The greatest mathematician that never lived - Pratik Aghor
-
0:07 - 0:12When Nicolas Bourbaki applied
to the American Mathematical Society -
0:12 - 0:13in the 1950s,
-
0:13 - 0:17he was already one of the most influential
mathematicians of his time. -
0:17 - 0:20He’d published articles
in international journals -
0:20 - 0:22and his textbooks were required reading.
-
0:22 - 0:27Yet his application was firmly rejected
for one simple reason— -
0:27 - 0:31Nicolas Bourbaki did not exist.
-
0:31 - 0:35Two decades earlier,
mathematics was in disarray. -
0:35 - 0:39Many established mathematicians had lost
their lives in the first World War, -
0:39 - 0:41and the field had become fragmented.
-
0:41 - 0:46Different branches used disparate
methodology to pursue their own goals. -
0:46 - 0:49And the lack of a shared
mathematical language -
0:49 - 0:52made it difficult to share
or expand their work. -
0:52 - 0:57In 1934, a group of French mathematicians
were particularly fed up. -
0:57 - 1:01While studying at the prestigious
École normale supérieure, -
1:01 - 1:05they found the textbook
for their calculus class so disjointed -
1:05 - 1:08that they decided to write a better one.
-
1:08 - 1:10The small group
quickly took on new members, -
1:10 - 1:14and as the project grew,
so did their ambition. -
1:14 - 1:16The result was
the "Éléments de mathématique," -
1:16 - 1:20a treatise that sought to create
a consistent logical framework -
1:20 - 1:23unifying every branch of mathematics.
-
1:23 - 1:26The text began
with a set of simple axioms— -
1:26 - 1:30laws and assumptions it would use
to build its argument. -
1:30 - 1:34From there, its authors derived
more and more complex theorems -
1:34 - 1:37that corresponded with work
being done across the field. -
1:37 - 1:40But to truly reveal common ground,
-
1:40 - 1:43the group needed to identify
consistent rules -
1:43 - 1:46that applied to a wide range of problems.
-
1:46 - 1:49To accomplish this, they gave new,
clear definitions -
1:49 - 1:52to some of the most important
mathematical objects, -
1:52 - 1:55including the function.
-
1:55 - 1:58It’s reasonable to think of functions
as machines -
1:58 - 2:01that accept inputs and produce an output.
-
2:01 - 2:05But if we think of functions
as bridges between two groups, -
2:05 - 2:09we can start to make claims about
the logical relationships between them. -
2:09 - 2:13For example, consider a group of numbers
and a group of letters. -
2:13 - 2:17We could define a function where
every numerical input corresponds -
2:17 - 2:20to the same alphabetical output,
-
2:20 - 2:24but this doesn’t establish
a particularly interesting relationship. -
2:24 - 2:28Alternatively, we could define a function
where every numerical input -
2:28 - 2:31corresponds to a different
alphabetical output. -
2:31 - 2:35This second function sets up
a logical relationship -
2:35 - 2:39where performing a process on the input
has corresponding effects -
2:39 - 2:41on its mapped output.
-
2:41 - 2:46The group began to define functions by how
they mapped elements across domains. -
2:46 - 2:50If a function’s output came
from a unique input, -
2:50 - 2:52they defined it as injective.
-
2:52 - 2:56If every output can be mapped
onto at least one input, -
2:56 - 2:58the function was surjective.
-
2:58 - 3:04And in bijective functions, each element
had perfect one to one correspondence. -
3:04 - 3:09This allowed mathematicians to establish
logic that could be translated -
3:09 - 3:13across the function’s domains
in both directions. -
3:13 - 3:16Their systematic approach
to abstract principles -
3:16 - 3:21was in stark contrast to the popular
belief that math was an intuitive science, -
3:21 - 3:25and an over-dependence on logic
constrained creativity. -
3:25 - 3:30But this rebellious band of scholars
gleefully ignored conventional wisdom. -
3:30 - 3:34They were revolutionizing the field,
and they wanted to mark the occasion -
3:34 - 3:36with their biggest stunt yet.
-
3:36 - 3:39They decided to publish
"Éléments de mathématique" -
3:39 - 3:43and all their subsequent work
under a collective pseudonym: -
3:43 - 3:46Nicolas Bourbaki.
-
3:46 - 3:51Over the next two decades, Bourbaki’s
publications became standard references. -
3:51 - 3:56And the group’s members took their prank
as seriously as their work. -
3:56 - 4:01Their invented mathematician claimed
to be a reclusive Russian genius -
4:01 - 4:04who would only meet
with his selected collaborators. -
4:04 - 4:08They sent telegrams in Bourbaki’s name,
announced his daughter’s wedding, -
4:08 - 4:13and publicly insulted anyone
who doubted his existence. -
4:13 - 4:17In 1968, when they could
no longer maintain the ruse, -
4:17 - 4:20the group ended their joke
the only way they could. -
4:20 - 4:26They printed Bourbaki’s obituary,
complete with mathematical puns. -
4:26 - 4:31Despite his apparent death, the group
bearing Bourbaki’s name lives on today. -
4:31 - 4:34Though he’s not associated
with any single major discovery, -
4:34 - 4:38Bourbaki’s influence informs
much current research. -
4:38 - 4:43And the modern emphasis on formal proofs
owes a great deal to his rigorous methods. -
4:43 - 4:49Nicolas 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.
- Video Language:
- English
- Team:
closed TED
- Project:
- TED-Ed
- Duration:
- 04:50
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lauren mcalpine accepted English subtitles for The greatest mathematician that never lived | |
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lauren mcalpine edited English subtitles for The greatest mathematician that never lived | |
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Tara Ahmadinejad edited English subtitles for The greatest mathematician that never lived | |
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Tara Ahmadinejad edited English subtitles for The greatest mathematician that never lived | |
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Tara Ahmadinejad edited English subtitles for The greatest mathematician that never lived |