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Except In Pure Mathematics, Nothing Is Known For Certain (although Much Is Certainly False).
-Carl Sagan
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Except In Pure Mathematics,

Carl Sagan
...
Except In Pure Mathematics, Nothing Is Known For Certain (although Much Is Certainly False).

Understanding the Quote: "except in pure mathematics, nothing is known for certain (although much is..."

This quote by Carl Sagan reflects deeply on the theme of mathematics. It connects to the universal human journey of purpose, motivation, and reflection. Often categorized under Mathematics, Certain, Pure, the quote offers insight, emotional clarity, and intellectual inspiration to readers worldwide.

Whether you’re a student exploring new ideas, a leader trying to motivate your team, or someone seeking direction in life — this quote provides value. It resonates because it’s more than words — it’s a bridge between experience and wisdom. It shows how Carl Sagan interprets life's core challenges and triumphs.

Lessons From the Quote

This quote teaches resilience and focus. It reminds readers that no matter where they stand in life, reflection and self-awareness lead to growth. Each word has meaning, and when studied, it becomes clear how impactful thoughtful language can be.

About Carl Sagan

Carl Sagan is celebrated for insightful thoughts on mathematics and certain. Their legacy lives on through writings that guide, comfort, and inspire. Discover more on their profile page.

Actionable Takeaways

  • Reflect on how this quote applies to your current life path.
  • Share the message with someone who needs inspiration.
  • Write your thoughts on this quote in a journal or blog post.
  • Use it as a daily affirmation or reminder.

Closing Thoughts

Quotes like this endure because they capture universal truths. They comfort us in solitude and empower us in groups. Carry this quote forward — live by its wisdom, share its message, and keep its essence alive.

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Topic
Mathematics
Certain
Pure
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Science
Wish
There Is No Other Species On Earth That Does Science. It Is, So Far, Entirely A Human Invention, Evolved By Natural Selection In The Cerebral Cortex For One Simple Reason: It Works. It Is Not Perfect. It Can Be Misused. It Is Only A Tool. But It Is By Far The Best Tool We Have, Self-correcting, Ongoing, Applicable To Everything.
Simple
Self
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Virtually Every Major Technological Advance In The History Of The Human Species - Back To The Invention Of Stone Tools And The Domestication Of Fire - Has Been Ethically Ambiguous.
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Fire
Religion
There Is A Reward Structure In Science That Is Very Interesting: Our Highest Honors Go To Those Who Disprove The Findings Of The Most Revered Among Us. So Einstein Is Revered Not Just Because He Made So Many Fundamental Contributions To Science, But Because He Found An Imperfection In The Fundamental Contribution Of Isaac Newton.
Science
Interesting
Imperfection
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Patterns
Things Change
If I Finish A Book A Week, I Will Read Only A Few Thousand Books In My Lifetime, About A Tenth Of A Percent Of The Contents Of The Greatest Libraries Of Our Time. The Trick Is To Know Which Books To Read.
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Library
Lifetime
One Glance At A Book And You Hear The Voice Of Another Person, Perhaps Someone Dead For 1,000 Years. To Read Is To Voyage Through Time.
Book
Years
Voice
In Many Cultures It Is Customary To Answer That God Created The Universe Out Of Nothing. But This Is Mere Temporizing. If We Wish Courageously To Pursue The Question, We Must, Of Course Ask Next Where God Comes From? And If We Decide This To Be Unanswerable, Why Not Save A Step And Conclude That The Universe Has Always Existed?
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Religion
Wish
They (i. E., The Pythagoreans) Did Not Advocate The Free Confrontation Of Conflicting Points Of View. Instead, Like All Orthodox Religions, They Practised A Rigidity That Prevented Them From Correcting Their Errors.
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Views
Rigidity
There Is Perhaps No Better A Demonstration Of The Folly Of Human Conceits Than This Distant Image Of Our Tiny World.
Space
Earth Day
Tiny
The Usual Rejoinder To Someone Who Says 'they Laughed At Columbus, They Laughed At Galileo' Is To Say 'but They Also Laughed At Bozo The Clown'.
Science
Usual
Columbus
If We Can't Think For Ourselves, If We're Unwilling To Question Authority, Then We're Just Putty In The Hands Of Those In Power.
Thinking
Hands
Scientific Method
An Extraterrestrial Being, Newly Arrived On Earth - Scrutinizing What We Mainly Present To Our Children In Television, Radio, Movies, Newspapers, Magazines, The Comics, And Many Books - Might Easily Conclude That We Are Intent On Teaching Them Murder, Rape, Cruelty, Superstition, Credulity, And Consumerism. We Keep At It, And Through Constant Repetition Many Of Them Finally Get It.
Children
Book
Teaching
In The Vastness Of Space And The Immensity Of Time, It Is My Joy To Share A Planet And An Epoch With Annie.
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Space
Joy
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Science
Thinking
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Knowledge
Responsibility
My Wonder Button Is Being Pushed All The Time.
Buttons
Wonder
'in His Celebrated Book, 'on Liberty', The English Philosopher John Stuart Mill Argued That Silencing An Opinion Is "a Peculiar Evil." If The Opinion Is Right, We Are Robbed Of The "opportunity Of Exchanging Error For Truth"; And If It's Wrong, We Are Deprived Of A Deeper Understanding Of The Truth In Its "collision With Error." If We Know Only Our Own Side Of The Argument, We Hardly Know Even That: It Becomes Stale, Soon Learned By Rote, Untested, A Pallid And Lifeless Truth.'
Truth
Book
Opportunity
Think Of How Many Religions Attempt To Validate Themselves With Prophecy. Think Of How Many People Rely On These Prophecies, However Vague, However Unfulfilled, To Support Or Prop Up Their Beliefs. Yet Has There Ever Been A Religion With The Prophetic Accuracy And Reliability Of Science? ... No Other Human Institution Comes Close.
Science
Thinking
People
The Passion To Explore Is At The Heart Of Being Human.
Nature
Passion
Heart
Who Are We? We Find That We Live On An Insignificant Planet Of A Humdrum Star Lost In A Galaxy Tucked Away In Some Forgotten Corner Of A Universe In Which There Are Far More Galaxies Than People.
Stars
Science
People
After The Earth Dies, Some 5 Billion Years From Now, After It's Burned To A Crisp, Or Even Swallowed By The Sun, There Will Be Other Worlds And Stars And Galaxies Coming Into Being - And They Will Know Nothing Of A Place Once Called Earth.
Stars
Years
Other Worlds
The Price We Pay For Anticipation Of The Future Is Anxiety About It
Anxiety
Pay
Anticipation
Otherwise We Don't Run The Government The Government Runs Us
Running
Government
We Are The Universe Experiencing Itself.
Universe
It Is All A Matter Of Time Scale. An Event That Would Be Unthinkable In A Hundred Years May Be Inevitable In A Hundred Million.
Years
May
Matter
There Are Many Instances In Science, Where Those Closest To The Intricacies Of The Subject Have A More Highly Developed Sense Of Its Intractability Than Those At Some Remove. On The Other Hand, Those At Too Great A Distance May, I Am Well Aware, Mistake Ignorance For Perspective.
Mistake
Distance
Ignorance
The Vast Distances That Separate The Stars Are Providential. Beings And Worlds Are Quarantined From One Another. The Quarantine Is Lifted Only For Those With Sufficient Self-knowledge And Judgment To Have Safely Traveled From Star To Star.
Travel
Stars
Distance
A Religion Old Or New, That Stressed The Magnificence Of The Universe As Revealed By Modern Science, Might Be Able To Draw Forth Reserves Of Reverence And Awe Hardly Tapped By The Conventional Faiths. Sooner Or Later Such A Religion Will Emerge.
Science
Religion
Stressed
Extraordinary Claims Demand Extraordinary Evidence
Demand
Claims
Evidence
I Maintain There Is Much More Wonder In Science Than In Pseudoscience. And In Addition, To Whatever Measure This Term Has Any Meaning, Science Has The Additional Virtue, And It Is Not An Inconsiderable One, Of Being True.
Atheist
Science
Religion
And You Are Made Of A Hundred Trillion Cells. We Are, Each Of Us, A Multitude.
Cells
Hundred
Made
The Idea That God Is An Oversized White Male With A Flowing Beard, Who Sits In The Sky And Tallies The Fall Of Every Sparrow Is Ludicrous. But If By 'god,' One Means The Set Of Physical Laws That Govern The Universe, Then Clearly There Is Such A God. This God Is Emotionally Unsatisfying... It Does Not Make Much Sense To Pray To The Law Of Gravity.
Atheist
Fall
Mean
Science Is Merely An Extremely Powerful Method Of Winnowing What's True From What Feels Good.
Powerful
Science
Feel Good
If We Teach Only The Findings And Products Of Science - No Matter How Useful And Even Inspiring They May Be - Without Communicating Its Critical Method, How Can The Average Person Possibly Distinguish Science From Pseudoscience?
Pain
Average
Pseudoscience
I’m Struck Again By The Irony That Spaceflight-conceived In The Cauldron Of Nationalist Rivalries And Hatreds-brings With It A Stunning Transnational Vision. You Spend Even A Little Time Contemplating The Earth From Orbit And The Most Deeply Engrained Nationalisms Begin To Erode. They Seem The Squabbles Of Mites On A Plum.
Hatred
Vision
Earth
At A Few Hundred Kilometers Altitude, The Earth Fills Half Your Sky, And The Band Of Blue That Stretches From Mindanao To Bombay, Which Your Eye Encompasses In A Single Glance, Can Break Your Heart With Its Beauty. Home You Think. Home. This Is My World. This Is Where I Come From. Everyone I Know, Everyone I Ever Heard Of, Grew Up Down There, Under That Relentless And Exquisite Blue.
Home
Heart
Eye
The Dumbing Down Of American Is Most Evident In The Slow Decay Of Substantive Content In The Enormously Influential Media, The 30 Second Sound Bites (now Down To 10 Seconds Or Less), Lowest Common Denominator Programming, Credulous Presentations On Pseudoscience And Superstition, But Especially A Kind Of Celebration Of Ignorance.
Ignorance
Media
Sound
And After We Returned To The Savannahs And Abandoned The Trees, Did We Long For Those Great Graceful Leaps And Ecstatic Moments Of Weightlessness In The Shafts Of Sunlight Of The Forest Roof?
Long
Tree
Savannah
Humans Are Very Good At Dreaming, Although You'd Never Know It From Your Television.
Dream
Television
Vastness
If Intelligence Is Our Only Edge, We Must Learn To Use It Better, To Shape It, To Understand Its Limitations And Deficiencies -- To Use It As Cats Use Stealth, As Katydids Use Camouflage -- To Make It The Tool Of Our Survival.
Cat
Survival
Tools
Humans - Who Enslave, Castrate, Experiment On, And Fillet Other Animals - Have Had An Understandable Penchant For Pretending Animals Do Not Feel Pain.
Inspirational
Pain
Animal
Is Mankind Alone In The Universe? Or Are There Somewhere Other Intelligent Beings Looking Up Into Their Night Sky From Very Different Worlds And Asking The Same Kind Of Question?
Intelligent
Night
Sky
Your God Is Too Small For My Universe.
Universe
Maxwell's Equations Have Had A Greater Impact On Human History Than Any Ten Presidents.
Impact
President
Maxwell
We Make Our World Significant By The Courage Of Our Questions And The Depth Of Our Answers
Patience
Our World
Depth
Since, In The Long Run, Every Planetary Society Will Be Endangered By Impacts From Space, Every Surviving Civilization Is Obliged To Become Spacefaring — Not Because Of Exploratory Or Romantic Zeal, But For The Most Practical Reason Imaginable: Staying Alive.
Running
Responsibility
Space
The Words "question" And "quest" Are Cognates. Only Through Inquiry Can We Discover Truth.
Truth
Inquiry
Quests
Imagination Will Often Carry Us To Worlds That Never Were. But Without It We Go Nowhere.
Life
Art
Motivation
The Fact That Someone Says Something Doesn't Mean It's True. Doesn't Mean They're Lying, But It Doesn't Mean It's True.
Education
Lying
Mean
Science Is A Way Of Thinking That Helps You Not To Fool Yourself.
Thinking
Way
Fool
I Would Be Very Ashamed Of My Civilization If We Did Not Try To Find Out If There Is Life In Outer Space.
Civilization
Space
Trying
Those With The Courage To Explore The Weave And Structure Of The Cosmos, Even Where It Differs Profoundly From Their Wishes And Prejudices, Will Penetrate Its Deepest Mysteries.
Wish
Prejudice
Cosmos
It Is The Tension Between Creativity And Skepticism That Has Produced The Stunning And Unexpected Findings Of Science.
Creativity
Science
Unexpected
We Can Judge Our Progress By The Courage Of Our Questions And The Depth Of Our Answers, Our Willingness To Embrace What Is True Rather Than What Feels Good.
Inspirational
Motivational
Atheist
I Hold That Popularization Of Science Is Successful If, At First, It Does No More Than Spark The Sense Of Wonder.
Successful
Science
Doe
You Are Worth About 3 Dollars Worth In Chemicals.
Dollars
Chemicals
A Book Is Made From A Tree. It Is An Assemblage Of Flat, Flexible Parts (still Called "leaves") Imprinted With Dark Pigmented Squiggles. One Glance At It And You Hear The Voice Of Another Person, Perhaps Someone Dead For Thousands Of Years. Across The Millennia, The Author Is Speaking, Clearly And Silently, Inside Your Head, Directly To You. Writing Is Perhaps The Greatest Of Human Inventions, Binding Together People, Citizens Of Distant Epochs, Who Never Knew One Another. Books Break The Shackles Of Time ― Proof That Humans Can Work Magic.
Inspirational
Funny
Reading
War Is Murder Writ Large.
War
Murder
If You Are Only Skeptical, Then No New Ideas Make It Through To You.
Science
Acceptance
Ideas
The Sacred Truth Of Science Is That There Are No Sacred Truths.
Sacred
...the Idea Of A Spiritual Part Of Our Nature That Survives Death, The Notion Of An Afterlife, Ought To Be Easy For Religions And Nations To Sell. This Is Not An Issue Of Which We Might Anticipate Widespread Skepticism. People Will Want To Believe It, Even If The Evidence Is Meager To Nil... Compelling Testimony ... Provides That Our Personality, Character, Memory ... Resides In The Matter Of The Brain, It Is Easy Not To Focus On It, To Find Ways To Evade The Weight Of The Evidence.
Spiritual
Memories
Believe
Who Are We, If Not Measured By Our Impact On Others?
Impact
Ifs
I Would Suggest That Science Is, At Least In My Part, Informed Worship.
Worship
Cosmology
Each Of Us Is A Tiny Being, Permitted To Ride On The Outermost Skin Of One Of The Smaller Planets For A Few Dozen Trips Around The Local Star.
Stars
Skins
Dozen
I Believe That Even A Smattering Of Such Findings In Modern Science And Mathematics Is Far More Compelling And Exciting Than Most Of The Doctrines Of Pseudoscience, Whose Practitioners Were Condemned As Early As The Fifth Century B.c. By The Ionian Philosopher Heraclitus As “nigh -walkers, Magicians, Priests Of Bacchus, Priestesses Of The Wine-vat, Mystery-mongers.” But Science Is More Intricate And Subtle, Reveals A Much Richer Imiverse, And Powerfully Evokes Our Sense Of Wonder.
Wine
Science
Night
We Are Made Of Star Stuff. For The Most Part, Atoms Heavier Than Hydrogen Were Created In The Interiors Of Stars And Then Expelled Into Space To Be Incorporated Into Later Stars. The Sun Is Probably A Third Generation Star.
Stars
Space
Atoms
Scientists Can Routinely Predict A Solar Eclipse, To The Minute, A Millennium In Advance. You Can Go To The Witch Doctor To Lift The Spell That Causes Your Pernicious Anaemia, Or You Can Take Vitamin B12. If You Want To Save Your Child From Polio, You Can Pray Or You Can Inoculate. If You're Interested In The Sex Of Your Unborn Child, You Can Consult Plumb-bob Danglers All You Want . . . But They'll Be Right, On Average, Only One Time In Two. If You Want Real Accuracy . . . Try Amniocentesis And Sonograms. Try Science.
Sex
Children
Real
How Is It That Hardly Any Major Religion Has Looked At Science And Concluded, “this Is Better Than We Thought! The Universe Is Much Bigger Than Our Prophets Said, Grander, More Subtle, More Elegant?” Instead They Say, “no, No, No! My God Is A Little God, And I Want Him To Stay That Way.” A Religion, Old Or New, That Stressed The Magnificence Of The Universe As Revealed By Modern Science Might Be Able To Draw Forth Reserves Of Reverence And Awe Hardly Tapped By The Conventional Faiths.
God
Science
Religion
Many Religions Have Attempted To Make Statues Of Their Gods Very Large, And The Idea, I Suppose, Is To Make Us Feel Small. But If That's Their Purpose, They Can Keep Their Paltry Icons. We Need Only Look Up If We Wish To Feel Small.
Ideas
Icons
Wish
Not All Bits Have Equal Value.
Equal
Science And Technology
Bits
If We Offer Too Much Silent Assent About Mysticism And Superstition - Even When It Seems To Be Doing A Little Good - We Abet A General Climate In Which Scepticism Is Considered Impolite, Science Tiresome, And Rigorous Thinking Somehow Stuffy And Inappropriate.
Thinking
Superstitions
Too Much
At The Heart Of Science Is An Essential Balance Between Two Seemingly Contradictory Attitudes-an Openness To New Ideas, No Matter How Bizarre Or Counterintuitive They May Be, And The Most Ruthless Skeptical Scrutiny Of All Ideas, Old And New. This Is How Deep Truths Are Winnowed From Deep Nonsense.
Attitude
Heart
Science
The Gears Of Poverty, Ignorance, Hopelessness And Low Self-esteem Interact To Create A Kind Of Perpetual Failure Machine That Grinds Down Dreams From Generation To Generation. We All Bear The Cost Of Keeping It Running. Illiteracy Is Its Linchpin.
Running
Dream
Self Esteem
As The Ancient Myth Makers Knew, We Are Children Equally Of The Earth And The Sky.
Children
Sky
Earth
We Are Star Stuff Which Has Taken Its Destiny Into Its Own Hands.
Stars
Taken
Destiny
If The Greenhouse Effect Is A Blanket In Which We Wrap Ourselves To Keep Warm, Nuclear Winter Kicks The Blanket Off.
Winter
Science
Nuclear
Atoms Are Mainly Empty Space. Matter Is Composed Chiefly Of Nothing.
Space
Atoms
Matter
The Romans Called The Christians Atheists. Why? Well, The Christians Had A God Of Sorts, But It Wasn't A Real God. They Didn't Believe In The Divinity Of Apotheosized Emperors Or Olympian Gods. They Had A Peculiar, Different Kind Of God. So It Was Very Easy To Call People Who Believed In A Different Kind Of God Atheists. And That General Sense That An Atheist Is Anybody Who Doesn't Believe Exactly As I Do Prevails In Our Own Time.
Christian
Atheist
Real
We Have Also Arranged Things So That Almost No One Understands Science And Technology. This Is A Prescription For Disaster. We Might Get Away With It For A While, But Sooner Or Later This Combustible Mixture Of Ignorance And Power Is Going To Blow Up In Our Faces.
Motivational
Education
Ignorance
Except For Fools And Madmen, Everyone Knows That Nuclear War Would He An Unprecedented Human Catastrophe.
War
Nuclear
Fool
The Hindu Religion Is The Only Of The World's Great Faiths Dedicated To The Idea That The Cosmos Itself Undergoes An Immense, Indeed An Infinite, Number Of Deaths And Rebirths.
Ideas
Numbers
Cosmos
Understanding Is A Kind Of Ecstasy
Understanding
Curiosity
Kind
There Are Many Other (besides Testosterone) Behaviour-eliciting Hormones Fundamental For Humen Well-being, Including Estrogen And Progesterone In Females. The Fact That Complex Behavioural Patterns Can Be Triggered By A Tiny Concentration Of Moleculas Coursing Through The Bloodstream, And That Different Animals Of The Same Species Generate Different Amounts Of These Hormones, Is Something Worth Thinking About When It's Time To Judge Such Matters As Free Will, Individual Responsibility, And Law And Order.
Responsibility
Thinking
Animal
We Are Rare And Precious Because We Are Alive, Because We Can Think As Well As We Can. We Are Privileged To Influence And Perhaps Control Our Future. I Believe We Have An Obligation To Fight For Life On Earth - Not Just For Ourselves, But For All Those, Humans And Others, Who Came Before Us, And To Whom We Are Beholden, And For All Those Who, If We Are Wise Enough, Will Come After.
Wise
Believe
Fighting
Present Global Culture Is A Kind Of Arrogant Newcomer. It Arrives On The Planetary Stage Following Four And A Half Billion Years Of Other Acts, And After Looking About For A Few Thousand Years Declares Itself In Possession Of Eternal Truths. But In A World That Is Changing As Fast As Ours, This Is A Prescription For Disaster. No Nation, No Religion, No Economic System, No Body Of Knowledge, Is Likely To Have All The Answers For Our Survival. There Must Be Many Social Systems That Would Work Far Better Than Any Now In Existence. In The Scientific Tradition, Our Task Is To Find Them.
Years
Survival
Answers
One Of The Greatest Gifts Adults Can Give - To Their Offspring And To Their Society - Is To Read To Children.
Education
Children
Giving
Cutting Off Fundamental, Curiosity-driven Science Is Like Eating The Seed Corn. We May Have A Little More To Eat Next Winter But What Will We Plant So We And Our Children Will Have Enough To Get Through The Winters To Come?
Children
Cutting
Winter
We've Arranged A Civilization In Which Most Crucial Elements Profoundly Depend On Science And Technology.
Technology
Civilization
Elements
I Would Love To Believe That When I Die I Will Live Again, That Some Thinking, Feeling, Remembering Part Of Me Will Continue.
Atheist
Believe
Thinking
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