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Is Water H₂O? (2): The puzzle of water electrolysis

9 September 2026 at 14:00

Author: José Luis Granados Mateo is a postdoctoral researcher in the Department of Philosophy at the University of the Basque Country (EHU) and a member of the Integrated History and Philosophy of Science (iHPS) research group. His work focuses on history and philosophy of science, science and values, and the epistemology of scientific practices.

By 1800, water had already changed once. It was no longer one of nature’s simple terms, but a compound of hydrogen and oxygen (see Is Water H₂O? (1) From Element to Compound). The new chemistry had a powerful account of that change. What it still wanted was a more direct experiment: water itself, giving up its constituents.

Then came Volta’s pile.

It was not a spectacular object. Discs of metal stacked in pairs, pieces of moist material between them. Yet it altered the experimental life of electricity. Static machines produced sparks, shocks and theatrical moments. The pile offered something steadier. Electricity could now be made to act for long enough to enter chemistry.

electrolysis
Figure 1 Voltaic pile, the first electric battery, invented by Alessandro Volta in 1800. It did not look spectacular, but it changed what experimenters could do with electricity: it provided a sustained electrical action, long enough for electricity to become a chemical instrument. Source: Science History Institute / Public Domain

Nicholson and Carlisle tried it on water almost at once. They placed wires from the pile in the liquid. Gas appeared, or rather the two sides of the reaction began to declare themselves. Hydrogen was released at one wire; oxygen, in the earliest arrangement, fixed itself to the other, nearly two inches away. Later, with gold or platinum electrodes, oxygen could be collected as gas. The awkward fact remained. The two supposed products of one decomposition appeared at opposite electrical ends of the apparatus.

At first glance, this looked like the experiment the new chemistry had been waiting for.

The trouble was that it looked a little too good.

 

A cleaner decomposition

The first article in this series followed water from element to compound. That change had not been a simple passage from error to fact. It involved a wider transformation of chemical practice: new gases, new names, balances, combustion experiments, recomposition, and a growing confidence in quantitative composition.

Electrolysis seemed to bypass much of that history. No flame, no combustion vessel, no burning of inflammable air with oxygen, no droplets collected on glass. The battery appeared to make water surrender its constituents directly. If water was composed of hydrogen and oxygen, here was synthesis in reverse: pass electrical action through the liquid and the two gases would come out.

Strictly speaking, electrical decomposition of water was not new. In 1789, Adriaan Paets van Troostwijk and Jan Rudolph Deiman had used repeated sparks of static electricity to obtain a mixture of hydrogen and oxygen from water, then recombined that mixture into water. Their experiment mattered. It was also awkward. The gases came together, in small quantities, and separating them for testing was difficult.

Nicholson and Carlisle’s version looked sharper. The Voltaic pile produced sustained action. The products could be made to appear separately. Hydrogen here, oxygen there. Each could be collected, examined and identified.

That was the improvement. It was also where the puzzle began.

 

When neatness becomes suspicious

Suppose water is decomposed. What, exactly, has been decomposed? A particle of water, perhaps. Yet if that particle is split into hydrogen and oxygen, why do the products not appear together? Why does hydrogen emerge at one wire and oxygen at the other? Why should the layout of the battery govern the place where each product appears, while the water between the wires shows no visible sign of being torn apart?

This was not an experiment going wrong. The gases appeared reliably. They appeared at the expected poles. That was precisely what made the situation uncomfortable.

Nicholson noticed the difficulty at once. Hydrogen appeared at one wire; oxygen was found at the other, nearly two inches away. The space between them did not look like a region where water was being visibly pulled into its parts. No trail of bubbles marked the route. The products simply appeared at opposite ends of the electrical arrangement, as if the battery had assigned them places.

Others saw the same embarrassment. Cuvier put it bluntly: if oxygen and hydrogen came from the same particle of water, why did they appear at two distant points, each always at its own wire? Haüy pressed the problem in molecular terms. If one molecule of water was decomposed, why were its products separated? If two molecules were decomposed, why did one give only hydrogen and the other only oxygen?

The question was almost childishly simple. That was why it would not go away.

Today we speak of ions, electrodes and charge transport. Those words make the old difficulty vanish before we have properly felt it. Around 1800, chemists had poles, attractions, affinities, particles, electrical fluids, acids, alkalis, metals, and a growing suspicion that electricity and chemistry belonged together. The experiment was clear enough. The mechanism was not.

Chang calls this the distance problem. The phrase is exact. The gases appeared with too much order for a simple story of local decomposition.

 

The distance problem

The obvious interpretation could still be defended. Perhaps electricity pulled the constituents of water apart. Oxygen went to one pole, hydrogen to the other. Many experiments already suggested that substances had different electrical tendencies, so the idea was hardly absurd.

It left the hardest part untouched.

What travelled through the water? Hydrogen? Oxygen? Something already separated? Something charged? If the constituents were detached somewhere between the electrodes, why did they not appear on the way? If they moved invisibly, why did they not recombine? And if decomposition happened only at the wires, how could it be the decomposition of the same portion of water?

Changes in apparatus did not remove the difficulty. Davy tried water held in separate gold cups, connected only by a moist bridge of fine asbestos, an arrangement he attributed to William Hyde Wollaston. The products still appeared at distant sites. The more carefully experimenters separated the places of action, the more pressing the question became: where, exactly, was water being decomposed?

electrolysis
Figure 2. The distance problem in water electrolysis. Hydrogen appeared at one electrical pole and oxygen at the other, even when the sites of action were separated. The experiment seemed to show that water was decomposed, yet it left open the question of how the products travelled, or whether they were instead produced locally at the electrodes. Source: Diagram generated by the author using AI, based on Chang (2012) and Davy’s 1807 experiments.

 

That was the oddity. Electrolysis was not messy. If anything, it was too orderly. Hydrogen went one way, oxygen another. The battery gave a geography to the products of decomposition.

A flame did nothing like this. When inflammable air burned with oxygen, water appeared as the product of combination. There were difficulties, of course, but not difficulties of distance. Electrolysis changed the spatial form of chemical evidence. Water did not answer in one place. It answered at two.

Under electrical action, water no longer seemed merely something to be composed or decomposed. It seemed to contain routes.

 

Ritter changes the verb

Johann Wilhelm Ritter changed the verb.

For Lavoisierian chemists, electrolysis was analysis. Electricity decomposed water into hydrogen and oxygen. Ritter proposed the reverse. Electrolysis was synthesis.

At the negative pole, water combined with negative electricity and yielded hydrogen. At the positive pole, water combined with positive electricity and yielded oxygen. No product needed to travel from a decomposed particle somewhere in the middle of the liquid. The gases were made where they appeared.

It was a radical move. It was not foolish. Ritter took the most striking feature of the experiment seriously: the gases emerged at different poles. He did not treat that separation as an inconvenience to be patched up later. He built his interpretation around it. If hydrogen appears here and oxygen there, perhaps the two gases are being formed locally by two different electrical processes.

The price was high. Water became elementary again. Hydrogen and oxygen became compounds of water and electricity.

To modern chemistry, this looks perverse. Seen from the apparatus, it had one plain advantage: the gases were produced where they were found. Electricity was still widely treated as something with material agency. If a pile drove something into a liquid, why could that something not combine chemically with the liquid? Why must electricity be only the knife, and never part of what is made?

The phlogistonist echo was clear enough. If inflammable air could be read as water combined with phlogiston, hydrogen could be read as water combined with negative electricity. Identify phlogiston with negative electricity, and Ritter’s scheme comes surprisingly close to older anti-Lavoisierian accounts of water.

Priestley, from America, also saw that the new experiment did not force the Lavoisierian reading. He followed the debate through Nicholson’s journal and argued that electrolysis need not be understood as the decomposition of compound water. His intervention matters because it shows how differently the same electrical process could be read. For Lavoisierians, the gases were constituents released from water. For Priestley, they could still be products of another chemical-electrical process.

Ritter’s view did not last. Chemistry was becoming more firmly Lavoisierian, and elementary water had little room left in the emerging discipline. Still, electrolysis itself had not supplied a neat refutation. Ritter had solved the distance problem rather well. His view lost ground as chemists built an electrochemical practice around compound water.

Keeping water a compound

The Lavoisierian problem was delicate. Chemists had to hold three claims together. Water was composed of hydrogen and oxygen. Electricity decomposed it. Yet the products appeared at different electrodes, with no visible decomposition in between.

So the theory needed help.

One option was invisible transfer: one constituent moved through the liquid to its proper pole. Another was a chain of decompositions and recompositions, in which neighbouring particles handed hydrogen and oxygen along until the products emerged at the ends. In related versions, the whole liquid was imagined as electrically ordered, so that the final gases appeared only where that order met the metal.

These were rescue hypotheses. The phrase can sound dismissive, although it need not be. They were attempts to make a powerful practice intelligible. Electrolysis worked. Its effects could be repeated, varied and extended. What was missing was a mechanism that made the spatial separation of the gases sit comfortably with compound water.

The chain idea had a certain elegance. No single particle of hydrogen or oxygen needed to travel the whole distance. A constituent could be passed along through a succession of exchanges, like a message moving through a crowd. The gas would appear only at the end of the chain.

But what exactly was being passed? How were the exchanges coordinated? Why did the process end at just the right pole? The explanation helped, though it left plenty in the dark.

The transfer idea had its own attraction. If chemical particles had electrical characters, perhaps they could be drawn through the liquid. Again, however, the path remained hidden. The water between the wires did not display the process one wanted to see. Without a developed theory of ions and charge transport, the mechanism remained speculative.

None of this made the hypotheses useless. They kept research going. They suggested new apparatuses, new distances, new electrodes, new liquids and new comparisons. An experiment need not be fully understood before it becomes useful.

That is more or less what happened.

 

When water stopped being negotiable

By the early nineteenth century, compound water was becoming part of the working furniture of chemistry. Not every detail had been explained. The distance problem remained. Yet fewer and fewer chemists were prepared to reopen the older question of whether water might be elementary.

Water as a compound was no longer simply a hypothesis under trial. Increasingly, it was a condition for further work.

That shift mattered. Once water was taken as compound, electrochemistry could ask other questions. What moved towards each pole? What kinds of substances were decomposed by the pile? How did acids, alkalis, salts and metals behave under electrical action? What changed when the electrode, distance or solution changed? How much chemical change corresponded to how much electrical action?

The material practice hardened. Trough batteries became easier to handle. Gold and platinum electrodes helped prevent the products from disappearing into reactions with the metal. Separate cups connected by wet asbestos became a standard arrangement. The theory remained unsettled, but the apparatus was becoming disciplined.

The unresolved puzzle did not stop electrochemistry. Experimenters varied the arrangement. They separated vessels, introduced bridges, changed electrodes, added acids and salts, and studied what appeared where. The field learnt to handle the phenomena before it possessed a settled account of what moved inside the liquid.

Later developments brought more discipline. Faraday gave electrolysis a quantitative discipline in the 1830s. By the end of the nineteenth century, Arrhenius’s theory of ionic dissociation would help make sense of processes that had long remained obscure. That later clarity, though, should not be read backwards into 1800. For decades, electrochemistry advanced with a problem at its centre.

 

What electricity did to water

Electrolysis changed what water could be made to do in the laboratory. It did not simply reveal a truth waiting inside the liquid. It altered the route by which that truth could be pursued.

The first article in this series followed water into the balance sheet of chemistry. Water became a substance that could be produced, analysed, recomposed, weighed and named through its constituents. Electrolysis added another sort of depth. Water could now be interrogated electrically. Its constitution became a problem of poles, currents, attractions, transport and hidden motion.

Lavoisierian chemistry had given water constituents. Electrochemistry gave it pathways.

The familiar classroom demonstration hides that difficulty. The bubbles are easy to see. Their meaning was not. Hydrogen here, oxygen there: that simple separation forced chemists to imagine invisible processes inside a liquid that otherwise looked continuous and unchanged.

Electrolysis made compound water harder to abandon, without making it transparent. It turned water into an electrochemical object: something that could conduct, polarise, transport, release and exchange. The question was no longer only whether hydrogen and oxygen belonged to water. It was how electrical action could make them appear at all.

Still, electrolysis could not settle the formula. It could make water yield hydrogen and oxygen. It could not tell chemists how those elements should be counted.

That was the next difficulty. Once water had constituents, chemistry still had to learn how to count them.

 

References

Chang, H. (2012). Is Water H2O? Evidence, Realism and Pluralism. Dordrecht: Springer. doi: 10.1007/978-94-007-3932-1.

Davy, H. (1807). ‘The Bakerian Lecture, on Some Chemical Agencies of Electricity’. Philosophical Transactions of the Royal Society of London, 97, pp. 1–56. doi: 10.1098/rstl.1807.0001.

Faraday, M. (1834). ‘Experimental Researches in Electricity.—Seventh Series’. Philosophical Transactions of the Royal Society of London, 124, pp. 77–122. doi: 10.1098/rstl.1834.0008.

Nicholson, W. (1800). ‘Account of the New Electrical or Galvanic Apparatus of Sig. Alex. Volta, and Experiments Performed with the Same’. Journal of Natural Philosophy, Chemistry, and the Arts, 4, pp. 179–187.

Singer, G. J. (1814). Elements of Electricity and Electro-Chemistry. London: Printed for Longman, Hurst, Rees, Orme, A. Brown, and R. Triphook.

Volta, A. (1800). ‘On the Electricity Excited by the Mere Contact of Conducting Substances of Different Kinds’. Philosophical Transactions of the Royal Society of London, 90, pp. 403–431. doi: 10.1098/rstl.1800.0018.

Wilkinson, C. H. (1804). Elements of Galvanism, in Theory and Practice: With a Comprehensive View of Its History, from the First Experiments of Galvani to the Present Time. 2 vols. London: John Murray.

 

The post Is Water H₂O? (2): The puzzle of water electrolysis appeared first on Mapping Ignorance.

Is water H₂O? (1): From element to compound

31 August 2026 at 14:00

Author: José Luis Granados Mateo is a postdoctoral researcher in the Department of Philosophy at the University of the Basque Country (EHU) and a member of the Integrated History and Philosophy of Science (iHPS) research group. His work focuses on history and philosophy of science, science and values, and the epistemology of scientific practices.

 

Take a glass of water. Nothing about it seems to ask for a theory. It has no colour worth naming, no dramatic smell, no visible architecture. It runs, freezes, boils, evaporates, dissolves, erodes, circulates and nourishes. It belongs to weather, geology, physiology, cooking and plumbing before it belongs to chemistry.

Then science gives us the famous abbreviation: H₂O.

There is a curious finality in those three symbols. They seem to do what ordinary experience cannot. Rain, steam, ice, rivers, blood and laboratory wash bottles are all brought under a clean chemical statement. Two atoms of hydrogen, one atom of oxygen. For many people, H₂O is more than a formula. It is almost an emblem of scientific knowledge, the moment when science gets behind appearances and tells us what something really is.

Yet the formula stands at the end of a long story. Before water could be written as H₂O, it had to acquire a chemical interior. Chemists first had to learn to treat the most familiar liquid in the world as something that could be taken apart, recomposed and assigned constituents. The first transformation was not from one formula to another. It was from element to compound.

H₂O
Figure 1. Experiment on the decomposition of water, from Antoine-Laurent Lavoisier’s Traité élémentaire de chimie (1789), Plate IV; engraving by Marie-Anne Pierrette Paulze Lavoisier. Before water could be written as H₂O, it had to become an experimental object, handled through gases, vessels, combustion and weighing. Source: Science History Institute, Public Domain Mark 1.0.

 

This is the starting point of Hasok Chang’s Is Water H₂O?, a book that does for water something close to what Inventing Temperature did for thermometry. Temperature now looks like a number waiting to be read from a scale. Chang showed that the scale had to earn that appearance of simplicity. Fixed points had to be stabilised, instruments compared, extrapolations justified. Measurement became routine only after it had first been constructed as a reliable practice.

Water presented another kind of difficulty. The problem was not how to make a phenomenon answer numerically, but how to make a familiar substance answer analytically. Chemists had to learn to look at water as more than something that flowed, froze, boiled, dissolved, condensed or could be purified. They had to ask whether it had an inside: whether it could be taken apart, made again, and understood through its constituents.

To us, that question feels almost unavoidable. In the eighteenth century, it was anything but.

 

When water had no parts

For much of European natural philosophy, water was an element. That claim can sound childish to us, though only because we hear it through the categories that later displaced it.

The idea was older than Aristotle. Thales had imagined water as the origin of things; Empedocles later placed it among the four basic “roots” of the world, alongside earth, air and fire. Aristotle gave that inherited scheme a more systematic form. But these were not elements in the modern chemical sense. No one was classifying them by atomic number, nuclear charge or molecular structure. They belonged to a physics of qualities and transformations, of hot and cold, wet and dry. Water was simple because, in that world, it occupied a basic place in the order of natural change.

By the eighteenth century, that older grammar had been heavily rewritten. Chemistry had become crowded with acids, alkalis, precipitates, metallic calxes, distillations and newly isolated “airs”. Water was everywhere in this world. It served as solvent, medium, reagent, product and experimental environment. It could be purified, frozen, boiled, condensed and recovered.

Still, none of that made it automatically compound. A substance can be experimentally familiar and still have no recognised chemical interior.

The difficulty is easy to miss because we already speak the language that solved it. We say that hydrogen burns in oxygen to form water. But eighteenth-century chemists did not begin with hydrogen and oxygen. They had inflammable air, dephlogisticated air, fixed air, nitrous air and other gaseous bodies whose identities were still unsettled. The experiment did not come with modern subtitles. The vocabulary in which its meaning now appears self-evident was itself one of the products of the revolution.

Water became a compound when certain operations began to count as analysis and synthesis: taking water apart, producing it again, and treating the substances involved as its constituents. This was more than a taxonomic adjustment. It changed the standard of chemical knowledge. To know a substance now meant, increasingly, to know what it was made of.

 

The wrong theory that worked

The defeated rival was phlogiston theory. Posterity has enjoyed defeating it again and again.

In the usual caricature, phlogiston was a ghostly fire-stuff. Combustible bodies contained it and released it when they burned. Metals contained it too. When heated in air, they lost phlogiston and became calxes. Heat the calx with charcoal, and the metal returned because phlogiston had been restored. Then Lavoisier introduced oxygen, and the ghost vanished.

What makes this story so satisfying? Precisely what makes it misleading. It tells the Chemical Revolution from the winner’s seat, where oxygen looks inevitable and phlogiston appears only to make its exit.

From inside the eighteenth-century laboratory, the story looks less like a comedy of error. Phlogiston was not a fantasy floating above the experiments. It belonged to things chemists and metallurgists handled every day. Metals dulled and lost their malleability when calcined. Calxes could be brought back to metal with charcoal. Ores became usable metals in furnaces. Fire, air, metals, respiration and reduction seemed to be tied together by a common traffic of activity. Phlogiston named that traffic. It was a mistaken name for a real pattern.

No one shows this better than Joseph Priestley. He was not a dim survivor of pre-modern chemistry, nor an experimental genius trapped in mere confusion, but one of the great investigators of the eighteenth century, a dissenting minister, political radical and virtuoso of pneumatic chemistry. In Leeds, living beside a brewery, he studied the “fixed air” rising from fermentation, now carbon dioxide. Later, by heating the red calx of mercury, he obtained a far more remarkable gas. Flames burned in it with unusual brilliance; animals could breathe it for longer than ordinary air; Priestley even tried it himself, noticing what he described as a peculiar lightness in his chest.

We call that gas oxygen. Priestley did not. To him, it was dephlogisticated air.

 

H₂O
Figure 2. Gas-manipulating apparatus associated with Joseph Priestley’s pneumatic chemistry, 1775. Priestley’s “dephlogisticated air” was not an arbitrary name, but part of a working experimental culture built around the production, collection and manipulation of gases. Source: Wellcome Collection, M0018264: Illustration of gas manipulating apparatus, 1775. Public Domain.

 

The name sounds absurd only when detached from the operations that made it meaningful. In phlogiston chemistry, ordinary air could become loaded with phlogiston. Air deprived of phlogiston would therefore be especially ready to absorb it again. It should support combustion powerfully and sustain respiration unusually well. That is exactly what Priestley saw. His interpretation was wrong, but it was not arbitrary. It made sense of real experimental behaviour.

Nor was the winning term free of theory. Lavoisier called the gas oxygen, meaning “acid-generator”, because he believed oxygen was the universal principle of acidity. That too was false. The defeated word preserved one mistake; the victorious word preserved another. One became a fossil of discarded chemistry. The other became familiar enough to hide its own history.

 

A few drops on the glass

The next turn in the story came from a gas with a wonderfully plain eighteenth-century name: inflammable air. We now call it hydrogen.

Henry Cavendish had studied this light, combustible gas in the 1760s. It could be produced by reacting metals with acids, and it burned readily. When inflammable air was burned together with dephlogisticated air, something extraordinary happened. Water appeared. Two invisible airs had produced the most familiar liquid in the world.

It is hard, now, not to let modern chemistry finish the sentence for us. Hydrogen combines with oxygen to form water. Of course. But the droplets on the glass did not settle the matter by themselves. They had to be interpreted.

A phlogistonist could tell the story differently. Perhaps inflammable air was water combined with phlogiston. Perhaps dephlogisticated air was water deprived of it, or at least air peculiarly ready to receive it. On that reading, the experiment did not reveal that water was composed of two gases. It showed that ordinary water could be restored through the right exchange of phlogiston.

That may sound evasive from our side of the Chemical Revolution. At the time, it was not an absurd reply. A flame, a gas, a misted vessel, a change in weight. None of these comes with its meaning attached. Evidence becomes evidence inside a working system of concepts, operations and standards. What counts as a substance? What counts as a component? What counts as analysis rather than transformation? Which variable should be trusted most, appearance, activity, weight, or reproducibility?

The new chemistry changed the setting in which the experiment was read. The appearance of water was no longer merely a striking event at the end of combustion. It became part of a quantitative account. How much inflammable air had disappeared? How much oxygen had been involved? How much water had been produced? Could water be decomposed and then recomposed, with the numbers matching closely enough to make the same substance appear on both sides of the operation?

At that point, water was no longer simply appearing on the glass. It was entering the balance sheet of chemistry.

 

The balance makes composition visible

A metal is heated in air. It dulls, loses its shine, gives up its malleability and turns into a calx. In phlogiston chemistry, this looked like a loss. The metal had given up the principle that made it metallic.

Then came the awkward fact on the bench. The calx was heavier.

Heavier, after a supposed loss.

That did not destroy phlogiston theory in a single blow. Good chemists could still defend it, and did. Yet the weight gain gave oxygen chemistry an opening. Perhaps calcination was better understood as combination with something from the air. Follow the weights carefully and chemical change begins to look different. Appearances still matter. Activity still matters. So do colour, heat, flame, residue and reversibility. But weight gives the whole operation a new discipline. It turns transformation into material accounting.

 

H₂O
Figure 3. Lavoisier’s laboratory balance and gas-measuring apparatus, from Antoine-Laurent Lavoisier’s Traité élémentaire de chimie (1789), Plate VIII; engraving by Marie-Anne Pierrette Paulze Lavoisier. In the new chemistry, weighing was not merely a technical aid. It helped make composition visible by turning chemical reactions into material accounts. Source: Science History Institute. Public Domain.

 

The same habit of attention changed the status of water. A substance that can be broken down into measured quantities of other substances, and then produced again from them, starts to lose its old simplicity. It has become analysable. It has constituents.

This was the strongest hand of the new chemistry. Combustion, calcination, gases and water could now be drawn into the same quantitative order. Chemical names changed too. A name was expected to do more than preserve origin, appearance, use or inherited convention. Ideally, it should tell chemists what a substance contained.

The point needs care. This was never a struggle between careful measurers and careless speculators. Cavendish was one of the most exact experimentalists of the century. Richard Kirwan, among the serious defenders of phlogiston, treated weight as a genuine difficulty. The disagreement concerned the authority of weight. Should it count as one experimental constraint among others, or should it become the privileged route to chemical identity?

That question slowly shifted the terrain. Phlogiston chemistry was most at home in a language of principles, powers and transformations. What gives a body combustibility? Why does a metal lose its metallic character? How can a calx be revived? What passes from one substance to another when reaction occurs?

The new chemistry pressed elsewhere. What does this substance contain? In what proportions? Can those constituents be separated and brought together again while the material account remains intact?

Once that style of reasoning became dominant, water’s old simplicity became harder to defend. Water could still be boiled, condensed, purified and recovered, just as before. Now it could also be weighed into a different story. It could be decomposed, recomposed, renamed and treated as a body with an interior.

 

No single knockout blow

The usual story of the Chemical Revolution likes a clean scene. Priestley isolates oxygen and fails to recognise it. Lavoisier understands what Priestley could not. Phlogiston collapses. Modern chemistry begins.

History was less obliging.

Priestley knew the new chemistry and resisted it. Cavendish remained cautious. Other competent chemists hesitated, adopted parts of the oxygen system, or kept some version of phlogiston alive. Their reluctance was not simple blindness. Phlogiston theory still connected combustion, respiration, calcination, reduction and the behaviour of airs. It had also helped produce many of the experimental facts that later counted in favour of oxygen chemistry.

Lavoisier’s system, for all its power, carried its own burdens. His theory of acidity was wrong. The very word oxygen preserved that mistake, since it named the gas as the supposed generator of acids. His chemistry also relied on caloric, an imponderable fluid of heat. Seen from the present, caloric does not look obviously more respectable than phlogiston. Lavoisierian chemistry was elegant, disciplined and transformative. It was not modern chemistry arriving whole and immaculate.

So the real historical question is more interesting than the textbook one. Why did one way of doing chemistry become more convincing, more portable, more teachable and more productive than another?

Much of the answer lies in the rise of compositionism. Oxygen chemistry made substances legible as combinations of measurable constituents. Reactions became material accounts. Chemical names began to function as compressed statements of composition. Laboratory operations, weights, gases and nomenclature could now be made to speak the same language.

Phlogiston still made sense of many transformations, but it sat uneasily in that emerging world. It named a principle of activity, a way of thinking about combustibility, metallic character, reduction and chemical power. The new chemistry increasingly wanted components. It asked what substances were made of, how much of each constituent they contained, and whether those constituents could be separated and brought together again.

As compositionism gained ground, phlogiston began to lose its natural habitat. It could still speak about combustion, reduction and chemical activity, but chemistry was moving towards another language: constituents, proportions, balances, material accounts. The revolution changed the answer, certainly. More importantly, it changed the kind of answer chemistry wanted.

The first metamorphosis of water

When water became a compound, it did more than shift from one scientific category to another. Its identity for chemistry changed.

Before this transition, water could pass through laboratory practice while keeping its apparent simplicity. It could be boiled, frozen, distilled, condensed, purified and recovered. It appeared everywhere, as liquid, vapour, solvent, medium, residue or product. Familiarity gave it stability. It did not yet give it an interior.

After the Chemical Revolution, the same substance began to occupy a different role. Water could be produced from other bodies, analysed through them, and assigned constituents. The liquid that returned from vapour or appeared after combustion now carried a hidden depth. It was no longer merely recovered; it could be accounted for.

Nobody saw that hidden constitution. There were no water molecules under a microscope, no direct image of hydrogen and oxygen joined together. The evidence came through laboratory work: gases prepared and collected, vessels sealed, mixtures burned, droplets condensed, weights compared, names revised. Compound water became credible through practice before it became imaginable as a molecular structure.

This is why the story should not run too quickly towards H₂O. Lavoisierian chemistry helped establish water as a compound of hydrogen and oxygen. It did not settle the formula. It was one thing to say that water was made from hydrogen and oxygen; it was another to decide how many atoms of each entered the compound. That question would take nineteenth-century chemistry into a different set of difficulties.

First came the more basic metamorphosis. Water ceased to be one of nature’s simple terms. It became a substance that could be decomposed, recomposed and written in the language of other substances.

 

The cost of clarity

The new chemistry clarified immensely. It disciplined measurement, stabilised nomenclature and helped make possible the modern science of composition. But clarity selects. It illuminates some things by pushing others into shadow.

Phlogiston theory had been concerned with chemical activity. Why do substances burn, reduce, revive, calcine, combine and transform? Early compositional chemistry was much better at saying what entered and left a reaction than at explaining why the reaction happened at all. It provided an excellent account book, though not yet a full theory of chemical agency.

Some questions once handled by phlogiston later returned in different forms. Chemical potential energy, oxidation-reduction and electrons all came to occupy parts of the conceptual space that phlogiston had once held. That does not vindicate phlogiston as a literal substance. It suggests something subtler and more useful. A false theory can preserve real questions. A victorious theory can be right and still leave work unfinished.

This is a more realistic picture of scientific progress. Oxygen chemistry won for good reasons. But those reasons were not contained in one devastating experiment before which only fools could hesitate. They belonged to a wider reorganisation of chemical practice.

Water’s first great chemical transformation was therefore not the discovery of a formula. It was the making of a new kind of object. The familiar liquid became something that could be analysed, recomposed, weighed and named through its constituents. Only after that could the later question become pressing: not whether water was compound, but what exactly its composition was.

Electricity seemed about to settle the matter. It made water yield hydrogen and oxygen directly, as if nature had finally supplied the decisive experiment.

Instead, the proof produced a new puzzle.

 

References

Chang, H. (2012). Is Water H₂O? Evidence, Realism and Pluralism. Springer. doi 10.1007/978-94-007-3932-1.

Chang, H. (2004). Inventing Temperature. Measurement and Scientific Progress. Oxford University Press.

Cavendish, H. (1784). ‘Experiments on Air’. Philosophical Transactions of the Royal Society of London, 74, 119–153.

Kirwan, R. (1789). An Essay on Phlogiston and the Constitution of Acids. London, J. Johnson.

Lavoisier, A.-L. ([1789] 1965). Elements of Chemistry. Dover.

Priestley, J. ([1796] 1969). Considerations on the Doctrine of Phlogiston, and the Decomposition of Water. Kraus Reprint.

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Generative AI has changed mathematics forever

12 August 2026 at 14:00

Author: Melissa Lee, Senior Lecturer, School of Mathematics, Monash University

Some weeks ago, artificial intelligence company OpenAI announced ten advances in mathematics and computer science made with their as-yet unreleased model Astra. The discoveries cover a wide range of mathematical fields, including geometry, cryptography and coding theory.

These ten are just the latest in a rapidly growing list of mathematical breakthroughs made by generative artificial intelligence (AI) systems.

OpenAI accompanied the announcement with a statement on “responsibility to the mathematical community”. Here, the company acknowledges concerns about attribution, accountability for the correctness of AI-assisted results, and the changing nature of mathematical discovery.

The statement reflects a growing understanding that the remarkable technical advances due to AI are only part of a bigger story about what mathematics means, and what its future will look like.

mathematics
Image created by ChatGPT when prompted this: illustration for an article titled “Generative AI has changed mathematics forever”. Source: OpenAI / ChatGPT

AI is raising big questions

Large language models (LLMs) such as ChatGPT and Claude are creating disruptions in all parts of the mathematical community.

University departments are grappling with the ethical implications of these tools in their research and teaching. Editorial boards of many peer-reviewed journals are being inundated with AI-written papers and must decide how to assess and disclose the use of generative AI. The arXiv preprint repository has seen a sharp increase in mathematical submissions in recent months.

Math papers uploaded to @arxiv per month. Jan 1992 to Jul 2026. Source: https://t.co/nrqjhJBtij pic.twitter.com/pmHvtbYK2X

— Pablo Groisman 🎲 (@pgroisma) August 3, 2026

Funding agencies are starting to develop policies governing acceptable use of AI in applications and assessment.

Broader philosophical questions about how and why mathematics is done in the first place are hard to avoid.

If an LLM can discover a proof, construct an example, or formulate a new question, is there anything uniquely valuable about human mathematical creativity? Is mathematics mostly about producing new theorems, or is it about developing understanding? When a machine contributes to a discovery, who should get the credit?

Growing concern – but little consensus

Among working mathematicians, there is little consensus about the answers. Some have genuine anxiety about the future of the discipline. One mathematician wrote that the advance of AI-assisted mathematics had triggered a “profound spiritual crisis”.

Others have tried to articulate principles for integrating AI into research in a responsible way. The recent Leiden Declaration, signed by thousands of mathematicians from around the world, argues AI should augment rather than replace human mathematical creativity. At the same time, it emphasises transparency, accountability, and proper attribution.

Two weeks ago at the International Congress of Mathematicians, the largest and most prestigious meeting in the field, Terence Tao spoke about “the age of AI”. The famous Fields medallist urged mathematicians to think ahead. In his view, the question is how AI systems might be incorporated into research to strengthen the culture and values of mathematics.

Two attitudes to AI

Two collaborations from my own research over the past few weeks show just how varied these attitudes have become.

My colleague Saul Freedman and I announced an answer to the “semiregularity problem” about highly symmetric networks. This had been the subject of dozens of peer-reviewed papers over several decades.

From the outset, Saul made it clear he did not want AI used in any way during our collaboration due to his concerns about the environmental and social impacts of the technology. Therefore, the work proceeded entirely without the use of these tools.

After we announced our result, two colleagues told me they had independently tried to use LLMs to solve the same problem without success.

AI-powered discovery – with human connection

In contrast, a couple of weeks ago another colleague, Aluna Rizzoli, emailed to tell me he had found an object that collaborators and I had spent over two years searching for. We had used considerable computing resources, but Aluna had used an OpenAI model and a supercomputing cluster. His computation took a mere 43 hours.

The method ChatGPT had generated, working within the intriguingly named “Monster group”, relied on a much more intricate version of an existing algorithm. It would have taken my collaborators and me months to develop this generalisation.

Perhaps the most striking aspect is what happened next. Rather than “scooping” our ongoing work, Aluna invited us to write a joint paper based on the discovery, which appeared on arXiv last week.

Working out where AI fits

Each of these collaborations produced important mathematical advances, yet they embody starkly contrasting attitudes to generative AI.

One deliberately excluded the technology on ethical grounds, while the other embraced it as an indispensable research partner, without abandoning the etiquette of mathematical research. Neither approach appears inherently incompatible with doing excellent mathematics.

That is perhaps the defining feature of the current moment. Rather than converging on a single view, mathematicians are still working out where AI fits within the research process.

The conversation is no longer about whether LLMs are capable of contributing to mathematics research. Instead, we are talking about how their use can be reconciled with the values of collaboration, transparency, and intellectual integrity that form the foundation of our discipline.The Conversation

 

This article is republished from The Conversation under a Creative Commons license.  Original article.

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