= Jean-Pierre Serre
{c}
<Jean-Pierre Serre> developed methods connecting <algebraic topology>, <algebraic geometry> and <number theory>. He received the first Abel Prize in 2003. https://abelprize.no/abel-prize-laureates/2003[Official laureate record and citation]{ref}
His 1951 work used <singular homology> to study <loop spaces> and <homotopy groups>. A <loop space> turns paths in a <topological space> $X$ that start and end at a fixed base point into points of a new space $\Omega X$. Serre treated $\Omega X$ as the fibre of a <fibration> whose total space is <contractible>, linking the topology of the fibre to that of $X$. The resulting <Serre spectral sequence> organizes the calculation into successive algebraic stages.<Homologie singulière des espaces fibrés. Applications by Jean-Pierre Serre>[printed page 425, Introduction and account of Chapter II]{ref}
The dimension shift
$$
\pi_i(\Omega X)\cong\pi_{i+1}(X),\qquad i\geq1,
$$
makes the strategy useful: information about families of loops becomes information about higher-dimensional <homotopy groups>. For example, a loop in $\Omega X$ describes a continuously varying family of loops in $X$, introducing a second parameter. Turning a geometric question into a calculation about another space is a characteristic strength of this approach.<Homologie singulière des espaces fibrés. Applications by Jean-Pierre Serre>[Introduction, loop-space relation and indirect method]{ref}
\Image[https://abelprize.no/sites/default/files/styles/gutenberg_style_rect_front/public/2021-04/2003_Serre_A.L.Flavik.jpg?itok=acZD6Txz]
{title=Jean-Pierre Serre}
{description=Official 2003 Abel Prize portrait, credited to Anne Lise Flavik on https://abelprize.no/abel-prize-laureates/2003[the laureate page].}
{height=300}
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