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展示了随机性可以以数学家从未想象过的方式被使用（完整短语，展示语言修辞上的对比）
"Erdős’ technique overcame this difficulty, demonstrating that randomness could be used in ways mathematicians had never imagined."
令人震惊的、极其惊人的（表示强烈的惊讶和赞叹）
"“It was just astounding that you would use randomness,” said Joel Spencer of New York University."
修补、不断微调（此处指科学家不断改进已有方法）
"For the past 80 years, mathematicians have been tinkering with Erdős’ randomness-based technique"
丰产的游戏场（比喻一个能持续产生新想法的领域）
"“It’s a very fruitful playground for ideas,” Sudakov said."
何必呢、为什么要费这个劲（一种质疑对方努力价值的反问）
"“Why bother?”"
一个看上去对一种颜色帮助很大、但对另一种颜色完全没有帮助的权衡（完整引用的口语化评论）
"“There’s a trade-off that looks like it really helps in one color, but it doesn’t help at all in the other color,” Conlon said."
明目张胆的隐藏（指答案明明在眼前却被所有人忽略）
"Their technique, he said, “was hidden in plain view.”"
权衡、折中（此处指在一种颜色上获益必在另一种上受损的平衡）
"“There’s a trade-off that looks like it really helps in one color, but it doesn’t help at all in the other color,” Conlon said."
迷住、深深吸引（此处指研究生被论文完全吸引）
"he came across a paper on Ramsey numbers that captivated him."
完全颠覆了我们所有的直觉（一种口语化的强调表达）
"These spheres “mess with all our intuitions completely,” said David Conlon of the California Institute of Technology."
大量、一连串（突然而来的许多进展）
"Ma, Shen, and Xie’s proof has already generated a spate of further progress."
离散数学（研究不连续对象的数学分支，与连续数学相对）
"It’s now one of the most ubiquitous techniques in “discrete” math, the study of objects (like graphs) that are separate rather than continuous."
缥缈的、难以捉摸的、非物质的（此处形容抽象数学概念的神秘性）
"“The randomness, I think, just helps us get at something that is otherwise very ethereal,” Horn said."
完全静止、纹丝不动（此处比喻数学进展停滞）
"progress remained stock-still for off-diagonal Ramsey numbers where the forbidden red and blue cliques are both relatively large."
无处不在的、普遍存在的（非常正式）
"It’s now one of the most ubiquitous techniques in “discrete” math"
这时出现了……（一种讲故事时引入新角色的叙事手法）
"Then along came a graduate student with barely any expertise in Ramsey theory."
不情愿的、厌恶的（此处指数学家不愿意接受他的方法）
"At first, mathematicians were loath to follow his lead."
与……一致、符合（强调前后的逻辑延续性）
"That’s in keeping with the probabilistic method’s long history."
基准线、起点（此处指经过范式转变后，新方法已成为常识）
"“Now, that’s the baseline.”"
限制条件、告诫性说明（此处指对染色的约束条件）
"Now color each edge either red or blue, but with one caveat: Don’t create any large clusters of nodes that are all connected by edges of the same color."
四处漂泊的、居无定所的（形容数学家经常旅行）
"In 1947, Paul Erdős, the itinerant Hungarian mathematician, introduced what would become one of math’s most powerful tools."
被禁止的结构（图论中指不允许出现的子图模式）
"These forbidden structures are called monochromatic cliques."
单色团（图论中指所有边颜色相同的完全子图）
"These forbidden structures are called monochromatic cliques."
拉姆齐数（图论中保证出现某种结构的最小节点数）
"Mathematicians therefore say that the “Ramsey number” for a clique of size 3, denoted R(3), is 6."
荒野中的呼声（比喻提出正确观点但无人理解的孤独先知）
"“For many years, Erdős was like a voice in the wilderness,” Spencer said."
荆棘丛，尤指黑莓或悬钩子属植物的带刺灌木丛
"Across Washington and Oregon, jagged walls of blackberry brambles choke out nearly every hiking trail, highway shoulder, and vacant lot in the region."
多汁的，鲜美多液的（形容水果）
"Upon opening it, he discovered that the seeds bore a hardy blackberry plant that thrived in temperate areas and produced large, succulent fruits."
用词不当，不准确的名称；名不副实
"The name was a misnomer, as the species, known scientifically as Rubus armeniacus, is actually native to Armenia and northern Iran."
剧毒的；致命的；引申为（比喻）恶毒的，仇恨极深的
"...ensuring that “evil” or “poisonous” traits do not influence the general stock or reproduce among themselves to create more “virulent” organisms that may wreak havoc on the social order."
造成严重破坏；引发大混乱
"...ensuring that “evil” or “poisonous” traits do not influence the general stock or reproduce among themselves to create more “virulent” organisms that may wreak havoc on the social order."
（彻底）检修，大修；全面改革
"In light of this potential, Burbank called for a long-term overhaul of American childrearing in order to immerse generations of children in favorable environments..."
可塑的；易受影响的；可适应的
"Under this view, human and plant species were entirely malleable, shaped profoundly by the pressures of the natural and artificial world around them."
堡垒；（引申为）某种思想、原则或社群的最后据点或坚守者
"If human traits were merely the accumulated imprints of past environments, then domestic and educational environments maintained by women could become bastions of human optimization."
首要地位；至高无上性
"By arguing that environment was the true “architect of heredity,” Burbank expanded the work of evolution into the American domestic sphere. As historian of science Katherine Pandora writes, this belief offered a vision of change that gave primacy to environment..."
推动力；驱使力；（此处指一种观念或力量引发的）动机、动力
"The industrial impulse that welcomed this hardy blackberry also manifested in Burbank’s vision for the future of American society."
有创业精神的；有事业心的；富于魄力的
"At the core of this innovation was the enterprising horticulturist Luther Burbank."
（植物）耐寒的，强壮的；坚韧的
"Upon opening it, he discovered that the seeds bore a hardy blackberry plant that thrived in temperate areas and produced large, succulent fruits."
（动词）显示，表明，显露（尤指通过外在表现或行动）
"The industrial impulse that welcomed this hardy blackberry also manifested in Burbank’s vision for the future of American society."
（化学）易挥发的；（引申为）易变的，动荡不定的，不稳定的
"To control the volatile biological mixing between the influx of American newcomers, he believed that human designers should dictate their surroundings and regulate reproduction..."
容量大的；宽敞的；内涵丰富的（此处比喻指‘法律定义宽泛、富有弹性’）
"Colonial administrators in the Philippines imported from the U.S. metropole the capacious crime of vagrancy to regulate... a range of nonnormative, unproductive, and habitually immoral bodies."
（殖民语境中的）宗主国；（与殖民地相对的）母国
"While sodomy was a social problem in the metropole, it was not, as colonial administrators would have it, a problem in the Philippines."
也就是；即（用于引出更具体的解释或列表）
"There was nothing, to wit, unnatural, immoral, or degenerate about U.S. colonial relations."
堕落的；退化的；腐化的（尤指道德标准或生理素质远低于正常水平）
"There was nothing, to wit, unnatural, immoral, or degenerate about U.S. colonial relations."
（尤指性行为或社会行为上的）异常，偏离（社会规范）
"suggests non-normative sexual behavior in the Philippines was treated by the colonial administration as racial deviancy."
（法律用语）一揽子指控；泛指性、涵盖面广的罪名
"colonial laws against so-called vagrancy 'enabled a range of umbrella charges to criminalize anyone who threatened social order.'"
（本该一致的事物之间的）差异，矛盾，不一致
"Scrutinizing this discrepancy, Victor Román Mendoza suggests non-normative sexual behavior in the Philippines was treated by the colonial administration as racial deviancy."
类似于……的；与……同类的
"administrators, already aware that the Philippines was perceived as akin to Sodom and Gomorrah, were eager to downplay negative views of their prized new American colony."
肛交（特指历史上法律和道德话语中所禁止的同性性行为）
"In 1905, Manila resident Pablo Trinidad was convicted of practicing sodomy."
淡化，贬低……的重要性；轻描淡写
"administrators...were eager to downplay negative views of their prized new American colony."
（市或地方政府颁布的）法令，法规
"he was prosecuted under an ordinance that made 'vagrancy' a misdemeanor."