具体描述
In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancée.
But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
作者简介
Peter Pesic is Tutor and Musician-in-Residence at St. John’s College, Santa Fe. He is the author of Labyrinth: A Search for the Hidden Meaning of Science; Seeing Double: Shared Identities in Physics, Philosophy, and Literature; Abel’s Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability; and Sky in a Bottle, all published by the MIT Press.
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阅读《Abel's Proof》的过程，与其说是在学习一个数学证明，不如说是在经历一场心灵的洗礼。我被阿贝尔身上那种不畏权威、敢于挑战的精神所折服。在那个时代，数学界的主流观点似乎已经将五次方程的根式解判定为不可能，然而阿贝尔却敢于质疑，敢于反驳，用自己严谨的数学语言，一点点构建起他的证明。这种独立思考和勇于创新的精神，对于身处信息爆炸时代的我们来说，尤为珍贵。书中对阿贝尔早逝的描述，也让我感到一丝惋惜，如果他能活得更长久一些，或许会有更多令人惊叹的数学发现。
评分《Abel's Proof》带给我的不仅仅是知识的增长，更是一种精神上的激励。我喜欢书中对阿贝尔的描绘，他不仅仅是一个伟大的数学家，更是一个有血有肉、有情感的人。他有他的骄傲，也有他的脆弱，但他对数学的热爱，始终是他生命中最耀眼的光芒。作者巧妙地将阿贝尔的人生轨迹与他所处的历史时期相结合，让我看到了数学发展背后的人文关怀。我尤其欣赏书中对于阿贝尔与伽罗瓦之间关系的探讨，虽然他们可能并未直接交流，但他们的研究却在冥冥之中产生了奇妙的联系，这不得不让人感叹数学世界的奇妙。
评分我被《Abel's Proof》中对阿贝尔研究历程的细致描绘所深深吸引。作者如同一个侦探，将零散的线索一一串联起来，为我们呈现了一个完整的数学探索图景。我尤其欣赏书中对阿贝尔在证明过程中遇到的困难以及他如何克服这些困难的详细叙述。这不仅仅是一项抽象的数学证明，更是一个个体在面对巨大挑战时所展现出的坚韧与智慧。我甚至能在字里行间感受到阿贝尔内心的激动与喜悦，当他最终找到那个关键的突破口时。
评分这本书最让我着迷的地方在于，它将一个复杂的数学证明，融入了一个充满人情味的故事之中。我不是数学家，但《Abel's Proof》让我对数学产生了前所未有的兴趣。作者在描述阿贝尔的证明过程时，并没有让我感到枯燥乏味，反而通过对阿贝尔思想脉络的梳理，让我仿佛置身于他的大脑之中，一同感受他思考的火花。那种抽丝剥茧，层层递进的逻辑推理，虽然我有时需要反复阅读才能完全理解，但每一次的豁然开朗，都给我带来了巨大的满足感。
评分《Abel's Proof》这本书带给我的震撼，远不止于对阿贝尔本人及其伟大成就的认识。它更像是一扇窗，让我得以窥见数学世界那深邃而迷人的魅力。我从未想过，一个看似枯燥的数学问题，背后竟然蕴含着如此跌宕起伏的思考过程和情感纠葛。作者对于细节的捕捉可谓是入木三分，从阿贝尔早年的求学经历，到他与同代数学家们的交流互动，再到他晚年病痛缠身却依旧奋笔疾书的场景，每一个片段都充满了生命力。我时常在想，如果我也能拥有阿贝尔那样的专注和热情，我的生活或许也会因此而变得更加丰富多彩。
评分在阅读《Abel's Proof》的过程中，我仿佛置身于19世纪的挪威，亲眼见证了阿贝尔是如何在艰苦的环境中，凭借着超乎常人的毅力和智慧，一步步逼近那个曾经被认为是不可解的难题——五次方程的根式解。书中的叙述语言流畅且富有感染力，即使是那些我难以完全理解的数学概念，通过作者生动形象的比喻和循序渐进的解释，也逐渐变得清晰起来。我惊叹于阿贝尔那敏锐的洞察力，他如何能在无数的尝试中，抓住那关键的一丝灵感，最终找到突破口。这本书不仅仅是关于一个数学定理的证明，更是关于一个灵魂在追求极致真理过程中的挣扎与升华，它教会了我，真正的热爱是可以跨越一切障碍的。
评分初次翻开《Abel's Proof》这本书，就被它那封面散发出的沉静而又充满智慧的气息所吸引。我并非数学专业人士，甚至可以说是对高等数学的理解仅停留在高中课本的浅显层面。然而，这本书所传达出的那种对知识的纯粹追求，对真理的执着探索，却深深打动了我。作者并非简单地罗列公式和定理，而是将阿贝尔的生平、他所处的时代背景、以及他那充满戏剧性的人生故事巧妙地编织在一起。我尤其喜欢其中关于阿贝尔在贫困潦倒中依然坚持研究的描写，那种面对现实的艰难，却不曾放弃内心对数学的热爱的精神，仿佛一道穿透黑暗的光芒，照亮了我内心的某个角落。
评分翻开《Abel's Proof》，我如同走进了一个充满智慧和激情的殿堂。我被阿贝尔身上那种对真理的极致追求所深深感动。他的一生虽然短暂，却在数学史上留下了不可磨灭的印记。作者用优美的笔触，将阿贝尔的数学贡献与他的人生经历有机地结合起来，使得这本书读起来既有知识性，又不乏趣味性。我尤其喜欢书中对阿贝尔在发表重要论文时所面临的种种阻碍的描述，这让我深刻体会到，伟大的思想往往需要经过艰难的孕育才能最终绽放。
评分《Abel's Proof》不仅仅是一部传记，更是一部关于坚持与梦想的史诗。我被阿贝尔身上那种不屈不挠的精神深深打动。他的一生充满了坎坷与挫折，贫困、病痛、学业上的不顺，似乎都在试图将他压垮。然而，他却从未放弃对数学的热爱，也从未放弃对真理的追寻。书中对阿贝尔在巴黎索邦大学求学期间的描写，让我看到了一个年轻的数学天才是如何在压力和挑战中成长的。他如何克服语言障碍，如何与顶尖数学家们交流，如何在这片陌生的土地上汲取养分，这一切都让我肃然起敬。
评分《Abel's Proof》这本书彻底改变了我对数学的看法。我一直以为数学是冰冷而枯燥的，但这本书让我看到了数学背后蕴含的激情与创造力。阿贝尔的生平故事，他那充满传奇色彩的数学探索，都深深地吸引着我。作者的叙述风格非常独特，既有学术的严谨，又不失文学的温度。我喜欢书中对阿贝尔早期生活和教育背景的描写，这有助于我理解他为何能够产生如此伟大的思想。这本书不仅仅是献给数学爱好者的，任何对人类探索精神感兴趣的人，都应该读一读。
评分The parts on history of math and biographies are inspiring or at least entertaining, but the presentation of math lacks clarity. The author sacrificed precision for a reduction in the number of formal statements; paradoxically this makes some math really hard to follow, at least for someone used to using precise mathematical language.
评分The parts on history of math and biographies are inspiring or at least entertaining, but the presentation of math lacks clarity. The author sacrificed precision for a reduction in the number of formal statements; paradoxically this makes some math really hard to follow, at least for someone used to using precise mathematical language.
评分The parts on history of math and biographies are inspiring or at least entertaining, but the presentation of math lacks clarity. The author sacrificed precision for a reduction in the number of formal statements; paradoxically this makes some math really hard to follow, at least for someone used to using precise mathematical language.
评分The parts on history of math and biographies are inspiring or at least entertaining, but the presentation of math lacks clarity. The author sacrificed precision for a reduction in the number of formal statements; paradoxically this makes some math really hard to follow, at least for someone used to using precise mathematical language.
评分The parts on history of math and biographies are inspiring or at least entertaining, but the presentation of math lacks clarity. The author sacrificed precision for a reduction in the number of formal statements; paradoxically this makes some math really hard to follow, at least for someone used to using precise mathematical language.
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