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The greatest mathematician that never lived - Pratik Aghor

  • 0:07 - 0:12
    When Nicolas Bourbaki applied
    to the American Mathematical Society
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    in the 1950s,
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    he was already one of the most influential
    mathematicians of his time.
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    He’d published articles
    in international journals
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    and his textbooks were required reading.
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    Yet his application was firmly rejected
    for one simple reason—
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    Nicolas Bourbaki did not exist.
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    Two decades earlier,
    mathematics was in disarray.
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    Many established mathematicians had lost
    their lives in the first World War,
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    and the field had become fragmented.
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    Different branches used disparate
    methodology to pursue their own goals.
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    And the lack of a shared
    mathematical language
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    made it difficult to share
    or expand their work.
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    In 1934, a group of French mathematicians
    were particularly fed up.
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    While studying at the prestigious
    École normale supérieure,
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    they found the textbook
    for their calculus class so disjointed
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    that they decided to write a better one.
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    The small group
    quickly took on new members,
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    and as the project grew,
    so did their ambition.
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    The result was
    the "Éléments de mathématique,"
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    a treatise that sought to create
    a consistent logical framework
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    unifying every branch of mathematics.
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    The text began
    with a set of simple axioms—
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    laws and assumptions it would use
    to build its argument.
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    From there, its authors derived
    more and more complex theorems
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    that corresponded with work
    being done across the field.
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    But to truly reveal common ground,
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    the group needed to identify
    consistent rules
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    that applied to a wide range of problems.
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    To accomplish this, they gave new,
    clear definitions
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    to some of the most important
    mathematical objects,
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    including the function.
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    It’s reasonable to think of functions
    as machines
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    that accept inputs and produce an output.
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    But if we think of functions
    as bridges between two groups,
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    we can start to make claims about
    the logical relationships between them.
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    For example, consider a group of numbers
    and a group of letters.
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    We could define a function where
    every numerical input corresponds
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    to the same alphabetical output,
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    but this doesn’t establish
    a particularly interesting relationship.
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    Alternatively, we could define a function
    where every numerical input
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    corresponds to a different
    alphabetical output.
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    This second function sets up
    a logical relationship
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    where performing a process on the input
    has corresponding effects
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    on its mapped output.
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    The group began to define functions by how
    they mapped elements across domains.
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    If a function’s output came
    from a unique input,
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    they defined it as injective.
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    If every output can be mapped
    onto at least one input,
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    the function was surjective.
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    And in bijective functions, each element
    had perfect one to one correspondence.
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    This allowed mathematicians to establish
    logic that could be translated
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    across the function’s domains
    in both directions.
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    Their systematic approach
    to abstract principles
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    was in stark contrast to the popular
    belief that math was an intuitive science,
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    and an over-dependence on logic
    constrained creativity.
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    But this rebellious band of scholars
    gleefully ignored conventional wisdom.
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    They were revolutionizing the field,
    and they wanted to mark the occasion
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    with their biggest stunt yet.
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    They decided to publish
    "Éléments de mathématique"
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    and all their subsequent work
    under a collective pseudonym:
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    Nicolas Bourbaki.
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    Over the next two decades, Bourbaki’s
    publications became standard references.
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    And the group’s members took their prank
    as seriously as their work.
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    Their invented mathematician claimed
    to be a reclusive Russian genius
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    who would only meet
    with his selected collaborators.
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    They sent telegrams in Bourbaki’s name,
    announced his daughter’s wedding,
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    and publicly insulted anyone
    who doubted his existence.
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    In 1968, when they could
    no longer maintain the ruse,
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    the group ended their joke
    the only way they could.
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    They printed Bourbaki’s obituary,
    complete with mathematical puns.
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    Despite his apparent death, the group
    bearing Bourbaki’s name lives on today.
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    Though he’s not associated
    with any single major discovery,
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    Bourbaki’s influence informs
    much current research.
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    And the modern emphasis on formal proofs
    owes a great deal to his rigorous methods.
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    Nicolas Bourbaki may have been imaginary—
    but his legacy is very real.
Title:
The greatest mathematician that never lived - Pratik Aghor
Speaker:
Pratik Aghor
Description:

View full lesson: https://ed.ted.com/lessons/the-greatest-mathematician-that-never-lived-pratik-aghor

When Nicolas Bourbaki applied to the American Mathematical Society in the 1950s, he was already one of the most influential mathematicians of his time. He'd published articles in international journals and his textbooks were required reading. Yet his application was firmly rejected for one simple reason: Nicolas Bourbaki did not exist. How is that possible? Pratik Aghor digs into the mystery.

Lesson by Pratik Aghor, directed by Província Studio.

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Video Language:
English
Team:
closed TED
Project:
TED-Ed
Duration:
04:50

English subtitles

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