t generate the gel that grows stem cells in a tube, what hope do we have for understanding real 3-dimensional human biology? If you’re building the kind of AI that mines biological knowledge from the literature, Matrigel has been featured in more than 12,000 publications https://pmc.ncbi.nlm.nih.gov/articles/PMC9733768/ . If you’re building the kind of AI that processes experimental data, Matrigel is already a core component in any number of high-throughput assays. Glory will flow to the first neolab to discover the formula for neo-Matrigel. It would improve experimental reproducibility of biotech across the board. It would unlock a tidy line of business, provided the synthetic reagent could be shipped for less than the $300 per vial they charge today. It would be a decisive, tangible demonstration that AI can deliver functional biology in the world of atoms. Success criteria for conjecture 1: - You create a synthetic Matrigel in which every molecule is defined. - Replication studies show that synthetic Matrigel reduces experimental variation. - You create a commercial lab reagent that is widely used for cell culture. Conjecture 2: It is possible to 10x the Calvin cycle Nearly all of the carbon in the biosphere enters life through the same enzyme: ribulose-1,5-bisphosphate carboxylase/oxygenase, or rubisco for short. Rubisco pulls carbon from the air and feeds it into the metabolic Calvin cycle where it is assembled into sugar and, eventually, the carbon backbones of all organic molecules. The problem is that rubisco sets a bottleneck on carbon assimilation and growth. It is the most abundant enzyme on earth, in part, because plants express it in large quantities to compensate for its slow catalytic rate. While a typical enzyme might catalyze 1000 reactions per second, rubisco performs only 10. Rubisco also struggles to distinguish CO<sub 2</sub from O<sub 2</sub , often adding oxygen to a growing carbon chain by mistake, resulting in the wasteful side-reaction of photorespiration. We conjecture that enzymatic carbon uptake can be improved. This might be achieved with a redesign of the rubisco enzyme, or it might require replacing the Calvin cycle with a different metabolic cycle that doesn’t rely on rubisco at all. Rubisco is the right challenge for frontier Bio-AI in 2026 because protein engineering already has such an impressive toolstack: Alphafold, RFdiffusion, etc. What better way to challenge those models than on the Holy Grail of biochemistry? No enzyme is more in need of improvement or more famously difficult to improve. Like Fermat’s Last Theorem, Rubisco 2.0 has gone unsolved for so long that it has become notorious. But if a solution exists, there is reason to believe that AI brings it within reach. Rubisco itself https://pubmed.ncbi.nlm.nih.gov/39843747/ is amenable to the kinds of high-throughput functional assays that produce AI-ready training data. A number of other pathways https://pmc.ncbi.nlm.nih.gov/articles/PMC10521678/ have been described that can convert CO<sub 2</sub into sugar, including both naturally occurring and engineered options. The neolab that claims this prize will need to do more than engineer a single protein in isolation. A carbon fixation pathway is an interdependent set of enzymes, cofactors, and transporters that must fold correctly, localize to the right compartment and integrate seamlessly with the broader metabolic network. And it all has to happen in one of the real plants we use to harvest carbon at scale: maize, rice, wheat, soybean, poplar or pine trees. The practical value of improved carbon capture is pretty obvious so we won’t dwell on it. You’d revolutionize agriculture, providing more food on less land for a hungry world. You’d have a tool for drawing down atmospheric CO<sub 2</sub levels at gigaton scale. And as if that wasn’t enough, you’d resolve a key question of novelty in Bio-AI. Can AI produce truly new biological functions, or does it merely shuffle around parts that already exist in nature? Evolution has had billions of years to improve rubisco but has found no better solution. To some, this is a strong argument that no better solution exists. For an AI lab to deliver faster carbon capture, they would need to out-evolve evolution itself. It would be a decisive demonstration that AI could create things utterly and totally new. Success criteria for conjecture 2: - An enzymatic pathway that captures carbon faster than rubisco without sacrificing accuracy. - A pathway that functions in a real organism and enables faster growth under atmospheric carbon conditions. - A metabolic trait that increases crop yields in an agricultural field trial. Conjecture 3: The square-cube law does not constrain bioreactor scaling economics A cow and a stainless steel bioreactor are both, in a sense, trying to solve the same problem. The cow was developed by evolution and selective human breeding to make more cows. The bioreactor was designed by engineers to make cells. Dollar for dollar, the cow does a much better job. There are many reasons why this is so. A complete accounting https://pubmed.ncbi.nlm.nih.gov/34101164/ would touch on basically every economic and operational aspect of industrial biotechnology. This challenge is focused on the constraints that arise from the physical shape of the machinery we use. A modern bioreactor is a cylindrical tank. The larger we build these tanks, the harder it gets to efficiently feed the cells inside. This is because when the tank grows in any linear dimension, L, the number of cells you need to feed grows like the volume L<sup 3</sup but the cross-section across which nutrients can flow grows like the surface area L<sup 2</sup . Give or take a million process-dependent details, this means that bioreactor feeding efficiency grows like L<sup 2/3</sup . The exponent is less than one, meaning the process becomes less efficient with scale. Cows and other animals break this scaling law and instead they follow Kleiber’s law https://en.wikipedia.org/wiki/Kleiber%27s law . It was first observed in the 1930s that animal metabolic rates grow as L<sup 3/4</sup , not L<sup 2/3</sup . That is to say, large animals are more metabolically efficient than naive scaling laws would predict. Cows and other animals achieve this by being very clever about how they distribute nutrients inside their bodies. The vascular system adopts a fractal geometry, moving blood through a series of branching tubes that deliver to every cell in the body. The architecture of an animal body effectively sub-divides a large bioreactor into a series of smaller, more efficient, bioreactors. We conjecture that new form factors can enable more efficient bioproduction at scale. Does this mean that industrial bioreactors should be supplied with veins and arteries? Maybe. But the living world is full of clever tricks that biology uses to produce more biology. Biological systems self-replicate, they recycle waste, they repel invaders and maintain internal equilibrium with extraordinary efficiency. There is no reason why our industrial manufacturing infrastructure can’t do these things too. The cow is a proof-by-construction that biology, properly organized, can deliver biomass at scale. But there is no reason to believe the cow represents peak performance. As AI enhances our ability to co-design biology and industrial hardware, today is the most expensive precision fermentation will ever be. Success criteria for conjecture 3: - You build a bioreactor with a completely novel architecture. - Your bioreactor scales efficiently in both theory and practice. - You produce a commodity fermentation product at a market-beating price. Conjecture 4: Superchocolate exists in flavor space Chocolate is a wonder of the world. There is not an official list of which inventions have produced the most total human happiness, but chocolate would have to be on it. Chocolate is also a weird fluke. Evolution did not select the cacao tree to be delicious to humans. Of the 80,000 plant species native to South America, the seeds of one particular tree, properly fermented and roasted, transform into the world’s most popular dessert ingredient. The deeper you look into chocolate, the more the mystery of chocolate stares back. Many of the flavors we experience are relatively simple at the molecular level. The essence of vanilla is a single molecule known as vanillin. Banana is isoamyl acetate. Pineapple is ethyl butyrate. But chocolate has more than 600 https://pubmed.ncbi.nlm.nih.gov/33371573/ different flavor-active volatile compounds. Even attempts to reduce chocolate to its barest chemical essence still require dozens of molecules. This means the experience of chocolate is extraordinarily high-dimensional. Hundreds of flavor molecules, each one with a specific binding profile across 30 human taste receptors and 400 human odor receptors. Their combined activation profile represents a kind of embedding, a neuronal signature unique to chocolate. We conjecture that the complexity of chocolate implies the possibility of superchocolate. Chocolate didn’t have to exist. If the cacao tree had gone extinct before humans arrived, the particular point in flavor space that chocolate encodes would simply be unknown to us. Given how extraordinarily large flavor space is, it seems likely that other exceptionally delicious embeddings exist that no human has ever experienced. And there is no particular reason to think that chocolate represents a maximum of delight. The right combination of molecules might make chocolate look like oatmeal. The process of flavor discovery is well aligned to the strengths of Bio-AI in 2026. It requires mapping flavor molecules to the receptors they activate, then mapping receptor activation profiles to flavor descriptions. Ultimately, the human experience of flavor is what matters, so the model will need to learn from reports of human tasters. As a challenge for Bio-AI, designing a molecular mix to produce a flavor response bears a remarkable similarity to designing a drug cocktail to produce a clinical response. Both require exploring large libraries of molecules, both require generating large datasets with relevant context for human biology. The chocolate challenge has the advantage of allowing much cheaper and safer design cycles - it is easier to find humans to describe new flavors than to trial new pharmaceuticals. Finally, the similarity between flavors and drugs extends to the molecular level. Human odor receptors are GPCRs G protein-coupled receptors , a versatile class of proteins used throughout the human body to sense signals and control cellular responses. This same protein class is an abnormally effective target for new medicines. More than 500 small molecules, about 36% of all approved drugs, target GPCRs https://www.nature.com/articles/s41573-025-01139-y . So there is a chance that, while solving generative flavor design, a Bio-AI team might also solve generative drug design. Ten years ago, a comprehensive theory of flavor seemed extraordinarily hard. Today it looks more like a necessary step toward solving the general problem of human pharmacology. Success criteria for conjecture 4: - You can predict the experience of a flavor from the structure of a molecule. - You can generate a new flavor as unique and delicious as chocolate. - You build the world-beating model for designing drugs that target GPCRs. Conclusion If taste is the last moat, then maybe superchocolate is the ultimate expression of taste. Scientific progress has always depended, in part, on the ability to select good problems. The most productive research teams have the ability to recognize when a particular idea’s time has come. In the AI era, it seems likely that many ideas will see their time come all at once. It is widely understood that AI accelerates the rate at which impossible problems become possible. There is an increasing sense of urgency at the frontier of Bio-AI. What does it take to stay on top of things? How to be the agent of change rather than being surprised by it? We have seen how, in mathematics, a problem like the Jacobian conjecture can sit unresolved for decades, only for the solution to arrive by tweet during the World Cup. In this environment, Bio-AI teams need new strategies for finding problems that are both interesting and solvable. We propose that AI also accelerates the rate that quirky problems become important. Formulating Matrigel, engineering rubisco, designing bioreactors or generating flavors - none of these problems are entirely new. But they take on a new sense of urgency because they are well-suited to the capabilities of frontier AI in 2026. They may not be as obvious as curing all diseases, but they will be stepping stones toward that goal. And because they don’t require human clinical data, they can be solved quickly and at a reasonable cost. Finally, we conjecture that there are many more AI-shaped problems out there in biology that are currently being slept on. If you’re looking for more strange and marvelous challenges to prove that your Bio-AI team can do the impossible, American Wetware https://americanwetware.com/ wants to help you find them.