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kē jì
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OpenAI (AI company)
OpenAI
OpenAI
new model
xīn móxíng
新模型
Astra (next-generation AI model)
Astra
Astra
to solve / to crack
pòjiě
破解
ten
shí gè
十个
mathematics
shùxué
数学
difficult open problem
nántí
难题
，
to cost / to consume
hàofèi
耗费
only approximately
jǐn yuē
仅约
$2,000 USD
liǎngqiān měiyuán
两千美元
。

OpenAI (AI company)
OpenAI
OpenAI
on (formal preposition)
yú
于
August
bāyuè
八月
the 1st
yī rì
一日
to announce
xuānbù
宣布
，
its
qí
其
next-generation
xià yī dài
下一代
model
móxíng
模型
Astra
Astra
Astra
(particle)
de
的
internal
nèibù
内部
version
bǎnběn
版本
successfully
chénggōng
成功
has solved
jiějuéle
解决了
mathematics
shùxué
数学
and (formal)
yǔ
与
theoretical
lǐlùn
理论
computer science
jìsuànjī kēxué
计算机科学
field / domain
lǐngyù
领域
(particle)
de
的
ten
shí gè
十个
long-standing
chángqī
长期
unsolved
wèijiě
未解
open problem
nántí
难题
。
all
suǒyǒu
所有
proof
zhèngmíng
证明
already
yǐ
已
on
zài
在
GitHub (code hosting platform)
GitHub
GitHub
publicly
gōngkāi
公开
to publish / to release
fābù
发布
，
this / the current
běn cì
本次
computation
jìsuàn
计算
to cost / to consume
hàofèi
耗费
approximately
yuē
约
$2,000 USD
liǎngqiān měiyuán
两千美元
。

August 5, 2026 at 6:05 PM

OpenAI (AI company)
OpenAI
OpenAI
on (formal)
yú
于
August
bāyuè
八月
the 1st
yī rì
一日
to publish
fābù
发布
announcement
gōnggào
公告
，
stating that
chēng
称
its
qí
其
next-generation
xià yī dài
下一代
model
móxíng
模型
Astra
Astra
Astra
(particle)
de
的
internal
nèibù
内部
version
bǎnběn
版本
successfully
chénggōng
成功
has solved
jiějuéle
解决了
ten
shí gè
十个
long-standing
chángqī
长期
unresolved for a long time
xuán ér wèijué
悬而未决
(particle)
de
的
mathematics
shùxué
数学
and (formal)
yǔ
与
computer science
jìsuànjī kēxué
计算机科学
open problem
nántí
难题
。
these
zhèxiē
这些
open problems
nántí
难题
spanning
héngkuà
横跨
eight
bā gè
八个
different
bùtóng
不同
field / domain
lǐngyù
领域
，
including
bāokuò
包括
group theory
qún lùn
群论
、
high-dimensional
gāo wéi
高维
geometry
jǐhé
几何
、
quantum
liàngzǐ
量子
complexity
fùzá xìng
复杂性
as well as
yǐjí
以及
lattice (math structure)
gé
格
cryptography
mìmǎ xué
密码学
。
among them
qízhōng
其中
most
zuì
最
to attract
shòu
受
attention
guānzhù
关注
(particle)
de
的
result / achievement
chéngguǒ
成果
is
shì
是
Astra
Astra
Astra
to provide / to give
gěichū
给出
(completed action)
le
了
one / a
yī gè
一个
non-
fēi
非
sofic (mathematical term)
sofic
sofic
group (math structure)
qún
群
(particle)
de
的
explicit
xiǎnshì
显式
construction
gòuzào
构造
，
has resolved
jiějuéle
解决了
since
zì
自
1999
1999 nián
1999年
since / starting from
qǐ
起
(particle)
de
的
open / publicly stated
gōngkāi
公开
problem / question
wèntí
问题
。
Astra
Astra
Astra
also
hái
还
to disprove / to refute
fǒu zhèng
否证
(completed action)
le
了
Connes (mathematician)
Connes
Connes
rigidity
gāngxìng
刚性
conjecture
cāixiǎng
猜想
，
to construct
gòuzào
构造
(completed action)
le
了
infinitely many
wúqióng duō
无穷多
(measure word)
gè
个
satisfying
mǎnzú
满足
the same / identical
xiāngtóng
相同
von Neumann
féng nuòyīmàn
冯诺依曼
algebra
dàishù
代数
(particle)
de
的
non-
fēi
非
isomorphic
tónggòu
同构
group (math)
qún
群
。
OpenAI
OpenAI
OpenAI
to state
biǎoshì
表示
，
artificial intelligence
réngōngzhìnéng
人工智能
(nominalizing particle)
suǒ
所
generated / to generate
shēngchéng
生成
(particle)
de
的
argument / reasoning
lùnzhèng
论证
after / through (formal)
jīng
经
researchers
yánjiū rényuán
研究人员
to organize / to compile
zhěnglǐ
整理
after / following
hòu
后
，
already
yǐ
已
in
zài
在
Lean (proof assistant)
Lean
Lean
in
zhōng
中
to complete
wánchéng
完成
formalization
xíngshì huà
形式化
verification
yànzhèng
验证
。
the entire
zhěnggè
整个
problem-solving
qiújiě
求解
process
guòchéng
过程
only / merely
jǐn
仅
to cost
hàofèi
耗费
approximately
yuē
约
$2,000 USD
liǎngqiān měiyuán
两千美元
(particle)
de
的
computing power
suànlì
算力
cost / expense
fèiyòng
费用
。
OpenAI
OpenAI
OpenAI
simultaneously
tóngshí
同时
to announce
xuānbù
宣布
to launch / to roll out
tuīchū
推出
academic
xuéshù
学术
researchers
yánjiū rényuán
研究人员
ChatGPT
ChatGPT
ChatGPT
program / plan
jìhuà
计划
，
to
xiàng
向
100,000
shíwàn
十万
(measure word for people)
míng
名
scientist
kēxuéjiā
科学家
and
yǔ
与
mathematician
shùxuéjiā
数学家
free of charge
miǎnfèi
免费
to open / to make available
kāifàng
开放
the most advanced / cutting-edge
zuì xiānjìn
最先进
(particle)
de
的
model
móxíng
模型
right of use / access
shǐyòng quán
使用权
。

News in English

Science & Technology

OpenAI Model Astra Solves Ten Long-Standing Mathematics Problems for About 2000 Dollars

OpenAI announced on August 1 that an internal version of its next-generation model Astra solved ten long-standing open problems in mathematics and theoretical computer science. All proofs were published on GitHub and the computation cost approximately $2,000.

More in Science & Technology

the European Union
ōuméng
欧盟
artificial intelligence
réngōngzhìnéng
人工智能
new regulation
xīn guī
新规
formally / officially
zhèngshì
正式
to take effect / to come into force
shēngxiào
生效
，
chatbot
liáotiān jīqìrén
聊天机器人
must / is required to
xū
须
to self-report / to declare
zì bào
自报
identity
shēnfèn
身份
。

EU AI Rules Take Effect, Requiring Chatbots to Declare Their Identity

liquid cooling
yèliáng
液冷
technology
jìshù
技术
breakthrough
túpò
突破
energy efficiency
néngxiào
能效
improved
tísheng
提升
60 percent
60%
60%
。

Liquid Cooling Technology Achieves Energy Efficiency Breakthrough

European Union
ōuméng
欧盟
AI Act
rénggōng zhìnéng fǎàn
《人工智能法案》
officially
zhèngshì
正式
takes effect
shēngxiào
生效
。

European Union AI Act Takes Effect

OpenAI (AI research company)
OpenAI
OpenAI
artificial intelligence
rénggōng zhìnéng
人工智能
model
móxíng
模型
to solve
jiějué
解决
ten major
shídà
十大
mathematics
shùxué
数学
difficult problem
nántí
难题
。

OpenAI AI Model Solves Ten Major Mathematics Problems