Discoveries in science are almost always about "standing on the shoulders of giants" and making connections between known facts. The famous announcement of the Woodward-Hoffmann rules based on orbital symmetry is a classic example of this. It is also a story interwoven with missed opportunities by those who preceded the famous duo, now affectionately known as WH.

My story will start around 180 years ago, with a young French mathematician Évariste Galois.
He died at the age of 20 after a duel, and left behind a manuscript that was the foundation
of groups and permutations. We now know this as *group theory*, and it has proved to
be the foundation stone for many a chemical theory. Abstract mathematical symbolism is not
for everyone and so the next phase of the story depended on chemists creating symbols
that they could use as a language to communicate the ideas of symmetry amongst themselves.
Emil Fischer for example developed the Fisher projection (from three into two dimensions)
that started the process of chemists thinking in 3D. Stereochemistry was born.
But it was a difficult journey. J. J. Thomson, who discovered the electron in 1896,
was still thinking of it in two dimensions as late as around 1918. In 1924, Robert
Robinson (following G. N. Lewis in 1916) started using arrows to represent the changes in electron pairs
that occur during a reaction (the "reaction arrows").
But he too thought only in two dimensions, and it was Hückel in 1930
who moved the understanding of such electrons into three dimensions,
in effect applying Galois's group theory to the solution of a simplified wave equation.
A decade later, organic chemists began formalising a more general 3D stereochemical
symbolism for molecules than Fischer's, although it took a further 30 years or so to become part of an organic chemist's DNA so to speak.

Enter Robert Burns Woodward. He had came to prominent attention with his synthesis of quinine in 1944. We see from his articles that he was not yet using stereochemical notation, as we will now call the representation of 3D chemistry. In his own discussions of the time, he had not yet mastered the art of controlling it in his syntheses (which we now describe as having been non-stereospecific). The person first credited with explicitly associating stereospecificity with a pericyclic synthesis was Gilbert Stork in 1951. By 1956, Woodward had moved on to the synthesis of LSD. Finally in this article, but literally only in a footnote, do we find a concise and clearly knowledgeable remark on the stereochemical implications of that molecule. At the same time however, Derek Barton had been busy utilising stereochemistry in developing an elegant theory of conformational analysis, for which he went on to win the Nobel prize. Clearly, mastering stereochemistry was becoming very important to organic chemists.

We go back in time five years at this stage to Michael Dewar. In a infamously inaccessible article in 1951, he set out his π-complex theory of chemistry, and it is clearly constructed using Galois' group theoretical ideas and applying this to molecular orbitals and how these orbitals can combine to form new molecules. For example, we see application of π-complex theory to alkene-metal complexes (also presented in a footnote!) and in particular focusing on the symmetry of the π-electrons of the alkene and how they might interact with the metal (the Dewar-Chatt-Duncanson model). When in 1964, WH came out with rules of pericyclic reactivity based on the conservation of orbital symmetry, their diagrams can be traced directly *via* Dewar's back to Galois. I make this point since I do not believe the association is sufficiently well known. But forward again to the period 1958-1963, when three separate groups following in Stork's stereospecific footsteps carried out experiments which directly showed that pericyclic reactions were more generally not only stereospecific, by inexplicably so (to them at least). The fruit, so to speak, was now hanging low. But neither Vogel (1958), Corey (1963) nor Havinga and Schlatmann (1961) managed to pick it, although the latter came within a cat's whisker.

Finally, Woodward did so. He too had observed a reaction very similar to that carried out by Corey and Havinga+Schlatmann, during his attempts to synthesize vitamin B12. He took these three observations and his own and talked to a chemist who was immersed in symmetry and Galois' group theory as applied to molecular orbitals, Roald Hoffmann. Like most puzzles, the pieces just dropped into place! The review article of 1969 formalising the observations in a set of rules has become one of the most famous in the history of chemistry. Not least because there was a section entitled *predictions* (every good theory has to make verifiable ones) and the wonderfully teasing *Violations. There are none!* That remark alone probably provoked 5000 research projects alone, if not more!

I close by asking if the connection to Galois might have evolved differently? Hückel, back in 1930, is equally if not more famous for describing the group-theoretical-based molecular orbital pattern of benzene that we now associate with aromaticity (the so-called 4n+2 rule). Benzene of course is famously flat, and no stereochemistry is apparently needed to describe its chemistry. But in 1964, a chemical connection was made to the mathematics of *topology*, and in particular an object known as the Möbius strip. Heilbronner designed a thought molecule using the same π-electrons as studied by Hückel, asking what would happen if they were twisted into a Möbius strip. Such a molecule turned out to be stereochemically chiral (quite when this connection was made is not known). Stereochemistry would be needed after all to describe aromatic molecules! Over the years, an alternative approach to pericyclic stereoselectivity based on (what we now call) Hückel and Möbius aromaticity evolved, based on describing the *transition state model* for the pericyclic reaction. The key concept had evolved from symmetry to topology, and from Galois' group theory to Poincaré's topological transforms of 3D space-curves. Stereochemistry was being conceptually linked to topology; specifically for pericyclic reactions in terms of the topology of the electron density of an (aromatic) molecule (transition state) being described by objects such as *torus links* and *torus knots* and topological invariants known as *linking numbers*. Since the taxonomy of links and knots is extensive (it dates back to the time of Lord Kelvin) we can now start to ask whether a whole new host of connections are just waiting to be made in chemistry as a result of WH's work.