1.1. Salem Prize 2000.

Terence Tao was awarded the Salem Prize by the School of Mathematics at the Institute for Advanced Study in Princeton for:-

... his work in $L^{p}$ harmonic analysis and on related questions in geometric measure theory and partial differential equations.

1.2. Bôcher Memorial Prize 2002.

Terence Tao was awarded the Bôcher Memorial Prize by the American Mathematical Society:-

... for his recent fundamental breakthrough on the problem of critical regularity in Sobolev spaces of the wave maps equations, "Global regularity of wave maps I. Small critical Sobolev norm in high dimensions", International Mathematics Research Notices 2001 (6) (2001), 299-328 and "Global regularity of wave maps II. Small energy in two dimensions"
Communications in Mathematical Physics 2244 (2) (2001), 443-544.

The committee also recognises his remarkable series of papers, written in collaboration with J Colliander, M Keel, G Staffilani, and H Takaoka, on global regularity in optimal Sobolev spaces for KdV and other equations, as well as his many deep contributions to Strichartz and bilinear estimates.

1.3. Clay Research Award 2003.

Terence Tao was awarded the Clay Research Award by the Clay Mathematics Institute for:-

... his ground-breaking work in analysis, notably his optimal restriction theorems in Fourier analysis, his work on the wave map equation (the hyperbolic analogue of the harmonic map equation), his global existence theorems for KdV-type equations, as well as significant work in quite distant areas of mathematics, such as his solution with Allen Knutson of Horn's conjecture, a fundamental problem about Hermitian matrices that goes back to questions posed by Hermann Weyl in 1912.

1.4. Australian Mathematical Society Medal 2005.

Terence Tao was awarded the Australian Mathematical Society Medal by the Australian Mathematical Society:-

The Australian Mathematical Society Medal is awarded to a member of the Society within 15 years of the award of their PhD for distinguished research in the mathematical sciences. A significant portion of the research work should have been carried out in Australia.

1.5. Ostrowski Prize 2005.

Terence Tao and Ben Green were jointly awarded the Ostrowski Prize by the Ostrowski Foundation for:-

... their exceptional achievements in the area of analytic and combinatorial number theory. In joint work they have obtained a series of impressive results which implies a proof for the old conjecture that there exist arbitrary long arithmetic progressions of primes. Their methods open entirely new perspectives for prime number theory and some other parts of mathematics. ... Tao was already one of the world's top mathematicians by the time they got together. He has made major contributions in many subjects in analysis and combinatorics, such as startling work on the matrix multiplication conjecture with Knutson, contributions to the restriction problem and the Kakeya problem in harmonic analysis, and the development of sum-product formulas in finite fields. He was awarded the Fields medal in 2006, at the age of 31!

1.6. Levi L Conant Prize 2005.

Terence Tao and Allen Knutson were jointly awarded the Levi L Conant Prize for:-

... their expository article "Honeycombs and Sums of Hermitian Matrices", Notices of the American Mathematical Society 48 (2001), 175-186.

1.7. Fields Medal 2006.

Terence Tao was awarded the Fields Medal for:-

... his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.

1.8. MacArthur Award 2006.

Terence Tao was given the MacArthur Award by the MacArthur Foundation for:-

... bringing technical brilliance and profound insight to a host of seemingly intractable problems in such areas as partial differential equations, harmonic analysis, combinatorics, and number theory.

1.9. Shanmugha Arts, Science, Technology & Research Academy Ramanujan Prize.

The Ramanujan Prize is awarded by the Shanmugha Arts, Science, Technology & Research Academy (SASTRA) based near Srinivasa Ramanujan's hometown of Kumbakonam, India. The Prize:-

... is awarded every year to a young mathematician judged to have done outstanding work in Ramanujan's fields of interest.

1.10. Alan T Waterman Award 2008.

Terence Tao was awarded the Alan T Waterman Award by the U.S. National Science Foundation for:-

... his surprising and original contributions to many fields of mathematics, including number theory, differential equations, algebra, and harmonic analysis.

1.11. The Lars Onsager Lecture and Onsager Medal 2008.

Terence Tao was awarded the Onsager Medal at the Norwegian University of Science and Technology in December 2008 for:-

... his combination of mathematical depth, width and volume in a manner unprecedented in contemporary mathematics.

Tao's Lars Onsager lecture was entitled Structure and randomness in the prime numbers and delivered at the Norwegian University of Science and Technology on Monday, 8 December 2008. In addition, Professor Tao gave the lecture Compressed sensing on Tuesday, 9 December.

1.12. King Faisal International Prize 2010.

Terence Tao was awarded the King Faisal International Prize by the King Faisal Foundation for:-

... his highly original solutions of very difficult and important problems and for his technical brilliance in the use of the necessary mathematical machinery.

Terence Tao:-

... is a world-renowned mathematician working in a number of branches of mathematics, including harmonic analysis, partial differential equations, combinatorics, number theory, and signal processing. He is known for his highly original solutions of very difficult and important problems and for his technical brilliance in the use of the necessary mathematical machinery. Working with Ben Green, he proved there are arbitrarily long arithmetic progressions of prime numbers - a result now known as the Green-Tao theorem.

1.13. Nemmers Prize in Mathematics 2010.

Terence Tao was awarded the Nemmers Prize in Mathematics by Northwestern University. The Press Release states:-

Tao, a professor of mathematics at University of California, Los Angeles who has been dubbed the "Mozart of Math," has been awarded the ninth Frederic Esser Nemmers Prize in Mathematics "for mathematics of astonishing breadth, depth and originality.

Tao is well known for a proof, in collaboration with British mathematician Ben J Green, of the existence of arbitrarily long arithmetic progressions of prime numbers (the Green-Tao theorem). In 2006, he received a MacArthur Fellowship (nicknamed the genius award) and a Fields Medal, widely considered the top honour a mathematician 40 years of age or under can receive. Tao was awarded the Fields Medal for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory. Tao was cited as "a supreme problem-solver whose spectacular work has had an impact across several mathematical areas ... who combines sheer technical power and other-worldly ingenuity for hitting upon new ideas." In 2007, Tao was elected a Fellow of the Royal Society. In 2008, he became a foreign associate of the United States National Academy of Sciences and, in 2009, a member of the American Academy of Arts and Sciences. In 2010, he was the co-winner of the King Faisal International Prize in the field of science for his works in mathematics. A child prodigy, Tao started to learn calculus when he was 7, and when he was 20 earned his Ph.D. from Princeton University. He joined UCLA's faculty that year and was promoted to full professor at age 24.

1.14. Polya Prize 2010.

Terence Tao and Emmanuel Candès were awarded the Polya Prize by the Society for Industrial and Applied Mathematics. The Press Release states:-

Professor Emmanuel Candès from Stanford University and Professor Terence Tao from University of California, Los Angeles (UCLA) were the 2010 recipients of the George Pólya Prize, which was awarded at the Prizes and Awards Luncheon at the SIAM Annual Meeting held July 12-16 in Pittsburgh, Pennsylvania.

The award recognises their role in developing the theory of compressed sensing and matrix completion, which enables efficient reconstruction of sparse, high-dimensional data based on very few measurements. According to the selection committee, the algorithms and analysis are not only beautiful mathematics, worthy of study for their own sake, but they also lead to remarkable solutions of practical engineering problems.

Tao has been a professor of mathematics at the University of California, Los Angeles since 1999 and was appointed to UCLA's James and Carol Collins Chair in the College of Letters and Science in 2007. He completed his PhD under Professor Elias M Stein at Princeton University in 1996. In August 2006, he won the prestigious Fields Medal, often touted as the "Nobel Prize in mathematics."

1.15. Crafoord Prize 2012.

Jean Bourgain and Terence Tao were awarded the Crafoord Prize by the Crafoord Foundation, The Royal Swedish Academy of Sciences, for:-

... for their brilliant and groundbreaking work in harmonic analysis, partial differential equations, ergodic theory, number theory, combinatorics, functional analysis and theoretical computer science.

For more information about Terence Tao winning the Crafoord Prize, see Section 2 below.

1.16. Simons Investigator 2012.

Terence Tao was made a Simons Investigator by the Simons Foundation. Simons Investigators were outstanding theoretical scientists who receive a stable base of research support from the foundation, enabling them to undertake the long-term study of fundamental questions.

Terry Tao is one of the most universal, penetrating and prolific mathematicians in the world. In over 200 publications (in just 15 years) spanning collaborations with nearly 70 mathematicians, he has established himself as a major player in the disparate fields of harmonic analysis, partial differential equations, number theory, random matrices, and more. He has made deep contributions to the development of additive combinatorics through a blend of harmonic analysis, ergodic theory, geometry and number theory, establishing this field as central to the modern study of many mathematical subjects. This work has led to extraordinary breakthroughs in our understanding of the distribution of primes, expanders in groups, and various questions in theoretical computer science. For example, Green, Tao, and Ziegler have proved that any finite set of linear forms over the integers, of which no two are linearly dependent over the rationals, all take on prime values simultaneously infinitely often, provided there are no local obstructions.

1.17. Breakthrough Prize in Mathematics 2014.

Terence Tao was awarded the Breakthrough Prize in Mathematics:-

... for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory.

For more information about Terence Tao being awarded the Breakthrough Prize in Mathematics, see Section 3 below.

1.18. Royal Medal 2014.

Terence Tao was selected by the Royal Society of London to receive the 2014 Royal Medal for physical sciences:-

... for his many deep and varied contributions to mathematics, including harmonic analysis, prime number theory, partial differential equations, combinatorics, computer science, statistics, representation theory, and much more.

1.19. PROSE award in the category of "Mathematics" 2015.

The PROSE awards are the Association of American Publishers Awards for Professional and Scholarly Excellence. Terence Tao received the award for best Mathematics book:-
Hilbert's Fifth Problem and Related Topics (American Mathematical Society).

1.20. Riemann Prize 2019.

Terence Tao was awarded the inaugural Riemann Prize from the Riemann International School of Mathematics, Varese, Italy. The Riemann Prize was established in 2019, on the occasion of the tenth anniversary of the Riemann International School of Mathematics. Along with the Riemann International School of Mathematics, its co-sponsors include all public and private universities of Lombardia, the government of Regione Lombardia, and the municipality of Varese.

Terence Chi-Shen Tao is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, geometric combinatorics, arithmetic combinatorics, analytic number theory, compressed sensing, and algebraic combinatorics. Tao was a recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He is also a 2006 MacArthur Fellow. This prolific mathematician has been the author or co-author of 275 research papers, his most impressive results being those on three-dimensional Navier-Stokes existence and smoothness.

1.21. Great Immigrants 2019.

Terence Tao was given the Great Immigrants 2019 award by the Carnegie Corporation of New York. Every Fourth of July, Carnegie Corporation of New York celebrates the exemplary contributions of immigrants to American life.

1.22. Princess of Asturias Award for Technical & Scientific Research 2020.

Yves Meyer, Ingrid Daubechies, Terence Tao and Emmanuel Candès were given the award by the Fundación Princesa de Asturias.

Yves Meyer (French), Ingrid Daubechies (Belgian and American), Terence Tao (Australian and American), and Emmanuel Candès (French) have made immeasurable, ground-breaking contributions to modern theories and techniques of mathematical data and signal processing. These constitute the foundations and backbone of the digital age (by enabling the compression of graphic files with little loss of resolution), of medical imaging and diagnosis (by enabling accurate images to be reconstructed from a small number of data) and of engineering and scientific research (by eliminating interference and background noise). As regards this last point, these techniques serve as the key, for example, to the deconvolution of Hubble Space Telescope images and have been crucial in the detection by LIGO of gravitational waves resulting from the collision of two black holes. The outstanding contributions of these world leaders in mathematics to modern mathematical data and signal processing are essentially based on two different yet complementary tools: wavelets and compressed sensing or matrix completion.

For their part, Yves Meyer and Ingrid Daubechies have led the development of the modern mathematical theory of wavelets, which are like mathematical heartbeats that enable us to approach Van Gogh and discover his style or to listen to the music enclosed in the apparent noise of the Universe, among many other applications of all kinds. In short, they enable us to visualise what we cannot see and listen to what we cannot hear. On the other hand, in addition to the undeniable advances in medical imaging and other diagnostic tests derived from the collaboration between Terence Tao and Emmanuel Candès, their contributions to the techniques of compressed sensing enable us to complete electromagnetic signals or reconstruct melodies from which time has stolen notes. This Award highlights the social contribution of mathematics and its importance as a cross-cutting element in all branches of science.

1.23. Janos Bolyai International Mathematical Prize 2020.

Terence Tao was awarded the Janos Bolyai International Mathematical Prize by the Hungarian Academy of Sciences for his monograph Nonlinear Dispersive Equations: Local and Global Analysis (American Mathematical Society, 2006).

For more information about Terence Tao winning the Janos Bolyai International Mathematical Prize, see Section 4 below.

1.24. IEEE Jack S Kilby Signal Processing Medal 2021.

The IEEE Jack S Kilby Signal Processing Medal was awarded to Emmanuel Candès, Terence Tao and Justin Romberg:-

... for ground-breaking contributions to compressed sensing.

1.25. USIA Award Winner for Mathematics 2021.

Terence Tao was awarded the United Sigma Intelligence Association Award for Mathematics:-

The 2021 United Sigma Intelligence Association Award for Mathematics has been given to Terence Tao in recognition of having met the highest standards of excellence in his noteworthy achievement as an original investigator in a field of arts and sciences dedicated to providing intellectual inspiration to the world.

Terence Tao is a mathematician whose deep and original insights across a broad range of research areas have had a profound and lasting impact. Best known for his work on partial differential equations, he has also made significant contributions to computer science and statistical analysis.

In the field of number theory, Terence has conducted important research on identifying sequences of prime numbers, revealing that they can be found in evenly spaced progressions of any finite length. More recently, he has proposed an innovative new approach towards solving the Navier-Stokes Equation, one of the remaining unresolved Clay Millennium Problems.

Terence is one of the most acclaimed mathematicians of his generation, and in 2006 was awarded the Fields Medal for his extensive and wide-ranging research. A 2007 MacArthur Fellow, he is currently a Professor of Mathematics at UCLA.

1.26. Education and Research Award 2022.

Advance Global Australian Awards named Terence Tao winner of the Education and Research Award.

1.27. Global Australian of the Year 2022.

Advance Global Australian Awards named Terence Tao winner of the Global Australian of the Year Award 2022. For more information about Terence Tao winning this award, see Section 5 below.

1.28. Grande Médaille 2022.

Terence Tao was awarded the 2022 Grande Médaille of the French Academy of Sciences.

Terence Tao, Professor of Mathematics and the James and Carol Collins Chair in the College of Letters and Sciences at UCLA, has been awarded the 2022 Grande Médaille of the French Academy of Sciences. The Grand Medal has been conferred to him on Tuesday, 21 March 2023 at 2.30 p.m. in the Great Hall of the Institut de France. The Grande Médaille is awarded every year to scientists for making critical contributions to the development of science in the international landscape.

Terence Tao is a mathematician with a glittering career of success from his early years as a child prodigy to his most recent successes in solving long-held conjectures. What is amazing about him, apart from his unique qualities as a problem solver, is the ease with which he enters into fields as varied as partial differential equations, analytical number theory, 3-manifold geometry, non-standard analysis, group theory, model theory, quantum mechanics, probability, ergodic theory, combinatorics, harmonic analysis, image processing, functional analysis, and many others with a depth that matches that of the best specialists in these subjects.

It is no exaggeration to describe him as the "Mozart of mathematics" and he managed to go from being a child prodigy (we see him talking at the age of 10 with Paul Erdös), winning a gold medal at the Math Olympiads as a thirteen year old, being appointed permanent professor at the age of 21 at the University of California at Los Angeles etc.) to the stage of becoming a famous mathematician accumulating renowned prizes including the Fields medal.

One of his originalities is to keep a mathematical "blog" which is a wonderful source for entering into very varied subjects where his extraordinary conceptual intelligence guides the reader to overcome the difficulties.

2.1. Press release.

The Royal Swedish Academy of Sciences has decided to award the Crafoord Prize in Mathematics 2012 to Jean Bourgain, Institute for Advanced Study, Princeton, USA and Terence Tao, University of California, Los Angeles, USA, "for their brilliant and ground-breaking work in harmonic analysis, partial differential equations, ergodic theory, number theory, combinatorics, functional analysis and theoretical computer science."

The masters of mathematics

This year's Crafoord Prize Laureates have solved an impressive number of important problems in mathematics. Their deep mathematical erudition and exceptional problem-solving ability have enabled them to discover many new and fruitful connections and to make fundamental contributions to current research in several branches of mathematics.

On their own and jointly with others, Jean Bourgain and Terence Tao have made important contributions to many fields of mathematics - from number theory to the theory of non-linear waves. The majority of their most fundamental results are in the field of mathematical analysis. They have developed and used the toolbox of analysis in ground-breaking and surprising ways. Their ability to change perspective and view problems from new angles has led to many remarkable insights, attracting a great deal of attention among researchers worldwide.

2.2. Strides and leaps across challenging mathematical terrain.

To many people, mathematics seems done and dusted. It promises unchanging certainties. Everyone who, at school, toiled through multiplication tables, Pythagoras' theorem or algebraic equations has respect for the capacity of mathematics to deliver an incontrovertible answer to every question. But underlying this apparently sealed edifice is a vast mathematical landscape, open for exploration. For anyone who penetrates it, as researchers do, unknown expanses open up - a vista of mountains, valleys, and paths to follow.

Mathematics has evolved and emerged over millennia. New theories arise; existing ones are streamlined and expanded. New patterns and connections are sought. In fact, the scope of mathematical research in the past century exceeds that of everything done before.

Nonetheless, some problems remain unsolved. Some of them deal with prime numbers, i.e. numbers that are divisible only by 1 and themselves such as: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47... But how many prime numbers are there? Euclid, who lived and worked in Alexandria some 2,300 years ago, proved that they are infinitely many.

But a closely related question has continued to confound mathematicians: how many prime-number 'twins' exist? Twins are pairs of prime numbers that differ from each other by 2, such as: 3 and 5, 5 and 7, 11 and 13, 17 and 19... and so forth. Is there an infinite number of twin primes? The answer is not known. The difficulty lies partly in the fact that prime numbers become more sparse as whole numbers increase.

Terence Tao and his British colleague Ben Green jointly solved a difficult problem about sequences of prime numbers. A sequence of numbers is known as an 'arithmetic sequence' if the difference between a number and its immediate successor in the sequence is constant. For example, 5, 11, 17, 23 and 29 make up an arithmetic sequence of prime numbers of length 5, with a difference of 6 between consecutive elements. Green and Tao showed that for any desired length chosen in advance, no matter how high, there exists a finite arithmetic sequence consisting of prime numbers of exactly that length.

Finite arithmetic sequences composed of prime numbers, of arbitrary length, thus exist; on the other hand, no technique for explicitly finding such sequences has been found. So finding an arithmetic sequence of, say, 100 prime numbers is currently beyond our ability, even if Green and Tao have shown that such a sequence exists. Currently, the longest known arithmetic sequence of prime numbers contains 26 terms. It is a sequence of 26 prime numbers, starting with 43,142,746,595,714,191 and with a difference of 5,283,234,035,979,900 between successive terms.

The majority of Jean Bourgain's and Terence Tao's most fundamental results are to be found in the field of mathematical analysis. Isaac Newton and Gottfried Wilhelm von Leibniz developed mathematical analysis at the end of the 17th century.

Mathematical analysis studies functions. An example of a function may be a rule assigning a value to each number, as a squaring function, which to each number assigns its square. In this case the value of the function at 2 is 4, at 3 it is 9, at 10 it is 100 and so on.

Some functions can be represented graphically as curves, and the analysis then describes their shapes. It tells us how the function varies: does it change fast or gradually, does it move upward or downward, where is its highest or lowest value?

Newton used analysis to study mechanics and astronomy. Over the past three hundred years, analysis has come to permeate the language of physics and all other natural sciences. It is a key ingredient of quantitative methods used almost everywhere mathematics is applied. Our understanding of the reality around us is to a high degree governed, by its mathematical description.

A Frenchman, Jean-Baptiste Joseph Fourier, took an epoch-making step in the development of mathematical analysis nearly 200 years ago. He showed that, in principle, all functions consist of sums of simpler functions. So, for example, the sound (or 'harmonic') of a violin string is composed of a fundamental tone and several overtones. Their frequencies are multiples of the fundamental tone's frequency. Harmonic analysis was born.

Harmonic analysis became a key tool for solving differential equations, which are at the core of mathematical analysis. In turn, differential equations are a key tool for physics, engineering and other fields of science. Today, there is no limit to the applications of this branch of mathematics, which is constantly developing.

With the fundamental contributions of Jean Bourgain and Terence Tao, some of the most difficult, non-linear differential equations can now be studied successfully. These describe more "messy" processes, such as turbulent currents, tsunami waves and chaos. Who knows how these equations can be used in the future?

What sets mathematics apart is that its major advances can long lie hidden from the world, intelligible only to a handful of experts. One such example is Bernhard Riemann's geometry, which only after several decades found its application in physics, and became the basis of Albert Einstein's general theory of relativity.

Within mathematics itself, specialised areas may be concealed from other mathematicians' eyes. In modern mathematical research, dialogue and communication with other mathematicians have been increasingly crucial for progress. On their own and jointly with others, Jean Bourgain and Terence Tao have made astounding contributions to many fields of mathematics. They have developed and used the toolbox of harmonic analysis in ground-breaking and surprising ways, attracting a great deal of attention among researchers worldwide.

Ideas from harmonic analysis, an area whose tools have the capacity to find hidden patterns in seemingly random data, have proved extremely useful for research on prime numbers as well. Studying them is like finding the music in a noisy recording. Prime numbers appear to crop up randomly among all the whole numbers and thus, in a way, can be interpreted as 'noise'.

Fascination with hidden patterns among prime numbers was long regarded as a mathematician's 'art for art's sake'. Nowadays, our best encryption methods used for secure data transmission rely on the difficulty of dealing with very large prime numbers.

Another indispensable tool for modern cryptography, and for other parts of computer science as well, is the ability to obtain high-quality random numbers. A decent level of randomness can, for example, be obtained from noise in a computer's microphone or pictures of falling leaves in a webcam. By using methods from harmonic analysis, Jean Bourgain has shown how two good, independent sources of randomness can be used to create an almost perfect random number sequence.

One problem studied by both Jean Bourgain and Terence Tao, together and separately in cooperation with others, is what is known as the Kakeya problem. In 1917 Soichi Kakeya, a Japanese mathematician, posed a question that may be considered fairly bizarre: what is the minimum area on which a needle can be completely turned around? This might be described as making a U-turn with a car in the smallest possible area, assuming that the car is as thin as a needle. Ten years later, in 1927, came a surprising answer: a needle can be rotated on an arbitrarily small area.

The original question, relating to two dimensions (an area), was thereby answered. But in more dimensions a modified version lives on. This Kakeya problem has proved to have a fundamental bearing on a number of areas in mathematics, and has been a challenge taken on by both Crafoord Prize Laureates. However odd the original Kakeya needle problem may appear, attempts to solve the higher-dimensional Kakeya problem have sustained increasingly active mathematical attention over the past three decades. There exists no solution yet, but the concepts created in order to solve the problem may turn out to have more significance in mathematics than the answer to the original question may bring.

The study of the Kakeya problem has uncovered profound connections with harmonic analysis and issues relating to whole numbers. By changing the perspective and viewing the problem from new angles Bourgain and Tao have shown many surprising insights.

Yet again, mathematics has shown interconnections among its diverse branches. The fact that methods developed in one area become tools for solving problems in entirely different, and apparently unrelated areas, shows the underlying unity of mathematics.

Terence Tao, University of California, Los Angeles is awarded the 2015 Breakthrough Prize in Mathematics "for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations, and analytic number theory."

3.1. The Science.

Terence Tao has made important contributions to a very wide range of mathematical fields, but has perhaps made the most impact in number theory. Number theory is the study of integers, and prime numbers play a particularly central role: in the universe of numbers, primes are the atoms. Alone and with collaborators, Tao has solved several longstanding problems related to prime numbers. For example, he proved that every odd integer above 1 can be built from adding together five prime numbers or less; and that there are equally spaced progressions of primes (such as 3, 7, 11), of any desired length, to be found within the infinite series of integers.

3.2. Comments by Terence Tao.

Mathematics nowadays is increasingly a collaborative and interdisciplinary activity. A large fraction of the work I have done in mathematics could not have been accomplished without the crucial input of my many co-authors, colleagues, mentors, students, and even commenters on my blog. I am deeply indebted to all of them, but particularly to my early mentors Basil Rennie and Garth Gaudry, and my graduate advisor Elias Stein. And of course to my wife, Laura, for her constant support and understanding (and also for giving me the perspective of an electrical engineer on mathematics!).

3.3. Pulling back the curtain: Terence Tao on mathematics in the internet age.

How is the internet advancing science?

The internet has a huge potential to revolutionise science. We are just beginning to realise this. First of all it has made science much more open by sharing preprints before they are published, discussing them in blogs devoted to very specialised topics in science. It sort of pulls back the curtain. In mathematics, for example, you normally only publish techniques that work. You try attaching your problem, you try ten different things, nine don't work but the tenth one does and you publish the tenth one. But often the process of going through the other nine arguments, seeing why they don't work, is very instructive. I think it is very positive that mathematics is becoming much more open.

How was the Erdos Discrepancy Problem solved?

This was a conjecture which had ben open for eighty years or so. About three of four years ago there was a big push by Tim Gowers, who is a Fields Medalist, to attack this problem in a massive collaborative way. So he invented this new style of doing mathematics by online collaborative projects called polymath projects, where you get many together online and to work together on a problem and I participated in that. They didn't solve the problem but they managed to reduce the problem to a simpler problem. It was a problem of the number theory nature but at the time the number theory wasn't advanced enough to solve that problem so that the project kind of petered out. But earlier this year there was a big breakthrough in number theory. People understood a certain type of number theoretic function called a multiplicative function much better but I didn't realise the two were connected until I was writing on my own blog and some blog commentator who had worked on the previous polymath project commented that these new breakthroughs in number theory sounded connected to this Discrepancy Problem and the previous attempts to prove the Discrepancy Problem. At first I didn't believe him but I looked back and checked there was a connection so I worked on it. It only needed one more idea and it all came together.

What problem would you like to solve?

I kind of feel that doing mathematics is like climbing cliffs and trying to reach various goals. Some peaks are just completely out of reach. In number theory one of these is the Riemann hypothesis. It is a very old very famous conjecture about the prime numbers which would have so many implications but no one has a clue how to seriously attack it. The problem that I would love to solve which is most within reach is the Twin Prime conjecture. It is an old conjecture about whether there are infinitely many pairs of primes that are called twins which are two apart, like 11 and 13. Current methods are not quite able to solve that conjecture. We understand why there are limitations. We can get very close. A year of two ago I was involved in a project which showed you can get pairs of primes which are not 2 apart but at most 246 apart. This was quite a breakthrough compared with what had been done before. But we can't reach 2, but I think we are only one or two new ideas away. maybe in the next ten years that one will be solved.

4.1. János Bolyai International Mathematics Award to Terence Tao.

The prize is awarded every fifth year by the Hungarian Academy of Sciences to the author of the most excellent, ground-breaking mathematical monograph, published anywhere and in any language in the preceding fifteen years, presenting their own new results and methods, taking into account the author's previous scientific work.

The Hungarian Academy of Sciences awarded the 2020 János Bolyai International Mathematics Prize to Terence Tao, professor at the University of California, Los Angeles, for his book Nonlinear Dispersive Equations and for his influential mathematical outreach activities.

As academician Miklós Laczkovich, president of the Mathematical Sciences Department of the Hungarian Academy of Sciences, said in his eulogy, Terence Tao is one of the greatest figures in today's mathematics, who, from the theory of differential equations and dynamical systems to combinatorics, from number theory and group theory to random matrices and mathematical physics, he has achieved breakthrough and influential results in many fields.

Around the 2000s, he achieved ground-breaking results in the theory of nonlinear dispersive partial differential equations (which include the nonlinear Schrödinger equation, the wave equation, the Korteweg-de Vries equations and many of their variants), which were published in the book Nonlinear Dispersive Equations provided the basis for the award. Since the publication of the monograph, this has been the basic book of the field, which has proven to be a permanent reference work for both students and researchers, as well as a starting point for further high-quality research.

Over the past 15 years, Terence Tao has published 12 other books on a wide variety of topics - some of which were based on his popular maths blog. Since the start of this blog (2007), it has been the most read and most influential mathematical website, offering a wide range of mathematicians and those interested in mathematics the opportunity to get a glimpse of mathematical theories, results and methods that are far from them.

4.2. The János Bolyai International Mathematics Prize.

In honour of the 100th anniversary of the birth of the world-famous Hungarian mathematician János Bolyai, the Hungarian Academy of Sciences established the ten thousand kroner international recognition for outstanding mathematical works in 1902.

In addition to nurturing Bolyai's memory, one of the original goals of the award was to replace the missing Nobel Prize in mathematics.

The first laureate in 1905 was the French Henri Poincaré, one of the most versatile mathematicians of the 19th century, and in 1910 the German David Hilbert received the award. The awarding of the medal was interrupted after the outbreak of the First World War.

The Hungarian Academy of Sciences re-founded the award in 1994 under the name János Bolyai International Mathematics Award. The award carries US$25,000 and a gold-plated bronze medallion made using the original designs.

The Bolyai Prize is awarded every fifth year by the Hungarian Academy of Sciences to the author of the most outstanding, ground-breaking mathematical monograph presenting their own new results and methods published anywhere and in any language in the preceding fifteen (previously ten) years, taking into account the author's previous scientific work.

One year before the prize is awarded, the Mathematical Sciences Department of the Academy elects a committee consisting of five regular members and five outstanding foreign mathematicians and appoints its chairman. The committee will report its decision to the department chairman no later than three months before the prize is awarded. The committee itself chooses its speaker from among its members, who will present the prize winner's work in detail and prepare a written report. The president also votes in the committee and decides with his vote in the event of a tie.

The previous winners of the János Bolyai International Mathematics Prize were Saharon Shelah (2000), Misha Gromov (2005), Yuri Ivanovich Manin (2010), and Barry Simon (2015).

World's greatest mathematician named 2022 Global Australian of the Year.

Australian maths genius Professor Terence Tao is named the prestigious Global Australian of the Year for 2022, in recognition of his contribution to the field of mathematics and his efforts to turn complex maths into a simple tool for everyday problem solving.

The Global Australian Awards, presented by Advance Global Australians, recognise the soft power and significant influence of Australian expats and international alumni of Australian universities, who are leading crucial advancements on the global stage in industries critical to Australia.

Prof Tao's award was announced during the live broadcast of the 2022 Global Australian Awards, along with 12 category winners joining more than 160 eminent Australians recognised as Advance GameChangers over the past 11 years.

Advance Global Australians CEO Johanna Pitman said Professor Tao is a remarkable leader working at the cutting edge of his field, and someone to be celebrated across the nation.

"The Global Australian Awards are a powerful opportunity to spotlight and celebrate the immense contribution of Australian diaspora driving global impact around the world," Ms Pitman said.

"Prof Tao is a phenomenal example of the talent and contribution of Australian expats leading their professions on the global stage. His contribution to the field of mathematics is unparalleled. He is indeed one of the greatest mathematicians in the world."

A child prodigy who grew up in the hills of Adelaide, Prof Tao is regarded as the 'Mozart of Maths', recognised globally for his natural ability to solve enormously complicated problems across a broad range of mathematical fields. He completed his PhD in Mathematics at Princeton University at the age of 20, and at the age of 31, he was awarded the Fields Medal - regarded as the Nobel Prize of mathematics - for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory. He has been the author or co-author of over 350 research papers and 18 books, and continues to attract top students from all over the world, eager to study with him at UCLA, where he has been a professor since completing his PhD.

Prof Tao is determined to make his field more accessible by demystifying mathematics and showcasing its power as an everyday foundation for problem solving and creative thinking.

"Maths in school is often just about a whole bunch of sums, tests and exams - students don't get to see the connection to problem solving in the real world. I want to convey that the way we think about mathematics is coming from real-world common sense and intuition. There is a creative process to mathematical problem solving, and it can be applied in everyday situations," Professor Tao said.

Prof Tao focuses much of his energies today on mentoring and developing the next generation of mathematicians, both in his classes at UCLA and also through his engagement with the broader public. In January 2022, he teamed up with global learning platform MasterClass to launch their first series on mathematical thinking, in which he shares his approach to mathematical inquiry and shows viewers how they can apply maths in their daily lives.

"In these incredibly challenging times, it is inspiring to see Professor Tao's determination to share his wisdom and engage people of all walks of life in the power of maths as a tool for problem solving and creativity," Ms Pitman said.

"Prof Tao leads with such humility and is admired for his eagerness to collaborate and for the outcomes achieved as a result of his efforts to combine ideas and build connections across fields. He has worked with many of the world's other leading mathematicians and physicists to solve problems collectively, resulting in some of the greatest mathematical discoveries in areas of mathematical and scientific theory that had been considered impossible to solve for centuries. He is a global Australian we should all be proud of and a spectacular role model for learners - young and old - curious about opportunities in STEM."

This year's Global Australian Awards attracted more than 400 nominations, with 34 finalists selected and 12 category winners named. This year's Awards also included a new category recognising recent migrants to Australia who are having an outsized impact in future-facing industries.

"This year's award winners are tackling global challenges with purpose and persistence, driving impact across their professions, industries and sectors around the world," Ms Pitman said.

"Through their work and leadership, these often unknown Australian changemakers are collectively advancing human progress, protecting our planet, leading medical and scientific discoveries, revealing untold stories, and above all, advocating for equality, justice and human rights."