为了黑这个：“OpenAI发文表示，他们已经为Lean创建了一个神经定理证明器，用于解决各种具有挑战性的高中奥林匹克问题，包括两个改编自IMO的问题和来自AMC12、AIME竞赛的若干问题。该证明器使用一个语言模型来寻找形式化命题（formal statement）的证明。”

The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map)...

The Appel and Haken proof attracted a fair amount of criticism. Part of it concerned the proof style: the statement of the Four Colour Theorem is simple and elegant so many mathematicians expected a simple and elegant proof that would explain, at least informally, why the theorem was true - not opaque IBM 370 assembly language programs.

用Bing搜(ibm 370 1976), https://www.ibm.com/ibm/history/exhibits/mainframe/mainframe_PP3148.html

System/370 Model 148

The new model also offers increased system throughput -- the amount of time it takes to perform a given amount of work -- compared to the Models 135 and 145.

The Model 148 is available with 1,048,576 or 2,097,152 characters of memory. 高达1MB或2MB内存。同期Apple I默认4KB内存，CPU主频是1M Hz.

The Model 148, under the 48-month contract, can be leased for $17,280 a month with one million characters of memory and for $22,650 a month with two million characters. Monthly rental prices are $19,000 and $24,900. Purchase prices are $689,000 and $859,000. 2021年黄金价格约为1976年黄金价格的14倍。

https://www.ibm.com/ibm/history/exhibits/mainframe/mainframe_FS370B.html

CPU是个啥？Cycle Time (nanoseconds), Model 115 480ns, Model 148 180ns。按200ns算，there are a billion nanoseconds in a second, 主频5MHz。显然是单核，相当显然乘法需要不止一个时钟周期。

• 现在台式机CPU主频接近5G, 10核20线程 (Intel i9)，服务器主频低些，核数更多。5G是5M的1000倍。
• OpenAI有可能用了上千台服务器，每服务器可能至少22核。每服务器内存按64GB算，1000 * 64GB / 2MB = ?
• DDR4内存带宽是DDR内存的多少倍？System/370有CPU片内cache吗？

OpenAI的唯一卖点是“使用一个语言模型”。比如说鸡兔同笼问题，你不用晦涩地输入5, 16两个数，而是“OpenAI啊，鸡和兔共5个，腿共16条，鸡兔各几只？”
老笑话“小明购书两本，一共花了七毛钱，三角三角，几何几何？”，OpenAI目前可能还解决不了。

In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. Since then the proof has gained wide acceptance, although some doubters remain.

  

 

 

As far as is known, the conjecture was first proposed on October 23, 1852, when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed. At the time, Guthrie's brother, Frederick, was a student of Augustus De Morgan (the former advisor of Francis) at University College London. Francis inquired with Frederick regarding it, who then took it to De Morgan (Francis Guthrie graduated later in 1852, and later became a professor of mathematics in South Africa). According to De Morgan:

"A student of mine [Guthrie] asked me to day to give him a reason for a fact which I did not know was a fact—and do not yet. He says that if a figure be any how divided and the compartments differently colored so that figures with any portion of common boundary line are differently colored—four colors may be wanted but not more—the following is his case in which four colors are wanted. Query cannot a necessity for five or more be invented…" (Wilson 2014, p. 18)

"F.G.", perhaps one of the two Guthries, published the question in The Athenaeum in 1854, and De Morgan posed the question again in the same magazine in 1860. Another early published reference by Arthur Cayley (1879) in turn credits the conjecture to De Morgan.

六级/考研单词: lean, elegant, mathematics, opaque, assemble, exhibit, lease, million, billion, adjacent, curve, segment, mere, compute, notify, inquiry, graduate, professor, accord, compartment, portion, query, necessity, pose