36 Inspiring Mathematics Quotes

Mathematics often evokes a diverse range of emotions—curiosity, excitement, and sometimes even a bit of trepidation. Yet, at its core, mathematics is a universal language that has the power to unlock new dimensions of understanding, problem-solving, and creativity. Throughout history, brilliant minds—be they mathematicians, philosophers, or scientists—have offered profound insights that transcend the complexity of numbers and equations. In this blog post, we bring you an inspiring collection of 36 mathematics quotes that capture the beauty, elegance, and transformative power of this timeless discipline. Whether you’re a seasoned mathematician or someone simply intrigued by the world of numbers, these quotes are sure to ignite your passion and appreciation for the incredible realm of mathematics.

1. “The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones.” - Georg Simmel

2. “In every department of physical science there is only so much science, properly so-called, as there is mathematics.” - Immanuel Kant

3. “Nothing takes place in the world whose meaning is not that of some maximum or minimum.” - Leonhard Euler

4. “He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by the calculated chance of searching fire, even as he himself might be at any moment. Mathematics! Mathematics! Algebra! Geometry! When 1st and 3d Squads came diving and tumbling back over the tiny crest, Bell was content to throw himself prone, press his cheek to the earth, shut his eyes, and lie there. God, oh, God! Why am I here? Why am I here? After a moment's thought, he decided he better change it to: why are we here. That way, no agency of retribution could exact payment from him for being selfish.” - James Jones

5. “All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one.” - Sylvain Cappell

6. “Mathemata mathematicis scribuntur.” - Nicolaus Copernicus

7. “With me, everything turns into mathematics.” - René Descartes

8. “A mathematician is an individual who constructs space with 0D particles and then places a bowling ball on this invisible canvas to explain how gravity works.” - Bill Gaede

9. “The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.” - Alfred North Whitehead

10. “I should attempt to treat human vice and folly geometrically... the passions of hatred, anger, envy, and so on, considered in themselves, follow from the necessity and efficacy of nature... I shall, therefore, treat the nature and strength of the emotion in exactly the same manner, as though I were concerned with lines, planes, and solids.” - Baruch Spinoza

11. “[The Old Astronomer to His Pupil]Reach me down my Tycho Brahe, I would know him when we meet,When I share my later science, sitting humbly at his feet;He may know the law of all things, yet be ignorant of howWe are working to completion, working on from then to now.Pray remember that I leave you all my theory complete,Lacking only certain data for your adding, as is meet,And remember men will scorn it, 'tis original and true,And the obloquy of newness may fall bitterly on you.But, my pupil, as my pupil you have learned the worth of scorn,You have laughed with me at pity, we have joyed to be forlorn,What for us are all distractions of men's fellowship and smiles;What for us the Goddess Pleasure with her meretricious smiles.You may tell that German College that their honor comes too late,But they must not waste repentance on the grizzly savant's fate.Though my soul may set in darkness, it will rise in perfect light;I have loved the stars too fondly to be fearful of the night.What, my boy, you are not weeping? You should save your eyes for sight;You will need them, mine observer, yet for many another night.I leave none but you, my pupil, unto whom my plans are known.You 'have none but me,' you murmur, and I 'leave you quite alone'?Well then, kiss me, -- since my mother left her blessing on my brow,There has been a something wanting in my nature until now;I can dimly comprehend it, -- that I might have been more kind,Might have cherished you more wisely, as the one I leave behind.I 'have never failed in kindness'? No, we lived too high for strife,--Calmest coldness was the error which has crept into our life;But your spirit is untainted, I can dedicate you stillTo the service of our science: you will further it? you will!There are certain calculations I should like to make with you,To be sure that your deductions will be logical and true;And remember, 'Patience, Patience,' is the watchword of a sage,Not to-day nor yet to-morrow can complete a perfect age.I have sown, like Tycho Brahe, that a greater man may reap;But if none should do my reaping, 'twill disturb me in my sleepSo be careful and be faithful, though, like me, you leave no name;See, my boy, that nothing turn you to the mere pursuit of fame.I must say Good-bye, my pupil, for I cannot longer speak;Draw the curtain back for Venus, ere my vision grows too weak:It is strange the pearly planet should look red as fiery Mars,--God will mercifully guide me on my way amongst the stars.” - Sarah Williams

12. “Nothing comforted Sabine like long division. That was how she had passed time waiting for Phan and then Parsifal to come back from their tests. She figured the square root of the date while other people knit and read. Sabine blamed much of the world's unhappiness on the advent of calculators.” - Ann Patchett

13. “Real mathematics must be justified as art if it can be justified at all.” - G.H. Hardy

14. “A mathematician believes that describing the speed of Mercury with equations amounts to science.” - Bill Gaede

15. “A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space.” - Bill Gaede

16. “We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.” - Roger Penrose

17. “[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.” - Paul Lockhart

18. “In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world.” - Paul Lockhart

19. “Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.” - Paul Lockhart

20. “The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.” - Paul Lockhart

21. “99 percent of all statistics only tell 49 percent of the story.” - Ron DeLegge II

22. “College is the grinding machine of the Mathematical Establishment, a conveyor belt that takes individuals from one cookie cutter to another so that the product comes within tight control limits out of the assembly line.” - Bill Gaede

23. “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.” - Eugene Paul Wigner

24. “A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult.What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.” - Ellen Kaplan

25. “I abandoned the assigned problems in standard calculus textbooks and followed my curiosity. Wherever I happened to be--a Vegas casino, Disneyland, surfing in Hawaii, or sweating on the elliptical in Boesel's Green Microgym--I asked myself, "Where is the calculus in this experience?” - Jennifer Ouellette

26. “If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.” - Gary William Flake

27. “She would not have cared to confess how infinitely she preferred the exactitude, the star-like impersonality, of figures to the confusion, agitation, and vagueness of the finest prose.” - Virginia Woolf

28. “Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.” - Paul Lockhart

29. “Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.” - Bertrand Russell

30. “A brick can be used to represent the zero probability of this book being any good.” - Amy Riekhof

31. “My mathematics is simple: one plus one = one.” - Dejan Stojanovic

32. “Mathematics doesn’t care about those beyond the numbers.” - Dejan Stojanovic

33. “Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him.” - Blaise Pascal

34. “. . . the world in which we live has an increasing number of feedback loops, causing events to be the cause of more events (say, people buy a book because other people bought it), thus generating snowballs and arbitrary and unpredictable planet-wide winner-take-all effects.” - Nassim Nicholas Taleb

35. “Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.” - John D. Barrow

36. “People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, such as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a window-pane merge; does one plus one make one? A cloud breaks up into two clouds -more evidence of the same? It is not at all easy to draw a sharp line between cases where what is happening could be called “addition”, and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably fin a statement such as, “There are 17 languages in India, and 462 dialects.” There is something strange about the precise statements like that, when the concepts “language” and “dialect” are themselves fuzzy.” - Douglas R. Hofstadter