the analogy i make is imagine that you have an art class
imagine that you have an art class
imagine that you have an art class in which they teach you only how to
in which they teach you only how to
in which they teach you only how to paint fences and walls but never show
paint fences and walls but never show
paint fences and walls but never show you the paintings of the great masters
you the paintings of the great masters
you the paintings of the great masters so you never see picasso or van gogh
so you never see picasso or van gogh
so you never see picasso or van gogh what would you think of mathematics you
what would you think of mathematics you
what would you think of mathematics you know
know
know of art in the if it's if you had an art
of art in the if it's if you had an art
of art in the if it's if you had an art class like this you would think it's
class like this you would think it's
class like this you would think it's only about painting fences and walls you
only about painting fences and walls you
only about painting fences and walls you would think it's the most boring subject
would think it's the most boring subject
would think it's the most boring subject ever and that's what happens with
ever and that's what happens with
ever and that's what happens with mathematics unfortunately the
mathematics unfortunately the
mathematics unfortunately the kind of material that we present to our
kind of material that we present to our
kind of material that we present to our our students in school and it's not
our students in school and it's not
our students in school and it's not just it's it's universal it's everywhere
just it's it's universal it's everywhere
just it's it's universal it's everywhere around the world
around the world
around the world this material is most of it is more than
this material is most of it is more than
this material is most of it is more than 1 000 years old just think about it what
1 000 years old just think about it what
1 000 years old just think about it what do we usually talk about we talk about
do we usually talk about we talk about
do we usually talk about we talk about numbers we talk about quadratic
numbers we talk about quadratic
numbers we talk about quadratic equations or euclidean geometry
equations or euclidean geometry
equations or euclidean geometry euclidean geometry is 2 300 years old
euclidean geometry is 2 300 years old
euclidean geometry is 2 300 years old and it's a beautiful piece of
and it's a beautiful piece of
and it's a beautiful piece of mathematics which actually laid the
mathematics which actually laid the
mathematics which actually laid the foundation for the axiomatic method and
foundation for the axiomatic method and
foundation for the axiomatic method and so on but in literature around the same
so on but in literature around the same
so on but in literature around the same time homer wrote you know ulysses and
time homer wrote you know ulysses and
time homer wrote you know ulysses and iliad but in our literature classes we
iliad but in our literature classes we
iliad but in our literature classes we don't stop at homer we continue we read
don't stop at homer we continue we read
don't stop at homer we continue we read more recent works of of literature
more recent works of of literature
more recent works of of literature likewise with art likewise with science
likewise with art likewise with science
likewise with art likewise with science with physics
with physics
with physics with biology and so on so for instance
with biology and so on so for instance
with biology and so on so for instance what what are the things which are
what what are the things which are
what what are the things which are missing non-euclidean geometry and it
missing non-euclidean geometry and it
missing non-euclidean geometry and it sounds complicated
sounds complicated
sounds complicated and abstract but in fact
and abstract but in fact
and abstract but in fact it's closer to the real world the
it's closer to the real world the
it's closer to the real world the surface of the earth is spherical right
surface of the earth is spherical right
surface of the earth is spherical right and if you do try to do geometry on the
and if you do try to do geometry on the
and if you do try to do geometry on the sphere rather than on the plane that's
sphere rather than on the plane that's
sphere rather than on the plane that's the euclidean non-euclidean geometry
the euclidean non-euclidean geometry
the euclidean non-euclidean geometry where the sum of the angles of a
where the sum of the angles of a
where the sum of the angles of a triangle is not 180 degrees but it's
triangle is not 180 degrees but it's
triangle is not 180 degrees but it's greater than 180 degrees that's all it
greater than 180 degrees that's all it
greater than 180 degrees that's all it is
is
is so but in our classes
so but in our classes
so but in our classes the earth is flat as it were because we
the earth is flat as it were because we
the earth is flat as it were because we just restrict ourselves to this there
just restrict ourselves to this there
just restrict ourselves to this there are many other interesting
are many other interesting
are many other interesting topics which could be presented in
topics which could be presented in
topics which could be presented in school for example um
school for example um
school for example um cryptography
cryptography
cryptography is now
is now
is now widespread uh everywhere from from
widespread uh everywhere from from
widespread uh everywhere from from banking to cryptocurrency and so on
banking to cryptocurrency and so on
banking to cryptocurrency and so on uh it's based on what's called clock
uh it's based on what's called clock
uh it's based on what's called clock arithmetic where you do calculations
arithmetic where you do calculations
arithmetic where you do calculations where
where
where the way you do calculations with time
the way you do calculations with time
the way you do calculations with time where after 12 you have well in
where after 12 you have well in
where after 12 you have well in different countries in the united states
different countries in the united states
different countries in the united states after 12 instead of 13 you say 1 1 pm in
after 12 instead of 13 you say 1 1 pm in
after 12 instead of 13 you say 1 1 pm in europe you usually go all the way to 24
europe you usually go all the way to 24
europe you usually go all the way to 24 but 24 is like zero in 20 you don't say
but 24 is like zero in 20 you don't say
but 24 is like zero in 20 you don't say 25 hours but you say one o'clock and so
25 hours but you say one o'clock and so
25 hours but you say one o'clock and so on so likewise with angles you go up to
on so likewise with angles you go up to
on so likewise with angles you go up to 360 then it becomes circular it goes
360 then it becomes circular it goes
360 then it becomes circular it goes back to zero right
back to zero right
back to zero right and so this type of clock arithmetic is
and so this type of clock arithmetic is
and so this type of clock arithmetic is is very important in mathematics and you
is very important in mathematics and you
is very important in mathematics and you can look at the solutions of equations
can look at the solutions of equations
can look at the solutions of equations subject to this rule and this is what
subject to this rule and this is what
subject to this rule and this is what this is exactly the
this is exactly the
this is exactly the type of mathematics which is at the root
type of mathematics which is at the root
type of mathematics which is at the root of modern cryptography so for sure we
of modern cryptography so for sure we
of modern cryptography so for sure we can teach our students this stuff or we
can teach our students this stuff or we
can teach our students this stuff or we can talk about symmetries
can talk about symmetries
can talk about symmetries like a rubik's cube and things like that
like a rubik's cube and things like that
like a rubik's cube and things like that so unfortunately our um our math
so unfortunately our um our math
so unfortunately our um our math education today is is very limited and
education today is is very limited and
education today is is very limited and very few people get to see the
very few people get to see the
very few people get to see the masterpieces the masterpieces of
masterpieces the masterpieces of
masterpieces the masterpieces of mathematics the way we see masterpieces
mathematics the way we see masterpieces
mathematics the way we see masterpieces of art
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