P. A. Griffiths
good morning. I am very happy to get into the new millennium today. I can't think of a talk about science and mathematics.
A better topic, because science and technology in the new millennium may be more important than current. I am not a big trend.
Experts feel quite nervous when discussing the future. But I recently worked in the Scientific Policy Committee of the US Federal Government.
A job for government services is that you have to preach for a very big topic that doesn't know much. So everyone will
Forgive me for some guess today, I am discussing. If we agree that these big trends are indeed our today
Seeing what you see, then we will agree that at least in the near future, what will move to these trends
local.
The most important topics I have to talk about are how mathematics and science are interconnected. We are receiving all science and mathematics
Knowledge is interrelated and interdependent. We have also begun to see these knowledge as the aggregates of principles and relationships.
Extended from invisible atoms to huge biological and social systems on earth. The result made us more clearly understand that
Theoretical research and application research need to be closely close, and people in multiple fields need to cooperate.
I am a mathematician. My speech mainly looks at the problem from mathematics, so I can see that the current era is obviously one.
Golden age. One of the reasons is that mathematics begins with science and engineering very closely interact. This interaction promotes
Make science get a new field of view, and it has also prompted mathematics to get fundamental progress, I will intend to describe five in science and mathematics.
A main trend, and also talk about some of the challenges waiting for us in the 21st century.
Trend 1: Research from a straight model to dynamic model
The first important trend should be the way we describe research. Many people think that basic research is discussed when discussing scientific policies
Different from application research. They say that basic research is to explore knowledge for their own, without much thinking.
What is the purpose. The application research is different, which has a relatively specific goal in thinking. Many people talk about research
Straight model ", they said that knowledge is moved in one direction, from basic research to application research, and finally
use. But this model is not fully compliant with the situation in the real world, even in the simplest research projects, it also contains thinking.
I want to flow along a plurality of directions.
Researchers will not be surprised to this because their research has always been. But provide funding for researchers
The institutions may be surprised. If these agencies recognize this dynamic process of research, they may be more
Effectively funding research, making things better, for example, agency may simultaneously fund the foundation and should
Use research, not only funding a study, if they want to directly promote practical applications, but decide only funds
Studying, they may be severely distorted scientific processes.
We can think of many examples, showing the most founded research on how the foundation and application thinking, great
French biologist Louis Bathde (1) (Louis Pasteur) often produces wine from medicine, brewing beer, manufacturing wine and
The driving force of research in actual problems in agriculture has prompted him to get some basic biology and diseases.
Find. Gregov Mendel is studying how to improve crops in Gregov Mendel
When the problem, the basic law of genes was found. Lift a nearly example. Physical basic optical research has tradition
Target: Produce a better lens for the camera and telescope, but now give us the most important foundation of the modern telecommunications industry.
1: Fiber optics. We need to set up different types of researchers and make them together in a variety of ways to keep research work balance and diversify.
Trend 2: From theory experiment, to theory experiment calculation
The second trend is the research process itself. Not long ago, we concluded research methods into two means:
Theory and experiments. Now due to the development of computer capabilities, we added the third important means: calculation, this
Three means allow us to design its mathematical model for direct measurement or quantifying some of the complicated systems.
Some questions that cannot be understood in decades ago.
Ozone cave
An example of a person who requires a large-scale calculation is the mixture of oceans and atmosphere. We try to put fluid mechanics and non-
Linear kinetic combination understands this mixture, simulates its physical and chemical processes, but it is more than
Ink movement in water This rapid diffusion process is much more complicated.
For example, take a closer look, there is a non-mixed fluid in the two environments, and another medium cannot be pulled from the outside.
This phenomenon coming in in the ocean is critical to the life and death of the fish, because fish depends on nutrients, chemicals, floating
Biological and other fish in this hybrid environment, in the atmosphere, these islands can determine the spread of pollution and greenhouse gases. , For example
The ozone cavity formed over the Antarctic is one of the ozone cavities over the Nandem. Ozone in the cave is almost completely chemical by the upper cloud
The reaction is destroyed, the hole is surrounded by ozone, the atmosphere is turbulent, but the surrounding ozone cannot enter the hole, this is due to
It is in a powerful eddy current center. The mathematical model correctly predicts the outer edge of the vortex to hinder the mixed barrier. Spring
After the temperature rises, the eddy current is destroyed, hindered disappears, and new ozone returns to the cave.
Understanding this problem requires all three means of scientific research: the theory of fluid mechanics, experimenting at the atmospheric conditions
Finally, it also needs to be calculated, and then check it is consistent with the initial observation. In the past, we didn't have a powerful computer.
This study is impossible.
Kepier ball filling guess
The power of the computer can also make us solve a major problem of mathematics, which is about the ball (Sphere Packin)
G) Kepler guess, it has been difficult to fill nearly four centuries of mathematicians, this question begins with sixteen
At the second half of the century, Walter Raleigh wrote to the British mathematician Thomas Harrot, I hope he gives a fast
The method is estimated to estimate the number of shells accumulated on the ship deck. Harrot is also written to the German astronomer Copile, the latter is accumulated
Question: How to emissively emissively emissions, make the gap between the ball least? Cople can't find a bison
The most natural way of the shell or fruit store owner is better, this most natural way is to
The center of the face as the scheduling of the ball, the above inference becomes a famous Coppler.
This problem is difficult because it is necessary to exclude the likelihood of huge number. In the mid-20 century, mathematician principles
I know how to return it to a limited problem, even so, this problem is still the problem at the time.
too big. In 1953, significant progress has been made, Hungarian mathematician Laszlo Fejes-Tóth simplifies the problem into many special
A huge calculation of a special situation, he also proposed a new way to solve this problem.
The proof given by halas is very complicated. His equation has 150 variables, each variable changes, used to describe the various stacking methods of imaginary. A large number of methods, linear planning, and interval arithmetic methods are proved. Prove
There are 250 (textbooks) and 3 Gigabytes (3 × 10 ^ 9 bytes) computer programs and data. Only arrive
The end can you know that Haa is simplified to a limited problem is reasonable. He also admitted this prove
Long and complicated, others have to confirm that all details will take time.
It is worth mentioning that this work illuminates other related fields. Ball filling problem is an important part of mathematics,
Research on error detection code and error correction code. These two codes are widely used in storage information in the compressed disk, and
It is difficult to find more important applications in today's information society in today's information society.
Theoretical Computer Science
I would like to emphasize that calculating the big field of computer science, and its theory has become the most important and live today.
A scientific research area of jumping. It really started before half a century, then the modern computer still does not exist, Tuling
(Alan Turing) and his intertrs define computational concepts with mathematical methods and study the calculated power and limit. This guide
Von Neumann built the first electronic computer, then it is the calculation of our weekly today.
Machinery.
The actual use of the computer and the concept of "calculation" concept, so that the theoretical computer science has achieved greater expansion
. In the last 25 years, theoretical computer science has grown into a rich and beautiful field, and has been established with other science.
Contact, attracted a number of first-class young scientists, one of the important developments is to calculate the focus of research
"Go to" effective calculations "that are more difficult to touched. Other important issues are: NP-completeness, randomness make judgment
On revolutionization and the development of modern cryptography and complexity theory.
In addition to these internal development, theoretical computer science, there is also its mathematics (such as combined learning, algebra, topology and analysis.
Important crossings between crossings. Even the basic problems of computer science have spacious, enter the center of mathematics
The column of question. More and more mathematicians are considering the "calculation" problem in their research. In other words, they started
Theoretical results: "This problem is solved", then they follow: "Can you speed and how much approximate degree?
Look for solutions? "
The final aspect of theory computer science is also particularly interest, is a series of new series of other science.
Algorithm problem. The output required in these issues cannot be predefined, and it can almost start from any type.
Data: A picture, sound wave display, information read from Hubble Space Telescope, stock market, DNA sequence, movement
The mathematical model is trying to make these data meaningful, or predict their future
value.
In general, "Computing" itself and some of its main problems around it, both actually have a deep philosophical meaning.
Righteousness. This area focuses on several clear and profound issues. For example: Can randomness help calculate? constitute
What is the prove of a difficult problem? Can you make quantum or photon computer? In this new field, get
Surprisingly growing and deepening the new basic understanding of the opportunity.
Trend 3: Research from Interdisciplinary Research from Disciplinary
The current development trend of the third influence is: research on interdisciplinary research from the discipline. The college-style research institutions have traditionally been identified by some researchers in the same field by disciplines, research programs and results. A successful study
The career is still mainly on the success of the study in the subject, and this is mainly published by the published papers, academic title
(This is also based on the disciplined department) and the ability to get research funding is measured.
In general, the disciplines have achieved great success on the depth and focus issues of research: physics explore material
Structure parts, chemistry created new synthetic substances with specific properties, biology determination of control and regulation of life
Multi-gene and protein, at the same time, some modern issues require new and broad research attitudes, new interdisciplinary research
The team is exploring a bigger problem, which is much more complex, which is much larger than the problem in any discipline.
life sciences
In terms of life science, this trend is particularly obvious. Here, new technologies and knowledge greatly improve the normal life.
The ability to function and disease. The vast science discipline is beginning to intertwined, becoming biological, chemical, physics and mathematics
New polymers.
For example, physics provides basic principles for many public medical clinical practice, with X-light perspective, CAT scanning
, Fiber optic optometrics, laser surgery, ECHO tachycards and fetal sounds. Material science helps make new
Artificial joints, cardiac valves and other artificial organizations. Similarly, the understanding of nuclear magnetic resonance and positive electronics helps
Inspection, we can track the position and time of the brain accompanying the use, exercise, emotion, session, and drug use. base
In the three-dimensional protein structure, X-ray crystallography, chemical, and computer construction models are combined, and now you can use to improve the drug
design.
If there is no additional method of recombinant DNA, the human genome program (currently, the staining of organisms from microorganisms)
Body, not shown, and discharge nucleotide sequences will not exist. In turn, if there is no early synthesis, cut off and heavy
The study of various enzymes of Group DNAs is not possible to perform molecular clones. Further, today I plan to complete people in 2005.
3 × 10 ^ 9 basic sequences of body DNA, to rely on dry robots processing sampling and computer access to data
Combier. Other more specialized subsequent areas are indispensable. Currently working on DNA in commercialization
Sequence studies (such as screening a number of individuals that can lead to certain cancers), using nominate techniques and photochemicals
Learn, synthesize different short chains close to 10 ^ 5 DNAs to a small chip.
infectious disease
The combination of mathematics and biology in studying human infectious diseases is a new partnership. This work
The foundation is built in the 1920s, the Italian mathematician Vito Volterra developed prey and prey (PR
The first model of the EDATOR-PREY. He found that the addition and decrease in the predation and the predated population in the fish can be very good.
Description by mathematics. After World War II, the mathematical model established by the changes of animal groups was extended to epidemiological studies. Similar
Research on the changes in the disease in the large population in the process of population biology.
More often, the results in molecular genes have been inspired and encouraged scientists to use the same method to study infectious diseases.
At this time, the study object is not a group of organic or human groups, but a population of cells. For example, in a cellular system, predator is
Virus groups, and predators are human cell populations. These two groups come from complex Darwin's battle
And this combat can be described in mathematics.
Biological mathematicians can also quantify the lifetime of life after virus infection. Some wonderful results were discovered in studying AIDS infections, which in turn helped us understand the change of HIV in patients with infected patients.
. The popular point is that the HIV has a 10 years of incubation period and then starts infection of host cells and causes disease. but
It is a mathematical model that indicates that the HIV virus that causes major diseases has no incubation; they are not fast to grow rapidly, half life
The cycle is only about two days.
So why do you start infection after 10 years? It is also that the mathematical model shows that the progress of the disease may be caused by the disease.
The evolution of poison can be caused by inhibiting viruses for a long time, but in fact the virus varies into a number of new forms and more
The more, and finally overwhelmed the immune system.
The same mathematical model has made us understand why anti-HIV drugs should be combined and should be as early as possible during infection.
Take it. The combination is preferably used, which is due to a minimum of varying viruses. On the other hand, it should also be in the virus.
It is necessary to take it too far before it is too far.
Trend 4: Simplified theistism
The fourth main trend is to transfer to a simplified method from a conventional concentration to more to study complex systems. Make a system simple
Simplified the minimalism of some minimum systems has been mainstream until recently. Many people use the physics of the minimum particles as
The most authentic part of science. Rutherford Jazz has a famous saying: "All science or physics,
Or collect stamps. "Jazz, Luserford is clearly the enthusiasm of simplified the creed and early physical laws.
.
However, although the law relating to the world is concise and ordered, the world itself is not the case. Let's take a look at any one
Places, such as the outside of the classroom, everywhere is a complex phenomenon: the arrangement of rolling mountains, the chaos of the sand dunes
The mutual effects of financial markets, and the sudden rise in biology.
Because the world is complicated, there is a more complex model. Complex models are not just make the problem itself greater and more cumbersome
And there will be fundamental differences. We can't use the tools with a system with good behavior to score complex systems, only
It is not enough to use the basic law for the basic law for the large-scale equation group, and the research on complex systems is much more difficult than this.
Research climate is a good example. The basic equation for determining atmospheric changes - Navier-Stokes equation is non-linear
. This means that each variable (such as wind speed or wind direction) to be predicted is power in the equation. These indices make the system to the initial
The weight of the value or the measurement error is very sensitive: the initial value will have a lot of change, this is to make the sky
The gas forecast is only 3-5 days and longer forecasts.
Engineers have long encountered this complexity. For example, each Pentium chip contains millions of small components: transistors, connecting
And various gate components of crossientening. The basic functions of each component are clear, but these components are mutually
The way the impact is not simple. Designers should carefully make model programs to predict these interactions to eliminate errors (
Sensitivity of Bugs.
Life Science has been rich in research in complex systems. After decades of efforts, it has been successfully closed
The basic problem of life is due to the problem of individual genes and proteins. Now the interest of biologists is to use more
The method examines these components. Gene sorting and other techniques will separate the cells in the near future
And read their individual functions. Now the researchers want to know what is the function of a system.
An important challenge problem is to understand the chemical network of control cell function, which is a highly complex system. For example, a single gene expression (2) is usually not from 1, 2 or 5 proteins.
To control, you need a lot of protein. Some of them have been connected to DNA, and some are only temporary. Cells
The interaction between the molecules has a feedback effect, which increases or decreases expression of other molecules. What we said here is the initial attempt to model the model of cellular system, which can be called the third of physiology research.
aspect. The first aspect is "in vivo" (in living body), then "in vitro" (outside the living, the test tube),
It is "in Silico" (using a silicon, ie computer). This basic simulation can inform us to camp
How the cells react when the raising and a simple change occurs. Other interdisciplinary research programs currently underway
Force to understand how the virus "decides" it is replicated in the carrier or lasted to wait for a better opportunity. Look, sick
Poisonous seems to have a feedback control mechanism, which is its own inherent "noise", which is not all in the same conditions.
decision. This smart adaptability guarantees that there will always be some survival when there is a dangerous way.
Trend 5: Globalization and knowledge spread
The fifth trend affecting research work is scientific globalization. I have said before, we need various types of research.
Foundation and application. The extension of this idea is to do all the countries in each country in international competition.
Research, in the 1970s and 1980s, some people believe that a country can use other countries to study
As long as there is good manufacturing and market operation skills, you can benefit. But now, this "technology first"
The strategy is not as effective as we expected. In recent years, Japan, South Korea and other countries have adopted this strategy.
Home changes the policy and build its own research team. They realize that in order to understand and expand the discovery of others,
Have a high level of team.
The second layer of this trend refers to knowledge in developed countries and developing countries. This trend
For developing countries are particularly important, these countries are urgent to improve their technology strength. Before a generation, these
The country's scientists can only go to other countries to find the best research opportunities and equipment. Now the situation began to change, these countries are best
Scientists gradually willing to stay at home for their own scientific business.
Recently, the World Bank launched a motion that established small exemplary research institutes around the world, called "new
The Millennium Science Initiative. It gets from the Packard Foundation
Sub-funds, then work from World Bank loans. First Batch of New Thousand Years Institute (The Millennium SC
IENCE IENCE Institute, referred to as MSI) is now built in Chile, will also be held in Latin America and around the world.
The state established MSI.
These MSI's goal is to make scientists working in their own motherland, they are engaged in research and through training
Life and PhD came to train next-generation scientists. They will establish links with existing research units and help promote the economy.
development of. These research institutes will form a global network that is connected with electronic devices and has a common goal. I
It is predicted that you will hear more news that build this research institute in the future.
Some challenge
Finally, I want to talk about some of our huge difficulties and challenges in New Dry New Year, these difficulties and challenges will hinder the trend of interdisciplinary cooperation research. I said that we need high levels of disciplines, but there are some major obstacles to need
get over. I still take mathematics as an example, and the situation of other disciplines is similar.
An obstacle affecting each other is our own isolated tradition, and our mathematician has always separated from math others.
Absolutely isolated from other fields of science, is also isolated from non-academic fields, especially with private companies or units. Important
More bridges should be established between the Institute and the Institute. For example, the culture of university culture and private industries is very unhappy.
Same, there are almost no college students with minimum industrial knowledge, so that they can have a satisfactory career in the industry.
End. About 80% of new mathematics doctors only consider mathematical research. And I mentioned many very much in front.
Active industrial field, such as biological information and communication technology, there are many future development opportunities.
"Pure" cultural culture
Make us feel uncomfortable, more basic reasons may be in the twentieth century: the most difficult mathematics problem is
the most important. Our culture also teaches us to say: The most valuable is that mathematics is excited, mathematics
Exquisite and simple, and to explore the freedom of interesting issues, no matter where this explore will bring you.
In my graduate year, this tradition of studying mathematics plays a decisive role for mathematics. For example, Hardy (
A Mathematician's Apology has given me a lot of impact on the "Mathematician's Personnel". Hardon
Inner beauty of mathematics. He believes that our mathematics is because of its importance of activities as aesthetic and mental. Anyway
The actual application or association with the physical world is not appropriate or even we don't want. No teacher teaches us to study
It seems to be messy or unpleasant in terms of engineering, biological, chemical or meteorology. we
I always like "pure" problem, and the word "pure" gives a clear picture showing our attitude, as if
All other types of activities are not so pure.
However, let's go back to the history of mathematics to see, this will help. Best and Meng mentioned earlier
In two examples of Del, we see that foundations in basic mathematics are driven by practical problems. Let's think about Newton.
, Euler, Gauss, Limann, Pangola and other mathematicians, their mathematics is comparable to the study of physical world
. From most of the history, we have shared physics mathematics and found that they are actually very interesting.
However, in the twentieth century, it has gradually developed the tradition of mathematics for mathematics. During our designed universities, no need to encourage cross
The cooperation in the border of the venue. We personally divide the "application mathematics" department from "pure mathematics". This reflects
A narrow view of mathematics thinking,
For example, when I was in the seventy and 1980s of the 20th century, the math department of mathematics at the time was limited to pure concerns.
Copy study, of course, professors in this area are very beautiful. But we have a number of applying mathematicians, apply
Learning and computer science, controlism and other engineering, becoming part of the application science department. I used to have a time I plan
Hiring an excellent mathematician at the same time in two systems, he studies fluid mechanics, both from partial micro-division ("app"
Aspect?) Also studies from numerical analysis ("pure" aspects?). Unfortunately, others think of his work.
It is not "pure" for us. I think he is a great opportunity for interdisciplinary research, but others refused my opinion.
Today, this kind of thing has rarely happened, mathematics has interacted with science and engineering, this interaction has made science and number
The basic research of learning has benefited a lot. So we have to pay more attention to the fields other than our own research, including mathematics
Some disciplines outside.
I think that university can learn a lot from private agencies in an effective organizational research work. For example, in the new
Jersey's old Bell Lab is a very good research unit in the United States. There, the study is organized to be organized.
Subject team. In Bell Lab, it is not based on the organization structure, but is determined by scientific structure. At this
The problem has greater freedom and flexibility in the exploration, and has achieved great success in creating outstanding scientific achievements.
Very lucky, the wind direction seems to have changed. For example, last year, Meitu National Institute of Health (National Institute
The Of Health announces the establishment of a new bioengineering project, funding multidisciplinary research. Interdisciplinary assessment
The group seems to be able to follow this, and it is planning to set up some new interdisciplinary research centers, one of the suggested sets in Stan.
Fu University, focused on biophysics. The other is in Princeton, focusing on genes and proteins. American Packa
The RD Foundation has recently put into a huge funding to support interdisciplinary research projects. This type of project must be in the existing federal agency.
It is very difficult to fund.
in conclusion
In the conclusion, I would like to emphasize that, whether it is observing our research activities, we are working in the way we work.
See the big development trend of global mutual exchanges and cooperation. Research work is becoming more complicated because we want
Conduct a large number of calculations. The study also has to earn interdisciplines, because this is the best way to understand complex systems / world
Both countries have begun to realize that if they are necessary to participate in the 21st century knowledge and economic competition, they must have their own research.
force.
I am here to discuss an exciting thing with the Middle East scientist, which is intended to build a small and interdisciplinary in Beirut.
International Research Center of the Branch. This center will be part of the new millennium scientific launch project, and one of its goals is
I am convinced that scientific research is one between Arab countries and Israeli scientists.
A good venue not only makes technology knowledge, but also helps people learn cooperation across national borders.
. I really believe that the best way to meet the challenge of the 21st century is to understand and adapt to this powerful trend, to the old Bell
The organization of the laboratory learned, and they see the value of team work and interdisciplinary research many years ago. Today I
The challenge is to continue to improve this research model, extending them from the industrial community to academic research and education,
Training tomorrow scientists and engineers,
Thank you all.
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(1) Louis Baste (1822-1895), famous French chemist, microbiologist, prove that fermentation and infectious diseases are
The microorganism is caused; the first vaccination is used to prevent rabies, anthrax, etc .; invented the Papan disinfection method. -
School note
(2) Roughly said that "gene expression" refers to the gene in active "working state", "gene is not expressed" refers to the gene.
The "silent" state. The regulation of gene expression is the current important research topic. - School Note
-------------------------------------------------- ----- (Originally published "Mathematics Translation Forest" 2002/2, Feng Keqin, Infinite Eastern School)
