<s>
Mathematical	B-Language
Markup	I-Language
Language	I-Language
(	O
MathML	B-Language
)	O
is	O
a	O
mathematical	B-Language
markup	I-Language
language	I-Language
,	O
an	O
application	O
of	O
XML	B-Protocol
for	O
describing	O
mathematical	O
notations	O
and	O
capturing	O
both	O
its	O
structure	O
and	O
content	O
,	O
and	O
is	O
one	O
of	O
a	O
number	O
of	O
mathematical	B-Language
markup	I-Language
languages	I-Language
.	O
</s>
<s>
It	O
is	O
part	O
of	O
HTML5	B-Application
and	O
is	O
a	O
ISO/IEC	O
standard	O
since	O
2015	O
.	O
</s>
<s>
Following	O
some	O
experiments	O
in	O
the	O
Arena	B-Application
browser	I-Application
based	O
on	O
proposals	O
for	O
mathematical	O
markup	O
in	O
HTML	B-Language
,	O
MathML	B-Language
1	O
was	O
released	O
as	O
a	O
W3C	O
recommendation	O
in	O
April	O
1998	O
as	O
the	O
first	O
XML	B-Protocol
language	O
to	O
be	O
recommended	O
by	O
the	O
W3C	O
.	O
</s>
<s>
In	O
October	O
2003	O
,	O
the	O
second	O
edition	O
of	O
MathML	B-Language
Version	O
2.0	O
was	O
published	O
as	O
the	O
final	O
release	O
by	O
the	O
W3C	O
Math	O
Working	O
Group	O
.	O
</s>
<s>
MathML	B-Language
was	O
originally	O
designed	O
before	O
the	O
finalization	O
of	O
XML	B-Language
namespaces	I-Language
.	O
</s>
<s>
However	O
,	O
it	O
was	O
assigned	O
a	O
namespace	O
immediately	O
after	O
the	O
Namespace	O
Recommendation	O
was	O
completed	O
,	O
and	O
for	O
XML	B-Protocol
use	O
,	O
the	O
elements	O
should	O
be	O
in	O
the	O
namespace	O
with	O
namespace	O
URL	O
http://www.w3.org/1998/Math/MathML	O
.	O
</s>
<s>
When	O
MathML	B-Language
is	O
used	O
in	O
HTML	B-Language
(	O
as	O
opposed	O
to	O
XML	B-Protocol
)	O
this	O
namespace	O
is	O
automatically	O
inferred	O
by	O
the	O
HTML	B-Language
parser	O
and	O
need	O
not	O
be	O
specified	O
in	O
the	O
document	O
.	O
</s>
<s>
Version	O
3	O
of	O
the	O
MathML	B-Language
specification	O
was	O
released	O
as	O
a	O
W3C	O
recommendation	O
on	O
20	O
October	O
2010	O
.	O
</s>
<s>
A	O
recommendation	O
of	O
A	O
MathML	B-Language
for	O
CSS	B-Language
Profile	O
was	O
later	O
released	O
on	O
7	O
June	O
2011	O
;	O
this	O
is	O
a	O
subset	O
of	O
MathML	B-Language
suitable	O
for	O
CSS	B-Language
formatting	O
.	O
</s>
<s>
Another	O
subset	O
,	O
Strict	O
Content	O
MathML	B-Language
,	O
provides	O
a	O
subset	O
of	O
content	O
MathML	B-Language
with	O
a	O
uniform	O
structure	O
and	O
is	O
designed	O
to	O
be	O
compatible	O
with	O
OpenMath	B-Language
.	O
</s>
<s>
New	O
content	O
elements	O
include	O
which	O
associates	O
bound	O
variables	O
(	O
)	O
to	O
expressions	B-Algorithm
,	O
for	O
example	O
a	O
summation	O
index	O
.	O
</s>
<s>
The	O
development	O
of	O
MathML	B-Language
3.0	O
went	O
through	O
a	O
number	O
of	O
stages	O
.	O
</s>
<s>
In	O
June	O
2006	O
the	O
W3C	O
rechartered	O
the	O
MathML	B-Language
Working	O
Group	O
to	O
produce	O
a	O
MathML	B-Language
3	O
Recommendation	O
until	O
February	O
2008	O
and	O
in	O
November	O
2008	O
extended	O
the	O
charter	O
to	O
April	O
2010	O
.	O
</s>
<s>
A	O
sixth	O
Working	O
Draft	O
of	O
the	O
MathML	B-Language
3	O
revision	O
was	O
published	O
in	O
June	O
2009	O
.	O
</s>
<s>
An	O
implementation	O
of	O
MathML	B-Language
2	O
landed	O
in	O
WebKit	O
around	O
this	O
same	O
time	O
,	O
with	O
a	O
Chromium	O
implementation	O
following	O
a	O
couple	O
of	O
years	O
later	O
,	O
although	O
that	O
implementation	O
was	O
removed	O
from	O
Chromium	O
after	O
less	O
than	O
a	O
year	O
.	O
</s>
<s>
The	O
Second	O
Edition	O
of	O
MathML	B-Language
3.0	O
was	O
published	O
as	O
a	O
W3C	O
Recommendation	O
on	O
10	O
April	O
2014	O
.	O
</s>
<s>
Also	O
in	O
2015	O
,	O
the	O
MathML	B-Language
Association	O
was	O
founded	O
to	O
support	O
the	O
adoption	O
of	O
the	O
MathML	B-Language
standard	O
.	O
</s>
<s>
At	O
that	O
time	O
,	O
according	O
to	O
a	O
member	O
of	O
the	O
MathJax	B-Language
team	O
,	O
none	O
of	O
the	O
major	O
browser	B-Application
makers	O
paid	O
any	O
of	O
their	O
developers	O
for	O
any	O
MathML-rendering	O
work	O
;	O
whatever	O
support	O
existed	O
was	O
overwhelmingly	O
the	O
result	O
of	O
unpaid	O
volunteer	O
time/work	O
.	O
</s>
<s>
In	O
August	O
2021	O
,	O
a	O
new	O
specification	O
called	O
MathML	B-Language
Core	O
was	O
published	O
,	O
described	O
as	O
the	O
“	O
core	O
subset	O
of	O
Mathematical	B-Language
Markup	I-Language
Language	I-Language
,	O
or	O
MathML	B-Language
,	O
that	O
is	O
suitable	O
for	O
browser	B-Application
implementation.	O
”	O
MathML	B-Language
Core	O
set	O
itself	O
apart	O
from	O
MathML	B-Language
3.0	O
by	O
including	O
detailed	O
rendering	O
rules	O
and	O
integration	O
with	O
CSS	B-Language
,	O
automated	O
browser	B-Application
support	O
testing	O
resources	O
,	O
and	O
focusing	O
on	O
a	O
fundamental	O
subset	O
of	O
MathML	B-Language
.	O
</s>
<s>
MathML	B-Language
deals	O
not	O
only	O
with	O
the	O
presentation	O
but	O
also	O
the	O
meaning	O
of	O
formula	O
components	O
(	O
the	O
latter	O
part	O
of	O
MathML	B-Language
is	O
known	O
as	O
"	O
Content	O
MathML	B-Language
"	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
web	O
pages	O
with	O
MathML	B-Language
embedded	O
in	O
them	O
can	O
be	O
viewed	O
as	O
normal	O
web	O
pages	O
with	O
many	O
browsers	B-Application
,	O
but	O
visually	O
impaired	O
users	O
can	O
also	O
have	O
the	O
same	O
MathML	B-Language
read	O
to	O
them	O
through	O
the	O
use	O
of	O
screen	O
readers	O
(	O
e.g.	O
</s>
<s>
using	O
the	O
VoiceOver	B-Operating_System
in	O
Safari	O
)	O
.	O
</s>
<s>
JAWS	B-Application
from	O
version	O
16	O
onward	O
supports	O
MathML	B-Language
voicing	O
as	O
well	O
as	O
braille	O
output	O
.	O
</s>
<s>
The	O
quality	O
of	O
rendering	O
of	O
MathML	B-Language
in	O
a	O
browser	B-Application
depends	O
on	O
the	O
installed	O
fonts	O
.	O
</s>
<s>
A	O
valid	O
MathML	B-Language
document	O
typically	O
consists	O
of	O
the	O
XML	B-Protocol
declaration	O
,	O
DOCTYPE	O
declaration	O
,	O
and	O
document	O
element	O
.	O
</s>
<s>
The	O
document	O
body	O
then	O
contains	O
MathML	B-Language
expressions	B-Algorithm
which	O
appear	O
in	O
elements	O
as	O
needed	O
in	O
the	O
document	O
.	O
</s>
<s>
Often	O
,	O
MathML	B-Language
will	O
be	O
embedded	O
in	O
more	O
general	O
documents	O
,	O
such	O
as	O
HTML	B-Language
,	O
DocBook	B-Protocol
,	O
or	O
other	O
XML	B-Protocol
schemas	O
.	O
</s>
<s>
Presentation	O
MathML	B-Language
focuses	O
on	O
the	O
display	O
of	O
an	O
equation	O
,	O
and	O
has	O
about	O
30	O
elements	O
.	O
</s>
<s>
A	O
Presentation	O
MathML	B-Language
expression	O
is	O
built	O
up	O
out	O
of	O
tokens	O
that	O
are	O
combined	O
using	O
higher-level	O
elements	O
,	O
which	O
control	O
their	O
layout	O
.	O
</s>
<s>
MathML	B-Language
in	O
HTML5	B-Application
allows	O
most	O
inline	O
HTML	B-Language
markup	O
in	O
mtext	O
,	O
and	O
is	O
conforming	O
,	O
with	O
the	O
HTML	B-Language
markup	O
being	O
used	O
within	O
the	O
MathML	B-Language
to	O
mark	O
up	O
the	O
embedded	O
text	O
(	O
making	O
the	O
first	O
word	O
bold	O
in	O
this	O
example	O
)	O
.	O
</s>
<s>
As	O
usual	O
in	O
HTML	B-Language
and	O
XML	B-Protocol
,	O
many	O
entities	B-General_Concept
are	O
available	O
for	O
specifying	O
special	O
symbols	O
by	O
name	O
,	O
such	O
as	O
and	O
.	O
</s>
<s>
An	O
interesting	O
feature	O
of	O
MathML	B-Language
is	O
that	O
entities	B-General_Concept
also	O
exist	O
to	O
express	O
normally-invisible	O
operators	O
,	O
such	O
as	O
(	O
or	O
the	O
shorthand	O
)	O
for	O
implicit	O
multiplication	O
.	O
</s>
<s>
The	O
full	O
specification	O
of	O
MathML	B-Language
entities	B-General_Concept
is	O
closely	O
coordinated	O
with	O
the	O
corresponding	O
specifications	O
for	O
use	O
with	O
HTML	B-Language
and	O
XML	B-Protocol
in	O
general	O
.	O
</s>
<s>
A	O
complete	O
document	O
that	O
consists	O
of	O
just	O
the	O
MathML	B-Language
example	O
above	O
,	O
is	O
shown	O
here	O
:	O
</s>
<s>
Content	O
MathML	B-Language
focuses	O
on	O
the	O
semantics	O
,	O
or	O
meaning	O
,	O
of	O
the	O
expression	O
rather	O
than	O
its	O
layout	O
.	O
</s>
<s>
Central	O
to	O
Content	O
MathML	B-Language
is	O
the	O
element	O
that	O
represents	O
function	O
application	O
.	O
</s>
<s>
Content	O
MathML	B-Language
uses	O
only	O
a	O
few	O
attributes	O
.	O
</s>
<s>
Tokens	O
such	O
as	O
identifiers	O
and	O
numbers	O
are	O
individually	O
marked	O
up	O
,	O
much	O
as	O
for	O
Presentation	O
MathML	B-Language
,	O
but	O
with	O
elements	O
such	O
as	O
and	O
.	O
</s>
<s>
Rather	O
than	O
being	O
merely	O
another	O
type	O
of	O
token	O
,	O
operators	O
are	O
represented	O
by	O
specific	O
elements	O
,	O
whose	O
mathematical	O
semantics	O
are	O
known	O
to	O
MathML	B-Language
:	O
,	O
,	O
etc	O
.	O
</s>
<s>
Content	O
MathML	B-Language
is	O
nearly	O
isomorphic	O
to	O
expressions	B-Algorithm
in	O
a	O
functional	B-Language
language	I-Language
such	O
as	O
Scheme	B-Language
and	O
other	O
dialects	O
of	O
Lisp	B-Language
.	O
</s>
<s>
amounts	O
to	O
Scheme	B-Language
's	O
,	O
and	O
the	O
many	O
operator	O
and	O
function	O
elements	O
amount	O
to	O
Scheme	B-Language
functions	O
.	O
</s>
<s>
This	O
reflects	O
the	O
long-known	O
close	O
relationship	O
between	O
XML	B-Protocol
element	O
structures	O
,	O
and	O
LISP	B-Language
or	O
Scheme	B-Language
S-expressions	B-Protocol
.	O
</s>
<s>
According	O
to	O
the	O
OM	O
Society	O
,	O
OpenMath	B-Language
Content	O
Dictionaries	O
can	O
be	O
employed	O
as	O
collections	O
of	O
symbols	O
and	O
identifiers	O
with	O
declarations	O
of	O
their	O
semanticsnames	O
,	O
descriptions	O
and	O
rules	O
.	O
</s>
<s>
A	O
2018	O
paper	O
presented	O
at	O
the	O
SIGIR	O
conference	O
proposed	O
that	O
the	O
semantic	O
knowledge	O
base	O
Wikidata	O
could	O
be	O
used	O
as	O
an	O
OpenMath	B-Language
Content	O
Dictionary	O
to	O
link	O
semantic	O
elements	O
of	O
a	O
mathematical	O
formula	O
to	O
unique	O
and	O
language-independent	O
Wikidata	O
items	O
.	O
</s>
<s>
The	O
well-known	O
quadratic	O
formula	O
could	O
be	O
represented	O
in	O
Presentation	O
MathML	B-Language
as	O
an	O
expression	B-Algorithm
tree	I-Algorithm
made	O
up	O
from	O
layout	O
elements	O
like	O
mfrac	O
or	O
msqrt	O
elements	O
:	O
</s>
<s>
This	O
example	O
uses	O
the	O
element	O
,	O
which	O
can	O
be	O
used	O
to	O
embed	O
a	O
semantic	O
annotation	O
in	O
non-XML	O
format	O
,	O
for	O
example	O
to	O
store	O
the	O
formula	O
in	O
the	O
format	O
used	O
by	O
an	O
equation	B-Application
editor	I-Application
such	O
as	O
StarMath	B-Application
or	O
the	O
markup	O
using	O
LaTeX	B-Application
syntax	O
.	O
</s>
<s>
The	O
field	O
is	O
usually	O
a	O
MIME	B-Application
type	I-Application
,	O
although	O
most	O
of	O
the	O
equation	O
encodings	O
do	O
n't	O
have	O
such	O
a	O
registration	O
;	O
freeform	O
text	O
may	O
be	O
used	O
in	O
such	O
case	O
.	O
</s>
<s>
Although	O
less	O
compact	O
than	O
other	O
formats	O
,	O
the	O
XML	B-Protocol
structuring	O
of	O
MathML	B-Language
makes	O
its	O
content	O
widely	O
usable	O
and	O
accessible	O
,	O
allows	O
near-instant	O
display	O
in	O
applications	O
such	O
as	O
Web	B-Application
browsers	I-Application
,	O
and	O
facilitates	O
an	O
interpretation	O
of	O
its	O
meaning	O
in	O
mathematical	O
software	O
products	O
.	O
</s>
<s>
MathML	B-Language
is	O
not	O
intended	O
to	O
be	O
written	O
or	O
edited	O
directly	O
by	O
humans	O
.	O
</s>
<s>
MathML	B-Language
,	O
being	O
XML	B-Protocol
,	O
can	O
be	O
embedded	O
inside	O
other	O
XML	B-Protocol
files	O
such	O
as	O
XHTML	B-Language
files	O
using	O
XML	B-Language
namespaces	I-Language
.	O
</s>
<s>
Inline	O
MathML	B-Language
is	O
also	O
supported	O
in	O
HTML5	B-Application
files	O
.	O
</s>
<s>
There	O
is	O
no	O
need	O
to	O
specify	O
namespaces	O
as	O
there	O
was	O
in	O
XHTML	B-Language
.	O
</s>
<s>
Another	O
standard	O
called	O
OpenMath	B-Language
that	O
has	O
been	O
more	O
specifically	O
designed	O
(	O
largely	O
by	O
the	O
same	O
people	O
who	O
devised	O
Content	O
MathML	B-Language
)	O
for	O
storing	O
formulae	O
semantically	O
can	O
be	O
used	O
to	O
complement	O
MathML	B-Language
.	O
</s>
<s>
OpenMath	B-Language
data	O
can	O
be	O
embedded	O
in	O
MathML	B-Language
using	O
the	O
element	O
.	O
</s>
<s>
OpenMath	B-Language
content	O
dictionaries	O
can	O
be	O
used	O
to	O
define	O
the	O
meaning	O
of	O
elements	O
.	O
</s>
<s>
The	O
OMDoc	B-Language
format	O
has	O
been	O
created	O
for	O
markup	O
of	O
larger	O
mathematical	O
structures	O
than	O
formulae	O
,	O
from	O
statements	O
like	O
definitions	O
,	O
theorems	O
,	O
proofs	O
,	O
and	O
examples	O
,	O
to	O
complete	O
theories	O
and	O
even	O
entire	O
text	O
books	O
.	O
</s>
<s>
Formulae	O
in	O
OMDoc	B-Language
documents	O
can	O
either	O
be	O
written	O
in	O
Content	O
MathML	B-Language
or	O
in	O
OpenMath	B-Language
;	O
for	O
presentation	O
,	O
they	O
are	O
converted	O
to	O
Presentation	O
MathML	B-Language
.	O
</s>
<s>
The	O
ISO/IEC	O
standard	O
Office	B-Operating_System
Open	I-Operating_System
XML	I-Operating_System
(	O
OOXML	B-Operating_System
)	O
defines	O
a	O
different	O
XML	B-Protocol
math	O
syntax	O
,	O
derived	O
from	O
Microsoft	B-Application
Office	I-Application
products	O
.	O
</s>
<s>
However	O
,	O
it	O
is	O
partially	O
compatible	O
through	O
XSL	B-Application
Transformations	I-Application
.	O
</s>
