IELTS CAM Inspired 11 - Reading Test 3 with Practice Test, Answers And Explanation
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IELTS CAM Inspired 11 - Reading Test 3 With Practice Test, Answers And Explanation
Passage
❓ Câu hỏi passage 1
Question 1 - 9
Complete the notes below.
Choose ONE WORD ONLY from the passage for each answer.
THE STORY OF SILK
THE STORY OF SILK
The beginnings of silk in China
• About 3000 BC, as the legend runs:
– while the empress rested, a cocoon dropped into the hot
1.
at her side
– the empress built a
2.
for winding the threads off each cocoon
• Making silk was at first allowed only to
3.
• At the outset, only
4.
had the right to wear it
• Silk functioned as a type of
5.
– e.g. farmers handed over some of their taxes as silk
• Silk was put to many other uses
– e.g. a silk
6.
survives from about 165 AD
Silk spreads beyond China
• Along the Silk Road, merchants sent silk off to distant lands and brought home gold, silver and
7.
• 550 AD:
8.
carried silkworm eggs to Constantinople concealed in canes
• Silk-making passes across the Middle East and into Europe
• 1900s:
9.
and other man-made fibres drive silk into decline
Question 10 - 13
Do the following statements agree with the information given in the Reading Passage?
TRUE if the statement agrees with the information
FALSE if the statement contradicts the information
NOT GIVEN if it is impossible to say what the writer thinks about this
10
Silk was regarded as more precious than the gold carried in the other direction.
11
The market at Damascus dealt in a greater volume of goods than any other stop on the route.
12
Italy eventually replaced Spain as the leading silk producer in Europe.
13
Japan is still the world's largest supplier of raw silk.
Passage
❓ Câu hỏi passage 2
Question 14 - 18
Do the following statements agree with the information given in the Reading Passage?
TRUE if the statement agrees with the information
FALSE if the statement contradicts the information
NOT GIVEN if it is impossible to say what the writer thinks about this
14
When food is offered during the journey, the arctic tern behaves differently from the gulls in the area.
15
Aunay considers her definition of migration better than those used by other researchers.
16
An individual aphid usually goes back to the plant where its journey started.
17
Aphids respond to the same colour of light when landing as when taking off.
18
Solheim values his definition because it reveals what otherwise very dissimilar migrating animals share.
Question 19 - 22
Complete each of the following statements with the best ending A-G from the box below.
List of Endings
A
take in more food than their immediate needs demand.
B
carry on regardless of distractions.
C
be governed by how much water is available.
D
keep to a straight path rather than a winding one.
E
take place once every day.
F
be discouraged by the hardships they meet.
G
keep to high ground where predators can be spotted.
In Solheim's view, the paths that migrating animals take tend to
19
Ahead of a migration, animals are inclined to
20
Once a migration is under way, animals are not likely to
21
The arctic tern shows the capacity of migrating animals to
22
Question 23 - 26
Complete the summary below.
Choose ONE WORD ONLY from the passage for each answer.
The migration of the quandu
Quandu rely on their vision and to keep out of the way of predators. This population spends the summer in a mountain reserve and, in winter, moves to the , where it escapes the threat that snow poses at that season. Between the two ranges, its route tightens at three . A further danger is that houses are now being built on a narrow along the animals' path.
Passage
❓ Câu hỏi passage 3
Question 27 - 34
Reading Passage 3 has seven sections, A-G.
Which section contains the following information?
Write the correct letter, A-G.
27
a mention of books written for readers presumed to know little about mathematics
28
an explanation of how this book is unlike the usual work on mathematics
29
first-hand accounts from people who gained from mathematics
30
instances of individuals combining talents not usually found together
31
a reference to the varying emphases of mathematics books aimed at general readers
32
the different pace this book demands compared with everyday reading matter
33
an assertion that every part of the book can be followed by anyone
34
identification of the several kinds of reader the book is written for
Question 35 - 40
Complete the sentences below.
Choose ONE WORD ONLY from the passage for each answer.
35
The book sets out to show that mathematics calls for
just as much as for analytical ability.
36
In music, as in mathematics, some parts are easy enough for an outright
to perform.
37
At their hardest, these advanced results need only a small amount of basic
.
38
Readers without mathematical training are advised to carry out some of their own
as they read.
39
Certain popular-science books by
could not include the mathematical foundations of the ideas they present.
40
One lawyer singled out
as more useful for legal study than any other part of mathematics.
DOL IELTS Đình Lực
21/10/2026
📖 Bài đọc passage 1
The story of silk
From the courts of early China to the modern world, the tale of the finest of all fabrics
Silk is a delicate, lustrous cloth spun from the cocoons – the soft protective cases – that mulberry silkworms, the larvae of a particular moth, build around themselves. Its discovery is wrapped in legend. The tale most often repeated concerns Ai Ling, consort of the emperor Shenhuang, who is said to have governed China around 3000 BC. Strolling one day through the palace gardens, she noticed that several mulberry trees were being stripped bare by silkworms, and she gathered up a handful of their cocoons before settling down to rest. As she did so, one of the cocoons slipped from her grasp into the hot water beside her, and the warmth began to loosen it into a single slender filament. Finding that she could wind this thread about her fingers, she asked the emperor to let her raise silkworms on a stand of mulberries, and in time she built a spindle by which the fibres of a cocoon could be drawn off and twisted into a strand strong enough for weaving. How much of the story is genuine no one can say, yet there is no doubt that the Chinese have cultivated silk for thousands of years.
In the beginning, the rearing of silkworms was a sacred duty carried out only by priests, who supervised each stage from the feeding of the worms to the weaving of the cloth. Silk soon became a badge of rank, and in the earliest times only the nobles were allowed to dress in it; that restriction eased so slowly that not until much later dynasties could even the common people wear it. So greatly was the fabric valued that it also circulated as a kind of payment: officials drew their salaries in it, and farmers were permitted to meet part of their taxes with lengths of cloth rather than in coin. Rulers likewise sent it abroad as gifts of state. Bowstrings, fishing lines, the strings of instruments and even writing surfaces were fashioned from it. Among the most striking survivals is an early silk map, the oldest yet uncovered, recovered from the tomb of a nobleman thought to have died around 165 AD.
The craving for so rare a cloth in time gave rise to the celebrated trading route we now call the Silk Road, which carried silk out to the west and brought horses, along with gold and silver, back to the east. The road took its name from the single commodity that counted for most upon it, a fabric prized above gold itself. Stretching more than 6,000 kilometres between eastern China and the Mediterranean, it followed the line of the Great Wall, climbed the Pamir ranges, passed through what is now Afghanistan and reached the Middle East, where Damascus served as a great market; from there the wares were carried by ship across the sea. Scarcely any trader covered the whole distance, the goods passing instead through the hands of one middleman after another.
The mulberry silkworm being found nowhere but China, that land stayed for centuries the sole source of silk anywhere on earth. It was through the Byzantine Empire – master of the Mediterranean world of southern Europe, North Africa and the Middle East from 330 to 1453 AD – that knowledge of the craft at last leaked abroad. In one story, a pair of envoys acting for the Byzantine emperor are said to have smuggled silkworm eggs into Constantinople, today's Istanbul, in 550 AD, tucked away inside hollow walking canes. The Byzantines, though, proved every bit as close with the secret as the Chinese before them, and the weaving and selling of silk stayed a tight monopoly of the crown for hundreds of years. Not until the Arabs swept over Persia in the seventh century did its magnificent silks pass into other hands.
From Persia the art travelled on, spreading through Africa, Sicily and Spain in the wake of the Arab conquest. By the tenth century the Spanish region of Andalusia had grown into Europe's foremost centre of silk-making. Within a few hundred years, though, that lead had passed to Italy, whose merchants in Venice dealt heavily in the cloth and drew silk-growers to settle among them; even today the silk finished in the northern town of Como is held in high esteem.
In Europe, silk-making slid into decline once the nineteenth century and its factories arrived. Among the causes was a flood of cheaper Japanese silk, which the newly opened Suez Canal did much to speed on its way. A further blow landed in the twentieth century, when artificial fibres – polyester and the like – were increasingly substituted for silk in such goods as parachutes and stockings; the two world wars, meanwhile, severed Japan's supply of raw material and hurt the European trade still more. Once peace returned in 1945, Japan revived its industry with sharper methods and better raw silk, and right up to the 1970s it stood as the foremost producer of raw silk and very nearly its only exporter of any weight. Since then the lead has swung back to China, once again the world's principal maker and shipper of raw silk and silk yarn alike. Worldwide output today runs to some 125,000 tonnes a year, of which China accounts for very nearly two-thirds.
Whatever definition one settles on, animal migration is far more than creatures simply moving about. Loosely, it is travel undertaken at predictable intervals (commonly once a year) in which many members of a species may take part, and whose reward comes only after a long journey; inherited instinct seems to lie behind it. The biologist Reidar Solheim has set out five traits that recur, in varying mixtures and degrees, across all migrations. The movements are sustained ones that carry animals beyond their usual surroundings; they follow a broadly straight course rather than a meandering one; they call for distinctive routines at the outset, such as eating to excess, and on arrival; and they draw on unusual reserves of energy. To these Solheim adds a fifth: throughout the journey the traveller holds fast to an overriding purpose, so that neither tempting diversions nor the setbacks that deflect other creatures can turn it aside.
Consider an arctic tern on its 20,000-kilometre passage from the far south of South America up to the Arctic Circle. Should a bird-watcher hold out a fresh herring from a boat, the tern pays it no attention; the resident gulls plunge greedily after such scraps, yet the tern flies on. Why? At that instant it is gripped by an instinct people cannot help but admire — a sense of larger purpose — and this is why the offer fails to distract it. Reaching its destination is all that counts. Feeding, resting and breeding, the bird registers, can all wait; for now nothing matters except the journey, and its whole attention is fixed on arrival.
That larger purpose, moulded by evolution, is served the moment the bird touches down on some pebbly Arctic shore where its fellow terns have likewise gathered: here are the place, the season and the conditions in which it stands a chance of hatching its eggs and raising its young.
Migration, though, is a knotty subject, and the definitions biologists reach for differ partly according to the creatures they study. Delphine Aunay of the University of Valcourt, whose work centres on the quandu and other large land mammals, favours a definition she calls plain and workable, one that fits her animals: the shifting from one seasonal home range to another and back again. What usually drives this to-and-fro is the search for resources that no single territory can supply all year round.
Yet migration equally takes in the daily up-and-down journeys of ocean zooplankton, which rise after dark to feed and sink by daylight to escape predators. It also covers what aphids do: once one plant's tender leaves are used up, the next generation flies off to a fresh host, and not a single aphid ever finds its way back to where it began.
Solheim, an evolutionary biologist specialising in insects, offers a more elaborate definition than Aunay's, resting on those five features that mark migration off from other movement. His scheme makes room for the way an aphid grows responsive to the blue light of the open sky when the moment comes to launch its journey, and to the yellow light bouncing off soft young foliage when it is time to come down. It also accommodates the heavy feeding by which birds put on weight before a long flight. Its real worth, Solheim contends, lies in drawing attention to what wildebeest migration has in common with that of aphids, thereby steering researchers toward understanding how evolution shaped them all.
Human activity, however, is taking a growing toll on animal migration. The quandu (deer-like in appearance, though not in fact related to deer) ranks among the fleetest land mammals of southern South America. One herd passes the summer high in the Valdera ranges, within a mountain reserve, and each year threads a slender route out of the heights, over a river and down to the lowlands, where it waits out the frozen season by grazing scrub that the wind sweeps bare of snow. This herd is remarkable for how little its route varies and how tightly it is squeezed at three separate gaps. Miss any one of them on the way up in spring and the animals cannot reach the rich summer pasture; fail to get back through in autumn, retreating to the lowlands, and they will likely perish trying to last out the winter in deep snow. Depending on keen eyesight and sheer endurance to stay clear of predators, wearing pursuers down over long chases, the quandu favours high, open ground where it can watch and run. At one of the gaps, wooded slopes close in to form a V, leaving a bare strip of ground no more than 120 metres across, now crowded with private houses. Building of this kind is pushing the quandu toward a crisis, threatening to seal off the way through.
These days conservation scientists, with biologists and land managers in the national wildlife service and other bodies, work to safeguard not merely species and their habitats but the act of migration itself. Much of the quandu's route crosses a state forest, which has now designated it a protected migration route. Even so, what happens on privately owned land at one of the gaps lies beyond the reach of either the forest authority or the wildlife service. For some other migrating animals the problem is thornier still, stretched as their journeys are over far greater distances, across more borders, through more jurisdictions and more perils on the way. It will take good sense and firm resolve if we mean to let the world's migrating creatures carry on their travels a little longer.
Preface to 'How the other half thinks: Adventures in mathematical reasoning'
A
A. Among my reasons for writing these pages was a wish to open the mathematical habit of mind to people who have never met real mathematics or enjoyed it. I want the striking discoveries shown — but the reasoning behind them shown even more. On that count the book parts company with most writing on mathematics for a wide readership. In some such works the careers of vivid mathematicians fill the pages; in others the stress falls on where mathematics is applied; in others again its methods are set out on the assumption that the reader already handles algebra with ease.
B
B. My hope is that these chapters help close the famous divide between the two cultures — the arts on one side, the sciences on the other, or the intuitive right side of the brain against the analytical, number-handling left. Mathematics, the book tries to show, is not confined to calculation and analysis, for intuition is at work in it too. That divide is one any of us can shrink, since none of us comes near to using all that either half of the brain can offer. For our range, I point to a structural engineer who paints, an electrical engineer who sings opera, an opera singer who has published mathematical research, and a mathematician who writes short stories.
C
Now and then a hard piece of music holds a passage of real beauty that is still so easy a newcomer could play it, and mathematics is the same. Some results in higher mathematics ask no specialist training of the reader — no algebra, geometry or trigonometry. They call instead for common sense and, at the very most, a little everyday counting, such as knowing that two odd numbers add to an even one. Each of the book's eight chapters shows this, and not one step in the argument lies beyond an ordinary reader's grasp. Because the reasoning leans on nothing harder than the simplest counting, anyone who opens the book can share in doing mathematics and come to know a way of thought at once logical and guided by intuition.
D
Even so, a reader with no mathematical background can go a surprisingly long way into the reasoning. What the book sets out are just the details that bring the mathematical cast of mind alive — a patient, step-by-step working-through, broken by testing and by sudden insight. These pages are to be turned far more slowly than those of a newspaper or a novel. Keeping pencil and paper to hand often helps, so that the reader can check each claim and work small calculations of their own.
E
Books meant to make a field of science clear to the general public have been written by many other researchers, who had little choice but to leave the mathematics out, though it is the very thing their theories rest on. That leaves the reader a mere onlooker; for across much of science the fitting language for fine detail is mathematics itself, whether the topic is the swelling universe, the particles below the atom, or the chromosome. A theory's broad shape can be conveyed without symbols, yet once some corner of the physical world is finally grasped, the account of it reads like a page from a mathematics textbook.
F
Throughout the writing, two groups of readers were always in my mind. The first are people who liked mathematics until some sour experience — usually around the fifth grade — drove them from it; the second are the enthusiasts, for whom fresh material waits on every page. A further group is served too: those who simply want sharper powers of analysis. Many professions, law and medicine among them, demand long stretches of exact reasoning, and each chapter lets the reader practise holding to a lengthy, closely argued line of thought. Two testimonies show that mathematics can build that capacity.
G
One doctor put it this way: 'The rigorous, analytical habit of thought that mathematics instils was fine preparation for medical school. A doctor meets a problem that must be picked apart in full before a remedy appears, much as in mathematics.' A lawyer reached the same view: 'I came to law with nothing behind me — not a single course in political science — yet I did well at one of the finest law schools. For that I largely thank mathematics, and above all what working with proofs taught me about taking a tangled principle apart. A lawyer schooled in mathematics can master legal doctrine as others rarely can.' I hope you will feel, as I do, the pleasure of watching plain, even naive questions open onto striking answers, and of seeing discoveries made for their own sake prove unexpectedly useful.
Silk is a delicate, lustrous cloth spun from the cocoons – the soft protective cases – that mulberry silkworms, the larvae of a particular moth, build around themselves. Its discovery is wrapped in legend. The tale most often repeated concerns Ai Ling, consort of the emperor Shenhuang, who is said to have governed China around 3000 BC. Strolling one day through the palace gardens, she noticed that several mulberry trees were being stripped bare by silkworms, and she gathered up a handful of their cocoons before settling down to rest. As she did so, one of the cocoons slipped from her grasp into the hot water beside her, and the warmth began to loosen it into a single slender filament. Finding that she could wind this thread about her fingers, she asked the emperor to let her raise silkworms on a stand of mulberries, and in time she built a spindle by which the fibres of a cocoon could be drawn off and twisted into a strand strong enough for weaving. How much of the story is genuine no one can say, yet there is no doubt that the Chinese have cultivated silk for thousands of years.
In the beginning, the rearing of silkworms was a sacred duty carried out only by priests, who supervised each stage from the feeding of the worms to the weaving of the cloth. Silk soon became a badge of rank, and in the earliest times only the nobles were allowed to dress in it; that restriction eased so slowly that not until much later dynasties could even the common people wear it. So greatly was the fabric valued that it also circulated as a kind of payment: officials drew their salaries in it, and farmers were permitted to meet part of their taxes with lengths of cloth rather than in coin. Rulers likewise sent it abroad as gifts of state. Bowstrings, fishing lines, the strings of instruments and even writing surfaces were fashioned from it. Among the most striking survivals is an early silk map, the oldest yet uncovered, recovered from the tomb of a nobleman thought to have died around 165 AD.
The craving for so rare a cloth in time gave rise to the celebrated trading route we now call the Silk Road, which carried silk out to the west and brought horses, along with gold and silver, back to the east. The road took its name from the single commodity that counted for most upon it, a fabric prized above gold itself. Stretching more than 6,000 kilometres between eastern China and the Mediterranean, it followed the line of the Great Wall, climbed the Pamir ranges, passed through what is now Afghanistan and reached the Middle East, where Damascus served as a great market; from there the wares were carried by ship across the sea. Scarcely any trader covered the whole distance, the goods passing instead through the hands of one middleman after another.
The mulberry silkworm being found nowhere but China, that land stayed for centuries the sole source of silk anywhere on earth. It was through the Byzantine Empire – master of the Mediterranean world of southern Europe, North Africa and the Middle East from 330 to 1453 AD – that knowledge of the craft at last leaked abroad. In one story, a pair of envoys acting for the Byzantine emperor are said to have smuggled silkworm eggs into Constantinople, today's Istanbul, in 550 AD, tucked away inside hollow walking canes. The Byzantines, though, proved every bit as close with the secret as the Chinese before them, and the weaving and selling of silk stayed a tight monopoly of the crown for hundreds of years. Not until the Arabs swept over Persia in the seventh century did its magnificent silks pass into other hands.
From Persia the art travelled on, spreading through Africa, Sicily and Spain in the wake of the Arab conquest. By the tenth century the Spanish region of Andalusia had grown into Europe's foremost centre of silk-making. Within a few hundred years, though, that lead had passed to Italy, whose merchants in Venice dealt heavily in the cloth and drew silk-growers to settle among them; even today the silk finished in the northern town of Como is held in high esteem.
In Europe, silk-making slid into decline once the nineteenth century and its factories arrived. Among the causes was a flood of cheaper Japanese silk, which the newly opened Suez Canal did much to speed on its way. A further blow landed in the twentieth century, when artificial fibres – polyester and the like – were increasingly substituted for silk in such goods as parachutes and stockings; the two world wars, meanwhile, severed Japan's supply of raw material and hurt the European trade still more. Once peace returned in 1945, Japan revived its industry with sharper methods and better raw silk, and right up to the 1970s it stood as the foremost producer of raw silk and very nearly its only exporter of any weight. Since then the lead has swung back to China, once again the world's principal maker and shipper of raw silk and silk yarn alike. Worldwide output today runs to some 125,000 tonnes a year, of which China accounts for very nearly two-thirds.
Whatever definition one settles on, animal migration is far more than creatures simply moving about. Loosely, it is travel undertaken at predictable intervals (commonly once a year) in which many members of a species may take part, and whose reward comes only after a long journey; inherited instinct seems to lie behind it. The biologist Reidar Solheim has set out five traits that recur, in varying mixtures and degrees, across all migrations. The movements are sustained ones that carry animals beyond their usual surroundings; they follow a broadly straight course rather than a meandering one; they call for distinctive routines at the outset, such as eating to excess, and on arrival; and they draw on unusual reserves of energy. To these Solheim adds a fifth: throughout the journey the traveller holds fast to an overriding purpose, so that neither tempting diversions nor the setbacks that deflect other creatures can turn it aside.
Consider an arctic tern on its 20,000-kilometre passage from the far south of South America up to the Arctic Circle. Should a bird-watcher hold out a fresh herring from a boat, the tern pays it no attention; the resident gulls plunge greedily after such scraps, yet the tern flies on. Why? At that instant it is gripped by an instinct people cannot help but admire — a sense of larger purpose — and this is why the offer fails to distract it. Reaching its destination is all that counts. Feeding, resting and breeding, the bird registers, can all wait; for now nothing matters except the journey, and its whole attention is fixed on arrival.
That larger purpose, moulded by evolution, is served the moment the bird touches down on some pebbly Arctic shore where its fellow terns have likewise gathered: here are the place, the season and the conditions in which it stands a chance of hatching its eggs and raising its young.
Migration, though, is a knotty subject, and the definitions biologists reach for differ partly according to the creatures they study. Delphine Aunay of the University of Valcourt, whose work centres on the quandu and other large land mammals, favours a definition she calls plain and workable, one that fits her animals: the shifting from one seasonal home range to another and back again. What usually drives this to-and-fro is the search for resources that no single territory can supply all year round.
Yet migration equally takes in the daily up-and-down journeys of ocean zooplankton, which rise after dark to feed and sink by daylight to escape predators. It also covers what aphids do: once one plant's tender leaves are used up, the next generation flies off to a fresh host, and not a single aphid ever finds its way back to where it began.
Solheim, an evolutionary biologist specialising in insects, offers a more elaborate definition than Aunay's, resting on those five features that mark migration off from other movement. His scheme makes room for the way an aphid grows responsive to the blue light of the open sky when the moment comes to launch its journey, and to the yellow light bouncing off soft young foliage when it is time to come down. It also accommodates the heavy feeding by which birds put on weight before a long flight. Its real worth, Solheim contends, lies in drawing attention to what wildebeest migration has in common with that of aphids, thereby steering researchers toward understanding how evolution shaped them all.
Human activity, however, is taking a growing toll on animal migration. The quandu (deer-like in appearance, though not in fact related to deer) ranks among the fleetest land mammals of southern South America. One herd passes the summer high in the Valdera ranges, within a mountain reserve, and each year threads a slender route out of the heights, over a river and down to the lowlands, where it waits out the frozen season by grazing scrub that the wind sweeps bare of snow. This herd is remarkable for how little its route varies and how tightly it is squeezed at three separate gaps. Miss any one of them on the way up in spring and the animals cannot reach the rich summer pasture; fail to get back through in autumn, retreating to the lowlands, and they will likely perish trying to last out the winter in deep snow. Depending on keen eyesight and sheer endurance to stay clear of predators, wearing pursuers down over long chases, the quandu favours high, open ground where it can watch and run. At one of the gaps, wooded slopes close in to form a V, leaving a bare strip of ground no more than 120 metres across, now crowded with private houses. Building of this kind is pushing the quandu toward a crisis, threatening to seal off the way through.
These days conservation scientists, with biologists and land managers in the national wildlife service and other bodies, work to safeguard not merely species and their habitats but the act of migration itself. Much of the quandu's route crosses a state forest, which has now designated it a protected migration route. Even so, what happens on privately owned land at one of the gaps lies beyond the reach of either the forest authority or the wildlife service. For some other migrating animals the problem is thornier still, stretched as their journeys are over far greater distances, across more borders, through more jurisdictions and more perils on the way. It will take good sense and firm resolve if we mean to let the world's migrating creatures carry on their travels a little longer.
C. Now and then a hard piece of music holds a passage of real beauty that is still so easy a newcomer could play it, and mathematics is the same. Some results in higher mathematics ask no specialist training of the reader — no algebra, geometry or trigonometry. They call instead for common sense and, at the very most, a little everyday counting, such as knowing that two odd numbers add to an even one. Each of the book's eight chapters shows this, and not one step in the argument lies beyond an ordinary reader's grasp. Because the reasoning leans on nothing harder than the simplest counting, anyone who opens the book can share in doing mathematics and come to know a way of thought at once logical and guided by intuition.
D. Even so, a reader with no mathematical background can go a surprisingly long way into the reasoning. What the book sets out are just the details that bring the mathematical cast of mind alive — a patient, step-by-step working-through, broken by testing and by sudden insight. These pages are to be turned far more slowly than those of a newspaper or a novel. Keeping pencil and paper to hand often helps, so that the reader can check each claim and work small calculations of their own.
E. Books meant to make a field of science clear to the general public have been written by many other researchers, who had little choice but to leave the mathematics out, though it is the very thing their theories rest on. That leaves the reader a mere onlooker; for across much of science the fitting language for fine detail is mathematics itself, whether the topic is the swelling universe, the particles below the atom, or the chromosome. A theory's broad shape can be conveyed without symbols, yet once some corner of the physical world is finally grasped, the account of it reads like a page from a mathematics textbook.
F. Throughout the writing, two groups of readers were always in my mind. The first are people who liked mathematics until some sour experience — usually around the fifth grade — drove them from it; the second are the enthusiasts, for whom fresh material waits on every page. A further group is served too: those who simply want sharper powers of analysis. Many professions, law and medicine among them, demand long stretches of exact reasoning, and each chapter lets the reader practise holding to a lengthy, closely argued line of thought. Two testimonies show that mathematics can build that capacity.
G. One doctor put it this way: 'The rigorous, analytical habit of thought that mathematics instils was fine preparation for medical school. A doctor meets a problem that must be picked apart in full before a remedy appears, much as in mathematics.' A lawyer reached the same view: 'I came to law with nothing behind me — not a single course in political science — yet I did well at one of the finest law schools. For that I largely thank mathematics, and above all what working with proofs taught me about taking a tangled principle apart. A lawyer schooled in mathematics can master legal doctrine as others rarely can.' I hope you will feel, as I do, the pleasure of watching plain, even naive questions open onto striking answers, and of seeing discoveries made for their own sake prove unexpectedly useful.
