Math And Science Quotes

Too much math and science isn't nourishing to the soul.

But in my opinion, all things in nature occur mathematically.

It has become almost a cliché to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

[When asked why are numbers beautiful?] It’s like asking why is Ludwig van Beethoven’s Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.

Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend.

I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.

Procrastination expert Rita Emmett explains: “The dread of doing a task uses up more time and energy than doing the task itself.

Calculus was not math. It was a fucking science experiment gone wrong.

Dad claims that library science is the foundation of all sciences just as math is the key -- and we will survive or founder, depending on how well the librarians do their jobs. Librarians didn't look glamorous to me but maybe Dad had hit on a not very obvious truth.

When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?

The Law of Serendipity: Lady Luck favors the one who tries

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

Focus on the process (the way you spend your time) instead of the product (what you want to accomplish).

‎"There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else -- but persistent.

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.

Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.

[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 how We 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 still To 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 sleep So 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.

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.

When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarely, in your thoughts advanced to the stage of science.

Thiss sentence contains threee errors.

If you protect your routine, eventually it will protect you.

Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too try, philosophy too difficult, geology too petroleum-oriented, and math too mathematical - because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in.

An eternal question about children is, how should we educate them? Politicians and educators consider more school days in a year, more science and math, the use of computers and other technology in the classroom, more exams and tests, more certification for teachers, and less money for art. All of these responses come from the place where we want to make the child into the best adult possible, not in the ancient Greek sense of virtuous and wise, but in the sense of one who is an efficient part of the machinery of society. But on all these counts, soul is neglected.

Earth had two kinds of people: those who could do the math and follow the science, and those who were happier with their own truths. But in our hearts’ daily practice, whatever schools we went to, we all lived as if tomorrow would be a clone of now.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

What would you do if you weren’t afraid?

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

I don't believe that math and nature respond to democracy. Just because very clever people have rejected the role of the infinite, their collective opinions, however weighty, won't persuade mother nature to alter her ways. Nature is never wrong.

Personally, I think sex should be like math. At school. No one really cares if they're crap at math. They even proclaim it. They'll say to anyone, "Yeah, I don't mind science and English, but I'm absolutely shithouse at math." And other people will laugh and say,"Yeah, me too. I would have a clue about all that logarithm shit. You should be able to say that about sex too. You should be proudly able to say, "Yeah I wouldn't have a clue about all that orgasm shit, ay. I'm okay at everything else but when it comes to that part I wouldn't have a clue.

I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle, everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And actually not a year passed before it became an official credo, and it still is.

Procrastination is like addiction. It offers temporary excitement and relief from boring reality.

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.

If a book were written all in numbers, it would be true. It would be just. Nothing said in words ever came out quite even. Things in words got twisted and ran together, instead of staying straight and fitting together. But underneath the words, at the center, like the center of the Square, it all came out even. Everything could change, yet nothing would be lost. If you saw the numbers you could see that, the balance, the pattern. You saw the foundations of the world. And they were solid.

Process, Not Product If you find yourself avoiding certain tasks because they make you uncomfortable, there is a great way to reframe things: Learn to focus on process, not product

The biggest lie ever is that practice makes perfect. Not true—practice makes you better.

Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superstition.

Brilliant Muslim scholars applied Qur’anic insights to spark the medieval Islamic Golden Age filled with a mind-boggling outpouring of creativity in science, math, medicine, fashion, philosophy, economics, mental health therapy, architecture, art, and beyond.

Give me a place to stand, and I will move the Earth.

There is a deep connection between technical, scientific, and artistic creativity.

What the hell did magic wands have to do with helping girls learn math and science? He'd been good at both. He could have helped them with math and science. Weren't these girls supposed to be building skills? Screw magic wands. He'd have handed out some fucking calculators.

Here’s a challenge: try to do a full day of school (actually, that could be the whole challenge by itself), and then, afterward, go on a quest to find a goddess, knowing that when you get home, if you get home, you’ll still have a couple of hours of math and science homework to do.

Scientists and inventors of the USA (especially in the so-called "blue state" that voted overwhelmingly against Trump) have to think long and hard whether they want to continue research that will help their government remain the world's superpower. All the scientists who worked in and for Germany in the 1930s lived to regret that they directly helped a sociopath like Hitler harm millions of people. Let us not repeat the same mistakes over and over again.

We accept, reject, and discern through symbols. These are as important to our understanding of life, our understanding of existence and what has value, whats worthwhile, as math and science ... it's all part of how we work through things, how we make decisions.

My father would argue two side of a möbius strip.

He is like the fox, who effaces his tracks in the sand with his tail. {Describing the writing style of famous mathematician Carl Friedrich Gauss}

Seni sama pentingnya dengan matematika. Seni memanusiakan manusia. Seni menciptakan rasa empati

The only way to walk a journey of a thousand miles is to take one step at a time.

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

The sciences are not sectarian. People do not persecute each other on account of disagreements in mathematics. Families are not divided about botany, and astronomy does not even tend to make a man hate his father and mother. It is what people do not know, that they persecute each other about. Science will bring, not a sword, but peace.

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

Science Technology Engineering and Math is still necessary to know if you dream of being a filmmaker. Filmmaking is an art form, but with the use of STEM. - Kailin Gow.

In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.

Multitasking means that you are not able to make full, rich connections in your thinking, because the part of your brain that helps make connections is constantly being pulled away before neural connections can be firmed up.

I have some advice for the young generation who are wanting to become successful in life: become more grateful. Once you do that, Allah says, "If you are grateful, I will surely increase you (in everything)." If you're having a hard time in math, science, language and whatever else, become grateful to Allah and He will open doors for you. You'll even get better at basketball and become more athletic. I pray that Allah makes you grateful young people who are examples for others all over the world, ameen.

Life is more than a job; jobs are more than a paycheck; and a country is more than its wealth. Education is more than the acquisition of marketable skills, and you are more than your ability to contribute to your employer’s bottom line or the nation’s GDP, no matter what the rhetoric of politicians or executives would have you think. To ask what college is for is to ask what life is for, what society is for—what people are for. Do students ever hear this? What they hear is a constant drumbeat, in the public discourse, that seeks to march them in the opposite direction. When policy makers talk about higher education, from the president all the way down, they talk exclusively in terms of math and science. Journalists and pundits—some of whom were humanities majors and none of whom are nurses or engineers—never tire of lecturing the young about the necessity of thinking prudently when choosing a course of study, the naïveté of wanting to learn things just because you’re curious about them.

A bell cannot tell time, but it can be moved in just such a way as to say twelve o’clock – similarly, a man cannot calculate infinite numbers, but he can be moved in just such a way as to say pi.

It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics...

If I were king, I would redress an abuse which cuts back, as it were, one half of human kind. I would have women participate in all human rights, especially those of the mind.

Over the past decades, students who have blindly followed their passion, without rational analysis of whether their choice of career truly was wise, have been more unhappy with their job choices than those who coupled passion with rationality.

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

{Replying to G. H. Hardy's suggestion that the number of a taxi (1729) was 'dull', showing off his spontaneous mathematical genius} No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways, the two ways being 13 + 123 and 93 + 103.

The greatest mathematics has the simplicity and inevitableness of supreme poetry and music, standing on the borderland of all that is wonderful in Science, and all that is beautiful in Art.

Picture a thirteen-year-old boy sitting in the living room of his family home doing his math assignment while wearing his Walkman headphones or watching MTV. He enjoys the liberties hard won over centuries by the alliance of philosophic genius and political heroism, consecrated by the blood of martyrs; he is provided with comfort and leisure by the most productive economy ever known to mankind; science has penetrated the secrets of nature in order to provide him with the marvelous, lifelike electronic sound and image reproduction he is enjoying. And in what does progress culminate? A pubescent child whose body throbs with orgasmic rhythms; whose feelings are made articulate in hymns to the joys of onanism or the killing of parents; whose ambition is to win fame and wealth in imitating the drag-queen who makes the music. In short, life is made into a nonstop, commercially prepackaged masturbational fantasy.

No one shall expel us from the paradise which Cantor has created for us. {Expressing the importance of Georg Cantor's set theory in the development of mathematics.}

This is where the Law of Serendipity comes to play: Lady Luck favors the one who tries.

It’s normal to sit down with a few negative feelings about beginning your work. It’s how you handle those feelings that matters.

Learning organic chemistry is not any more challenging than getting to know some new characters. The elements each have their own unique personalities. The more you understand those personalities, the more you will be able to read their situations and predict the outcomes of reactions.” —Kathleen Nolta, Ph.D., Senior Lecturer in Chemistry

Most children, even very bright ones, need constant review and practice to truly own a concept in grammar, math or science. In schools today, on paper it may appear that kids are learning skills, but in reality they are only renting them, soon to forget what they've learned over the weekend or summer vacation.

One might suppose that reality must be held to at all costs. However, though that may be the moral thing to do, it is not necessarily the most useful thing to do. The Greeks themselves chose the ideal over the real in their geometry and demonstrated very well that far more could be achieved by consideration of abstract line and form than by a study of the real lines and forms of the world; the greater understanding achieved through abstraction could be applied most usefully to the very reality that was ignored in the process of gaining knowledge.

Music is a mixed mathematical science that concerns the origens, attributes, and distinctions of sound, out of which a cultivated and lovely melody and harmony are made, so that God is honored and praised but mankind is moved to devotion, virtue, joy, and sorrow.

Deficiencies of innate ability may be compensated for through persistent hard work and concentration. One might say that work substitutes for talent, or better yet that it creates talent.”6 —Santiago Ramón y Cajal

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.

Befuddlement is a healthy part of the learning process. When students approach a problem and don’t know how to do it, they’ll often decide they’re no good at the subject. Brighter students, in particular, can have difficulty in this way—their breezing through high school leaves them no reason to think that being confused is normal and necessary. But the learning process is all about working your way out of confusion. Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!” —Kenneth R. Leopold, Distinguished Teaching Professor, Department of Chemistry, University of Minnesota

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

On a plaque attached to the NASA deep space probe we [human beings] are described in symbols for the benefit of any aliens who might meet the spacecraft as “bilaterly symmetrical, sexually differentiated bipeds, located on one of the outer spiral arms of the Milky Way, capable of recognising the prime numbers and moved by one extraordinary quality that lasts longer than all our other urges—curiosity.

There is no more important homework than reading. Research shows that the highest achieving students are those who devote leisure time to reading, even when the school day and year are only mid-length and homework isn’t excessive. Recently, the largest-ever international study of reading found that the single most important predictor of academic success is the amount of time children spend reading books, more important even than economic or social status. And one of the few predictors of high achievement in math and science is the amount of time children devote to pleasure reading.

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact, some of the best ideas come when you least expect them, possibly through annoying industrial noise.

In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is concern for content.

You may think you really have to understand something in order to explain it. But observe what happens when you are talking to other people about what you are studying. You’ll be surprised to see how often understanding arises as a consequence of attempts to explain to others and yourself, rather than the explanation arising out of your previous understanding.

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.

The importance of C.F. Gauss for the development of modern physical theory and especially for the mathematical fundament of the theory of relativity is overwhelming indeed; also his achievement of the system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience.

Remember your math: an anecdote is not a trend. Remember your history: the fact that something is bad today doesn't mean it was better in the past. Remember your philosophy: one cannot reason that there's no such thing as reason, or that something is true or good because God said it is. And remember your psychology: much of what we know isn't so, especially when our comrades know it too. Keep some perspective. Not every problem is a Crisis, Plague, Epidemic, or Existential Threat, and not every change is the End of This, the Death of That, or the Dawn of a Post-Something Era. Don't confuse pessimism with profundity: problems are inevitable, but problems are solvable, and diagnosing every setback as a symptom of a sick society is a cheap grab for gravitas. Finally, drop the Nietzsche. His ideas may seem edgy, authentic, baad,while humanism seems sappy, unhip, uncool But what's so funny about peace, love, and understanding?

Students who are beginning to struggle in math and science often look at others who are intellectual racehorses and tell themselves they have to keep up. Then they don’t give themselves the extra time they need to truly master the material, and they fall still further behind. As a result of this uncomfortable and discouraging situation, students end up unnecessarily dropping out of math and science. Take a step back and look dispassionately at your strengths and weaknesses. If you need more time to learn math and science, that’s simply the reality. If you’re in high school, try to arrange your schedule to give yourself the time you need to focus on the more difficult materials, and limit these materials to manageable proportions. If you’re in college, try to avoid a full load of heavy courses, especially if you are working on the side. A lighter load of math and science courses can, for many, be the equivalent of a heavy load of other types of courses. Especially in the early stages of college, avoid the temptation to keep up with your peers.

Can’t you make yourself likeable? Can’t you even try?” Something shifted in Tavi then. She was always so flippant, trailing sarcasm behind her like a duchess trailing furs. But not this time. Hugo had pierced her armor and blood was dripping from the wound. “Try for whom, Hugo?” she repeated, her voice raw. “For the rich boys who get to go to the Sorbonne even though they’re too stupid to solve a simple quadratic equation? For the viscount I was seated next to at a dinner who tried to put his hand up my skirt through all five courses? For the smug society ladies who look me up and down and purse their lips and say no, I won’t do for their sons because my chin is too pointed, my nose is too large, I talk too much about numbers?” “Tavi …” Isabelle whispered. She went to her, tried to put an arm around her, but Tavi shook her off. “I wanted books. I wanted maths and science. I wanted an education,” Tavi said, her eyes bright with emotion. “I got corsets and gowns and high-heeled slippers instead. It made me sad, Hugo. And then it made me angry. So no, I can’t make myself likeable. I’ve tried. Over and over. It doesn’t work. If I don’t like who I am, why should you?

Language as putative science. - The significance of language for the evolution of culture lies in this, that mankind set up in language a separate world beside the other world, a place it took to be so firmly set that, standing upon it, it could lift the rest of the world off its hinges and make itself master of it. To the extent that man has for long ages believed in the concepts and names of things as in aeternae veritates he has appropriated to himself that pride by which he raised himself above the animal: he really thought that in language he possessed knowledge of the world. The sculptor of language was not so modest as to believe that he was only giving things designations, he conceived rather that with words he was expressing supreame knowledge of things; language is, in fact, the first stage of occupation with science. Here, too, it is the belief that the truth has been found out of which the mightiest sources of energy have flowed. A great deal later - only now - it dawns on men that in their belief in language they have propagated a tremendous error. Happily, it is too late for the evolution of reason, which depends on this belief, to be put back. - Logic too depends on presuppositions with which nothing in the real world corresponds, for example on the presupposition that there are identical things, that the same thing is identical at different points of time: but this science came into existence through the opposite belief (that such conditions do obtain in the real world). It is the same with mathematics, which would certainly not have come into existence if one had known from the beginning that there was in nature no exactly straight line, no real circle, no absolute magnitude.

I tell my students they can procrastinate as long as they follow three rules: 1. No going onto the computer during their procrastination time. It’s just too engrossing. 2. Before procrastinating, identify the easiest homework problem. (No solving is necessary at this point.) 3. Copy the equation or equations that are needed to solve the problem onto a small piece of paper and carry the paper around until they are ready to quit procrastinating and get back to work. “I have found this approach to be helpful because it allows the problem to linger in diffuse mode—students are working on it even while they are procrastinating.” —Elizabeth Ploughman, Lecturer of Physics, Camosun College, Victoria, British Columbia

If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.

There is no great religion without a great schism. All of them have it. And that's because you're dealing with something called faith. And faith is not something you can prove; faith is personal opinion. Uh, when you're dealing with something with certainty, like, y'know, science or logic, you don't have the--there's no wiggle room; that's why history is not filled with warring math cults, y'know, because you can settle the issue; you can prove something to be right or wrong, and that's the end of the argument: next case. Whereas, when you're dealing with faith, you can forever argue your point, or another point, because you're dealing with intangibles. Personally, I think, faith is what you ask of somebody when you don't have the goods to prove your point.

I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I studied languages and literature for two years. After two years I passed an examination with the result I have a teaching certificate for Latin and Hungarian for the lower classes of the gymnasium, for kids from 10 to 14. I never made use of this teaching certificate. And then I came to philosophy, physics, and mathematics. In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.

A remarkably consistent finding, starting with elementary school students, is that males are better at math than females. While the difference is minor when it comes to considering average scores, there is a huge difference when it comes to math stars at the upper extreme of the distribution. For example, in 1983, for every girl scoring in the highest percentile in the math SAT, there were 11 boys. Why the difference? There have always been suggestions that testosterone is central. During development, testosterone fuels the growth of a brain region involved in mathematical thinking and giving adults testosterone enhances their math skills. Oh, okay, it's biological. But consider a paper published in science in 2008. The authors examined the relationship between math scores and sexual equality in 40 countries based on economic, educational and political indices of gender equality. The worst was Turkey, United States was middling, and naturally, the Scandinavians were tops. Low and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries it's statistically insignificant. And by the time you examine the most gender equal country on earth at the time, Iceland, girls are better at math than boys. Footnote, note that the other reliable sex difference in cognition, namely better reading performance by girls than by boys doesn't disappear in more gender equal societies. It gets bigger. In other words, culture matters. We carry it with us wherever we go.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain ... But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes to authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.