Hillsdale College
Discover the fundamental principles of mathematical reasoning and logic in Hillsdale’s online course, “Mathematics and Logic: From Euclid to Modern Geometry.” Enroll in this free course today at: https://online.hillsdale.edu/landing/mathematics-and-logic-from-euclid-to-modern-geometry
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Visit our website: http://hillsdale.edu
Learn from our online courses: http://online.hillsdale.edu
Read First: https://imprimis.hillsdale.edu/
Undergraduate programs: https://www.hillsdale.edu/information-for/undergraduate-admissions/
Graduate School of Statesmanship: https://www.hillsdale.edu/academics/graduate-school/
Graduate School of Government: https://dc.hillsdale.edu/School-of-Government/Program-Overview/
Listen to Hillsdale Dialogues Podcast: http://blog.hillsdale.edu/online-courses
Hillsdale College is an independent institution of higher learning founded in 1844 by men and women “grateful to God for the inestimable blessings” resulting from civil and religious liberty and “believing that the diffusion of learning is essential to the perpetuity of these blessings.” It pursues the stated object of the founders: “to furnish all persons who wish, irrespective of nation, color, or sex, a literary, scientific, [and] theological education” outstanding among American colleges “and to combine with this such moral and social instruction as will best develop the minds and improve the hearts of its pupils.” As a nonsectarian Christian institution, Hillsdale College maintains “by precept and example” the immemorial teachings and practices of the Christian faith.
The College also considers itself a trustee of our Western philosophical and theological inheritance tracing to Athens and Jerusalem, a heritage finding its clearest expression in the American experiment of self-government under law.
By training the young in the liberal arts, Hillsdale College prepares students to become leaders worthy of that legacy. By encouraging the scholarship of its faculty, it contributes to the preservation of that legacy for future generations. By publicly defending that legacy, it enlists the aid of other friends of free civilization and thus secures the conditions of its own survival and independence.
🥱😭🤣🤣🤣
What is this sublime music?
Is the course really free
If Hillsdale were truthfully attempting to provide a honest historical span of mathematics and geometry, Hillsdale then would be required to begin far earleir than Euclid, since the foundations of mathematics and geometry that are deceptively attributed to the Greeks were developed in Egypt long before Greek civilization ever emerged. The Greeks themselves readily admitted that they were taught geometry and mathematics by ancient Egyptians.
"Thus your mathematical sciences first originated in Egypt. Egypt is the cradle of mathematics…that is the country origin for Greek mathematics"
Aristotle
Greek philosopher
"the mathematical arts had never before been formed, constitituted or elaborated anywhere else, originating in Egypt only"
Aristotle
Greek Philosopher
"We shall say following the general tradition that the Egyptians were the first to have invented Geometry, (that) Thales, the first Greek to have been in Egypt, brought this theory thereof to Greece"
Eudemus
Greek Historian
The fact of the matter is simply this, throngs of Greeks journeyed to Egypt to study, however, the reverse would certainly not be true.
MATHEMATICS AND LOGIC PROPOSITION MODERN GEOMETRY
__________
CALCULUS METRIC CURRENCY SYSTEM
TUSSHANNON SHANEA JOHNSON FORMERLY SHANNON JOHNSON OVERSEAS TUSSHIR SANEA ALLADIN VOLUNTEER CAMPAIGN EVENT SPEECHES AND REMARKS ABROAD GENERAL CASE STUDY
song name?
It's an awae inspiring ad
I will be donating to this organization. Harvard isn't bad either
Wow !!!🤯
Sad.
Much greatitud thank you
😻 NICE ! 😻
Geometry is liken to studying, of war associated w/…. THE LIGHT SIDE & DARK SIDE OF THE CREATOR… HOWEVER, TO MAKE SUCH MOCKERY ONLY RESULT IN CATASTROPHIC REPEATED MEDIEVAL OUT DATED CONJURED UP DANGERS & DISASTEROUS EVENTS LINKED TO VARIOUS COMBINATION OF HORRIBLE CATACLYSMIC SPIRITUAL WARFARE & SO THIS OUTMODE REASON OF STUDY LINKED TO THESE GREAT TUMULTUOUS PAST TRAGEDIES ETC. IS THE MAJOR WHY MANY MEN, WOMEN & CHILDREN TODAY MOVING FORWARD WILL AND AS OF RIGHT NOW TODAY ARE CONTINUING PERISH & MEET THEIR FATE WITH WAR, PESTILENCE, FAMINES MUTATED DISEASES AND DEATH WHICH IS DUE TO A LACK OF GODLY WISDOM & SIMPLE KNOWLEDGE 😮! FOR TO LONG, MAN HAS LEANED AND MANIPULATED UPON THEIR OWN KNOWLEDGE AND WRETCHED IDEAS OF FALLACY AND FAILURES w/ CONSISTENT SHORTCOMINGS OF ONES DEMISE… 😮
Im so intrigued by this subject.
What about the Kalcoolus ?
Thank you for making a video on how essential, necessary and overlooked and powerful geometry is as part of a complimentary visualization aid among the foundation of math, logic and sciences. Geometry has become a powerful product of the imagination for the many things we have created, rightfully, as it is our extended "GOD"-given ability to create and use to discern with.
I might have been interested until I saw that it is a product of Hillsdale College, which means that the scientific will be subordinate to and possibly undermined by conservative Christianity. You cannot trust today’s conservative Christian with the education of your children.
Hillsdale might be the only legitimate college left
I want to learn ,even at 60 years old, Theres so much to learn and enrich my life.
I would like to understand more,cause lam weak and do struggle alot in mathematics!
This sounds amazing! For anyone who has taken this, can a bright middle schooler follow along in this class? He is currently taking Harvard’s free CS50x class and enjoying it, if that helps. Thank you!
The background music in this video is incredible.
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As a carpenter I used my high school math skills to my advantage. When doubtful of skyscrapers collapsing due to fire I returned to basic skills to deduce it was not possible statistically for 90% of the buildings occupants bodies to go unrecovered. Numbers are powerful tools when rebuilding the truth !
You are right all start at grade school level, they need to learn about calculation, formula and much more.
Beautifully edited spot!!
So excited to be attending there this fall!!
I took 3yrs of drafting(by hand) and loved geometry because I had a whole year of drawing machine parts in various views. I could even do advanced geometry in my head, but decided not to go into engineering because, boys😅 oh well….😂
I love this. Already got the book, definitely Buying the DVD.
Automated Logical Navigation (ALN) in Pure Logic
Goal: Derive a target proposition efficiently using only logical relations.
—
1. Elements
Propositions : statements, axioms, or lemmas.
Implications : dependencies between propositions.
Recursive rules: meta-level statements like .
Alternative inference rules: different valid ways to derive consequences from premises.
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2. Procedure
1. Identify premises sufficient to reach .
2. Construct dependency chains .
Select chains minimizing the number of intermediate propositions.
3. Apply recursive reasoning
If appears repeatedly, generalize into a meta-rule.
4. Explore alternative derivations
For any , consider other valid inference sequences leading to .
5. Eliminate redundancy
Remove any propositions that do not contribute logically to .
6. Iterate until is derivable from with minimal steps and no contradictions.
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3. Key Logical Principles
Minimal derivation principle: Prefer shortest chains of implications.
Redundancy elimination principle: Remove unnecessary intermediate propositions.
Recursive derivation principle: Generalize repeated inference patterns.
Alternative derivation principle: Explore multiple valid sequences to find novel proofs.
Consistency principle: Ensure no chain contains and .
—
4. Outcome
A set of logical chains that:
Minimally derive
Avoid redundant or contradictory propositions
Incorporate generalized or recursive inference patterns
Include alternative derivations when beneficial
—
> In short:
CZM guides purely logical problem-solving by treating:
propositions as nodes,
implications as dependencies,
recursion and repeated patterns as meta-inference rules,
alternative derivations as exploration of valid inference sequences,
producing efficient, generalized, and potentially novel proofs entirely within the language of logic.
The Catholic Church, including its religious orders (especially the Jesuits, Benedictines, Dominicans, Augustinians, Franciscans, etc.), has been deeply involved in the birth, preservation, and development of nearly every branch of knowledge in the Western world.
Below is a comprehensive list of scientific and scholarly areas of study that the Church either developed, founded, institutionalized, or substantially advanced throughout the centuries — from Late Antiquity through the Renaissance, Enlightenment, and modern times.
I. Foundational Contributions to Knowledge Itself
1. Scholastic Method & Logic — systematized reasoning and dialectics (Aristotelian logic refined by Aquinas, Anselm, Ockham, etc.)
2. Natural Philosophy — precursor to all modern sciences; inquiry into nature and causes within a theological framework.
3. Scientific Method – the Church, notably the Jesuits and scholastics like Roger Bacon and Albertus Magnus, pioneered empirical reasoning, experimentation, and classification.
4. Education & Institutional Science — invention of the university system (Bologna, Paris, Oxford, Salamanca, etc.) and the seminary system; centers of multidisciplinary learning.
5. Library Science & Archiving — preservation, classification, and cataloging of manuscripts (Vatican Library, monastic scriptoria).
II. Physical and Natural Sciences
A. Astronomy & Cosmology
– Calendar reform (Gregorian calendar, 1582)
– Observatories founded by Jesuits worldwide (Beijing, Manila, Buenos Aires, Rome)
– Stellar mapping, comet tracking, heliographic studies
– Pioneers: Roger Bacon, Giovanni Battista Riccioli, Christopher Clavius, Angelo Secchi
B. Physics
– Optics (study of light and lenses — Roger Bacon, Jesuits in optics)
– Acoustics and sound propagation
– Mechanics and motion (Jesuit schools influenced Galileo and Newtonian physics)
– Electricity and magnetism (18th-century Jesuit physicists like Giambattista Beccaria)
C. Chemistry & Alchemy
– Early chemical experimentation in monasteries (distillation, metallurgy)
– Development of pharmacology and early medical chemistry by monastic apothecaries
– Jesuit study of minerals and acids (precursors to chemistry as a science)
D. Geology & Earth Sciences
– Study of volcanoes and earthquakes (Jesuits in Italy and South America)
– Early stratigraphy and fossils (Nicolaus Steno, “Father of Geology,” a Catholic bishop)
– Cartography of geological features
E. Meteorology
– Jesuit weather observation networks (from the 1600s)
– Establishment of global meteorological data collection systems
– Pioneering barometric and atmospheric studies
III. Life Sciences
A. Biology
– Early biological classification (Albertus Magnus, Francesco Redi)
– Study of anatomy (Vesalius, Jesuit anatomists)
– Zoology and botany (missionary work documenting species in the New World, Asia, Africa)
B. Botany
– First botanical gardens (Vatican, Padua)
– Classification of plants for medicine and agriculture
– Jesuit botanical documentation in South America, India, and China
C. Medicine & Health Sciences
– Hospitals: first organized hospitals in history (4th century, under St. Basil, later by monastic orders)
– Anatomy and physiology studies
– Development of public health, epidemiology, and medical ethics
– Contributions to tropical medicine by missionary scientists
D. Genetics (proto-studies)
– Gregor Mendel, Augustinian friar — founder of genetics
IV. Earth and Environmental Sciences
– Geography and exploration sciences (Jesuit cartographers and explorers)
– Cartography (Jesuit global mapping; Matteo Ricci’s world map for China)
– Oceanography and hydrology (Jesuit coastal mapping, harbor studies)
– Environmental observation and resource management
V. Applied Sciences & Engineering
A. Architecture & Engineering
– Church-sponsored civil and sacred architecture
– Structural engineering and geometry (cathedrals as feats of physics and math)
– Hydraulic and mechanical engineering in monasteries
– Acoustical engineering (for church design and bells)
B. Agriculture & Agronomy
– Monastic development of crop rotation, viticulture, and animal breeding
– Jesuit agricultural schools in the Americas and Asia
C. Technology
– Clockmaking (cathedral clocks)
– Printing and bookmaking by monastic presses
– Optical instruments, telescopes, and navigation devices
VI. Mathematics & Formal Sciences
– Arithmetic and algebra (adoption and teaching of Arabic numerals)
– Geometry (basis of architecture and astronomy)
– Trigonometry (for astronomy and navigation)
– Probability theory (Jesuit contributions, e.g., Jacob Bernoulli studied under Jesuits)
– Mathematical physics
VII. Social, Cognitive, and Human Sciences
A. Philosophy
– Logic, metaphysics, ethics, epistemology — Catholic scholasticism as core tradition
B. Psychology
– Early study of the soul, cognition, and behavior (Thomistic psychology, Jesuit education theory)
– Foundations of moral psychology and educational psychology
C. Sociology
– Catholic social teaching as precursor to modern sociology
– Jesuit studies of indigenous cultures and social structures
D. Anthropology & Ethnography
– Missionary fieldwork documenting cultures, languages, customs (Jesuits in the Americas, Asia, Africa)
– Linguistics and comparative language studies (Jesuit grammars of Chinese, Tamil, Guaraní, etc.)
E. Political Science & Economics
– Scholastics of Salamanca (Vitoria, Suárez) founded international law, human rights, and moral economics
– Early ideas of market theory and just price
– Catholic social thought on property, labor, and common good
VIII. Formal and Historical Sciences
A. History
– Church chroniclers and archivists preserved Western historiography
– Vatican Secret Archives (Archivum Secretum)
– Ecclesiastical history, cultural history, and preservation of classical texts
B. Linguistics & Philology
– Preservation and study of Latin, Greek, Hebrew, Syriac
– Creation of dictionaries and grammars (by missionaries)
– Comparative linguistics from missionary work
C. Archaeology
– Systematic excavation and preservation of Christian and Roman sites (Pontifical Academy of Archaeology)
– Foundations of modern Christian archaeology
D. Art & Aesthetics
– Mathematical perspective in painting (Brunelleschi, Alberti)
– Liturgical art theory and sacred architecture studies
IX. Emerging and Modern Scientific Engagements
– Bioethics and medical ethics (Pontifical Academy for Life)
– Astrophysics (Vatican Observatory’s work in planetary sciences)
– Artificial intelligence ethics and philosophy of technology
– Environmental science (Pope Francis’ Laudato si’ inspired Catholic ecological research)
• Representative Institutions
– Pontifical Academy of Sciences (1603, originally the "Accademia dei Lincei")
– Pontifical Academy for Life
– Jesuit universities (Gregorian, Georgetown, Fordham, etc.)
– Pontifical universities of Rome and Europe
– Vatican Observatory (Specola Vaticana)
Rome, both the imperial one and the ecclesiastical one, along with Ancient Greece, is what lays at the root of all modern geometry, science, mathematics, logic, knowledge and reason.
And since Greece and Rome belong to creation, it is GOD as the Mystery of the Trinity who is the source of all things, visible and invisible.
SUCH BEAUTIFUL AND FANTASTIC EDITING INCLUDING THE SOUNDS AND CINEMATOGRAPHY 😘
I just started this course, and am extremely disappointed. Lesson one is a boring speech by Larry Arnn. He is not only pretentious but seems to get obvious elements wrong. He talks about 'the soul' which has no place in this course. He is unaware of animals that can use numbers or count. He mislabels a compass as a protractor. He is ignorant of non-transitivity (in which A is better than B, B is better than C, but C is better than A.) He ignores non-Euclidean geometry and it applications, like the surface of the earth. Lastly he presumes the standard order of geometry followed by arithmetic followed by calculus is superior to other orders. I suggest that probability and statistics are of much greater educational and practical value in our everyday lives, and should certainly precede calculus.