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narSimha retweeted
Jan 23
Not only did we do it first, we did it BETTER. Hence, new calculus course.
No one outside India understood it earlier. Certainly NOT the thieves Newton and Leibniz.
So, Indian calculus was 100% original.
PS. Pic mentioned in QT now attached.
Jan 23
Gr8 e.g. of ur ULTRA-lousy "scholarship", Elst!🤣
My continued post (pic also below) says I teach calculus using Aryabhata (5th c.) and Brahmagupta (7th c.), from LONG before Kerala school.
So, ur 1st defence of Xtian thieves Newton and Leibniz down the drain!🤣🤣 ../contd
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The calculus is keeping Hoyle,Salinas and Bynum mostly intact while cracking Portland
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narSimha retweeted
Jan 23
Gr8 e.g. of ur ULTRA-lousy "scholarship", Elst!🤣
My continued post (pic also below) says I teach calculus using Aryabhata (5th c.) and Brahmagupta (7th c.), from LONG before Kerala school.
So, ur 1st defence of Xtian thieves Newton and Leibniz down the drain!🤣🤣 ../contd
Jan 22
Newton & Leibniz thieves? Quite possibly, though nameless borrowing of inventions has gone on worldwide for long w/out being called thievery. But in that case, so were the Kerala mathematicians. Calculus already flourished in 13-c. China, see:
mitpress.mit.edu/97802621204…
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koims retweeted
Jun 13
dood a calculus ego renegade boy parody showed up on my fyp the other day and it was actually so beautiful
Jun 12
Final project for a lot of ap calculus classes allows you to make a calculus song parody so there is a moment every year that a wave of amazing stupid math songs release.
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☁️🌷 nicole status *̥˚✧
— June 14, 2026, #commstwt ! I’m open for rush and non rush commissions ^^ dms are open for inquiries
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narSimha retweeted
Jan 23
Calculus in India-stolen by Cochin basd Jesuits-usd
fr navigation-thn creditd to Newton & Leibniz-ths
plagiarism in histry caught by CK Raju & explaind in
hs paper-which ws plagiarizd by George
Gheverghese Joseph & Dennis Almeida who wrote th
book.
ckraju.net/wordpress_F/?p=13…
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To Be Fair, You Have To Have a Very High IQ to Understand Advanced Calculus
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narSimha retweeted
Jan 22
Who stole calculus? So asks a TOI article (pic1).
Obviously, both Newton and Leibniz were thieves.🤣
They justified their theft on the evil dogma of Christian discovery.(pic2) (Jesuit got it from India. Later it spread to Protestants.)
This is known for 2 CENTURIES (pic3). But our journos not educated and never check FACTS, the imp. thing for them is the STORY.
Once respectable ToI is now reduced to a जमूरा to echo and amplify Western propaganda.😒
Probably the article is a paid plant bcoz no journalist could be so lacking in GK. But I wouldn't call these journos presstitutes because sex-work is far more respectable then spreading lies for money. ..\contd.
ALT https://timesofindia.indiatimes.com/education/learning-with-toi/newton-vs-leibniz-the-calculus-war-classrooms-never-teach/articleshow/126820193.cms
ALT Raju, C. K. Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE. Pearson Longman, 2007.
ALT Whish, Charles M. ‘On the Hindu Quadrature of the Circle and the Infinite Series of the Proportion of the Circumference to the Diameter Exhibited in the Four Shastras, the Tantrasamgraham, Yukti-Bhasa, Carana Padhati and Sadratnamala”’. Trans. R. Asiatic Soc. Gr. Britain and Ireland 3 (1835): 509–23.
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There are strong institutional pressures not to fail anyone. I had lots of students over the years who had taken calculus and couldn’t do hs algebra.
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Modern scientific method
Experimental science
Classical physics
Modern astronomy
Calculus (developed independently by Isaac Newton and Gottfried Wilhelm Leibniz)
Modern chemistry
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No calculus or other advanced math? physics of radiation transfer? thermodynamics?
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Pookie doing God's work I will glaze u to the day I perish (<- Barely passed calculus)
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认知透镜
空间/景观类
适应度景观（Fitness Landscape）
Sewall Wright 提出。把所有可能的基因型/策略铺成一张地形图，适应度是高度。演化、学习、优化都变成"在崎岖地形上爬山"的问题。局部最优、山谷、平台、鞍点，这些词突然对应真实的东西。几乎能重新解释所有优化过程。
相空间（Phase Space）
不只是位置，而是系统所有自由度构成的空间。一个钟摆的运动轨迹在相空间里是个椭圆。理解了这个，"系统状态"和"系统演化"就有了几何直觉。
配置空间（Configuration Space）
机器人手臂的每个关节角度是一个维度，障碍物在这个空间里是"禁区"。路径规划问题瞬间变形。
信息/压缩类
压缩即理解（Compression = Understanding）
Kolmogorov 复杂度的核心思想：一个对象的描述最短能有多短，就代表你对它理解得有多深。能被压缩的部分是规律，压不掉的是噪声。这个视角把"理解"和"预测"都变成了信息问题。
信息熵（Shannon Entropy）
不确定性是可以定量的。一旦接受这点，你会开始把"学到了什么"理解为"消除了多少不确定性"。最大熵原理（MaxEnt）是它的推论：在约束条件下，最诚实的分布就是熵最大的那个。
信息瓶颈（Information Bottleneck）
把输入压缩，但保留对输出的预测能力。神经网络学到的是什么？这个框架给出了一种答案。
结构/对称类
不变量（Invariant）
在变换下保持不变的东西就是本质。诺特定理：每一种对称性对应一个守恒量。找到不变量就找到了问题的核心。解题方法和理论物理都用这个。
对偶性（Duality）
几乎所有重要的数学结构都有对偶：原问题/对偶问题（线性规划），波/粒子，时域/频域，图的顶点/边。理解了对偶，你会开始主动寻找每个问题的镜像版本。
同构（Isomorphism）
两个看起来完全不同的结构其实是一回事。群论、图论、类型论……很多"新发现"其实是发现了同构。
范畴论（Category Theory）
对象本身不重要，对象之间的态射（箭头）才是关键。"组合"是核心操作。一旦用这个视角看，函数组合、接口设计、概念关系都变成同一件事。
动力学/系统类
吸引子（Attractor）
动力系统不是随机游走，它会收敛到某些特定状态。不动点、极限环、奇怪吸引子（混沌）。理解了这个，你会开始问：这个系统的吸引子是什么？均衡、习惯、制度，都可以是吸引子。
相变（Phase Transition）
量变积累到临界点发生质变。冰变水，舆论翻转，神经网络的顿悟，市场崩溃。临界性（Criticality）是它的推论：系统在临界点附近会有幂律分布和长程关联。
涌现（Emergence）
整体的行为无法从部件推导，只能在更高层次上描述。还原论的边界在这里。蚁群、市场、意识，都被这个词点名了。
遍历性/遍历性破缺（Ergodicity / Ergodicity Breaking）
时间平均 ≠ 集合平均。这个听起来抽象，但 Ole Peters 用它重新解释了为什么期望值会误导真实决策，为什么财富不平等会自我加剧。一旦理解，你会质疑所有基于"平均"的推理。
计算/逻辑类
不完备性（Incompleteness）
任何足够强的形式系统里都有真命题无法被证明。Gödel 定理的推论：系统无法完全自我描述。自指（Self-Reference）带来根本性的限制。
停机问题（Halting Problem）
有些问题在计算上根本无法判定。这不是"还没解决"，是"原则上无解"。可计算性的边界。
因果类
因果图（Causal Directed Acyclic Graph）
Pearl 的框架。观察和干预是两种不同的操作，混淆它们是大多数因果错误的来源。do-calculus 把这个精确化了。辛普森悖论、混淆变量，在这个框架下都有了结构性解释。
反事实（Counterfactual）
"如果 X 没发生，Y 还会发生吗"。因果推断、法律责任、历史分析，核心都是反事实推理。
概率/决策类
贝叶斯更新（Bayesian Updating）
信念是有强度的，证据改变信念强度。不是"对或错"，是"概率分布"。一旦内化，你会对所有"确定的结论"保持警惕。
纳什均衡（Nash Equilibrium）
没有人可以通过单方面改变策略获益。很多社会现象（交通拥堵、军备竞赛、平台生态）都是均衡，而均衡不一定是好的。
真正想推荐的几个
如果只能选五个最划算的：
1. 适应度景观——理解所有优化和演化
2. 遍历性破缺——质疑所有期望值推理
3. 不变量——找本质的通用方法
4. 涌现——理解还原论的边界
5. 因果图——区分关联和因果
这些概念的共同特点是：它们不是某领域的知识，而是"看世界的操作系统升级"。
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You are a special breed Dr, cum laude in pure maths❤️❤️
I remember when I came to varsity & decided to register for Calculus bcz I was good at high school Maths & loved it.
Yooh, it was my first time getting a single digit mark in Maths. I had to deregister the whole course 😂
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Jordan, if you look at this morons tweets, you can see he doesn't even understand the concept of "maintenance"
Asking him to do any critical thinking whatsoever is like asking a chimpanzee to do calculus.
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Pfizer's calculus was simple: spend a few hundred million buying politicians and bureaucrats, then collect tens of billions in revenue pumping their mRNA toxins into unsuspecting victims.
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louis pipipi popopo retweeted
Jun 10
While you were learning calculus I was mastering the abacus...
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