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In Integers We Trust: The Periodic Table of Materials From Mendeleev to Topology
Materials science has always balanced on the twin pillars of observation
and abstraction—from the alchemists’ crude recipes to today’s AI-driven
materials design. In this talk, we begin by revisiting the pre-quantum era,
when early chemists grappled with the nature of elements and
compounds, and examine how Mendeleev’s periodic table first imposed
order on the chemical world. We then show that what underpins this table
is the surprising power of integers and discrete mathematics—why you
can’t “slip in” between whole numbers—and trace how that insight
underlies quantum mechanics, blurring the boundary between chemistry
and physics.
Building on these foundations, we survey modern families of functional
materials—superconductors, antiferromagnets, charge-density waves,
high-temperature superconductors, and semiconductors—and ask what
makes them uniquely useful, from microchips to maglev trains. Just as
Mendeleev used patterns to predict new elements, we discuss the
quantum strategies for classifying the much larger set of materials,
formed by these elements, today—introducing topology and topological
invariants, showing how band-structure integers classify phases of matter.
We highlight online databases that catalog these discoveries. Finally, we
look ahead to how machine learning and artificial intelligence, guided by
our new periodic table of materials, are revolutionizing the search for
novel compounds, ushering in a new era of predictive materials discovery.
View all episodes
By The Arnold Sommerfeld Center for Theoretical Physics (ASC)Materials science has always balanced on the twin pillars of observation
and abstraction—from the alchemists’ crude recipes to today’s AI-driven
materials design. In this talk, we begin by revisiting the pre-quantum era,
when early chemists grappled with the nature of elements and
compounds, and examine how Mendeleev’s periodic table first imposed
order on the chemical world. We then show that what underpins this table
is the surprising power of integers and discrete mathematics—why you
can’t “slip in” between whole numbers—and trace how that insight
underlies quantum mechanics, blurring the boundary between chemistry
and physics.
Building on these foundations, we survey modern families of functional
materials—superconductors, antiferromagnets, charge-density waves,
high-temperature superconductors, and semiconductors—and ask what
makes them uniquely useful, from microchips to maglev trains. Just as
Mendeleev used patterns to predict new elements, we discuss the
quantum strategies for classifying the much larger set of materials,
formed by these elements, today—introducing topology and topological
invariants, showing how band-structure integers classify phases of matter.
We highlight online databases that catalog these discoveries. Finally, we
look ahead to how machine learning and artificial intelligence, guided by
our new periodic table of materials, are revolutionizing the search for
novel compounds, ushering in a new era of predictive materials discovery.
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