Most influential mathematicians during 21st century

 Mathematicians who have made significant contributions and have had a notable impact on the field during 21st century:

Andrew Wiles: Wiles is best known for proving Fermat's Last Theorem, one of the most famous unsolved problems in mathematics, in 1994. His work revolutionized the study of number theory and brought significant attention to the field.

Terence Tao: Tao is a Fields Medalist who has made groundbreaking contributions to a wide range of mathematical areas, including harmonic analysis, partial differential equations, and number theory. He is known for his deep insights and problem-solving skills.

Grigori Perelman: Perelman gained international fame for proving the Poincaré conjecture, a significant problem in topology. He was awarded the Fields Medal in 2006, although he declined the honor. Perelman's work had a profound impact on our understanding of three-dimensional manifolds.

Maryam Mirzakhani: Mirzakhani became the first woman to win the Fields Medal in 2014 for her contributions to the fields of geometry and dynamical systems, particularly in the study of moduli spaces of Riemann surfaces. Her innovative approaches and insights opened up new avenues in these areas.

Elon Lindenstrauss: Lindenstrauss is a mathematician known for his work in ergodic theory, a branch of mathematics that studies the behavior of dynamic systems. He was awarded the Fields Medal in 2010 for his groundbreaking results in this field.

Richard Taylor: Taylor is a mathematician who has made significant contributions to number theory, especially in the areas of modular forms and Galois representations. He received the Fields Medal in 1998 for his joint work with Andrew Wiles on the proof of Fermat's Last Theorem.

Jean Bourgain: Bourgain was a prolific mathematician who made fundamental contributions to various branches of mathematics, including harmonic analysis, partial differential equations, and number theory. His work has had a profound impact on these fields and has influenced numerous mathematicians.

Peter Scholze: Scholze is a mathematician who has made remarkable contributions to arithmetic geometry and the theory of perfectoid spaces. He received the Fields Medal in 2018 for his revolutionary work, which has opened up new perspectives in these areas.

Manjul Bhargava: Bhargava is a number theorist who has made significant contributions to the study of quadratic forms and higher-degree forms. He received the Fields Medal in 2014 for his groundbreaking discoveries in number theory and his development of new techniques.

Cédric Villani: Villani is a mathematician known for his work in partial differential equations, optimal transport, and mathematical physics. He received the Fields Medal in 2010 for his exceptional contributions to these fields and his ability to bridge mathematics and other disciplines.

Golden Ratio and Nature

    The golden ratio is a special number approximately equal to 1.618. It is often denoted by the Greek letter phi. The golden ratio has been found in many different places in nature, art, and architecture.

    One of the most famous examples of the golden ratio in architecture is the Great Pyramid of Giza. The ratio of the slant height of the pyramid to half the base dimension is 1.618, which is very close to the golden ratio. This suggests that the ancient Egyptians may have used the golden ratio in the design of the Great Pyramid.

     Another example of the golden ratio in architecture can be found in the Parthenon in Athens, Greece. The ratio of the length of the Parthenon to its width is 1.618, as is the ratio of the height of the Parthenon to the length of its front porch.

    The golden ratio has also been found in other ancient structures, such as the Temple of Solomon in Jerusalem and the Pyramids of Teotihuacan in Mexico.

     In modern architecture, the golden ratio has been used by architects such as Le Corbusier and Frank Lloyd Wright. Le Corbusier used the golden ratio in the design of his Villa Savoye, while Wright used it in the design of his Fallingwater house.

     The golden ratio is also found in many works of art, including paintings, sculptures, and music. Some of the most famous artists who have used the golden ratio in their work include Leonardo da Vinci, Michelangelo, and Johannes Vermeer.

     The golden ratio is a fascinating and mysterious number that has been found in many different places in the world. It is a reminder of the beauty and order that can be found in nature, art, and architecture.

Mathematics behind Google page ranking

              

                Google's PageRank algorithm is a mathematical formula that is used to rank web pages in search results. The algorithm is based on the idea that the more important and authoritative a web page is, the more other pages will link to it. Therefore, a page that has many other pages linking to it is more likely to be ranked higher in search results.

The PageRank algorithm is based on the following steps:

1) The web is represented as a graph, where each page is a node and each link between pages is an edge.

2) Each node is assigned a PageRank value, which is a measure of how important the page is.

3) The PageRank values are updated iteratively, until they converge to a stable state.

The PageRank value of a page is calculated using the following formula:

Code snippet

PR(A) = (1-d) + d * Σ PR(B) / outdegree(B)

Use code with caution. Learn more

where:

PR(A) is the PageRank of page A

d is a damping factor, which is a value between 0 and 1 that controls how much PageRank is transferred from one page to another

Σ PR(B) is the sum of the PageRank values of all pages that link to page A

outdegree(B) is the number of pages that link to page B

The damping factor is used to prevent PageRank from being transferred infinitely between pages. The default value of the damping factor is 0.85.

        The PageRank algorithm is a very effective way of ranking web pages. It is used by Google and other search engines to rank billions of web pages. The algorithm is also used in other applications, such as social media and recommender systems.

        The PageRank algorithm is a recursive algorithm, which means that it calls itself to calculate the PageRank values of all pages.

         The PageRank algorithm is a probabilistic algorithm, which means that it does not guarantee that the PageRank values will be accurate. However, the PageRank algorithm has been shown to be very effective in practice.

        The PageRank algorithm is a scalable algorithm, which means that it can be used to rank billions of web pages.

      The PageRank algorithm is a complex algorithm, but it is a very important part of Google's search engine. The algorithm is responsible for ranking billions of web pages, and it is a key factor in the success of Google.

      The more incoming links a page has from other pages, the higher its PageRank score.However, not all incoming links are equal. The algorithm assigns different weights to incoming links based on the PageRank scores of the pages that are linking to the given page.

       Pages with high PageRank scores pass on more "voting power" to the pages they link to than pages with low PageRank scores. The algorithm takes into account the number and quality of outbound links on a page. Pages with too many outbound links, or links to low-quality sites, may be penalized.

     The mathematics behind PageRank involves a matrix algebra approach. The algorithm uses a matrix of all the web pages on the internet, with columns representing the pages and rows representing the links between them. The matrix is then transformed into a Markov chain, where each web page is a state and the links between them are the transition probabilities. This Markov chain is then used to iteratively calculate the PageRank scores for each web page until convergence is reached.

          Overall, PageRank is a complex algorithm that involves advanced mathematics, but its basic principles are simple: incoming links to a page are considered "votes" of confidence for its content, and the more high-quality votes a page has, the higher its PageRank score and its position in Google's search results.

Data collection: Google Bard and Chatgpt 

Mathematical Psychology

         Mathematical psychology is a subfield of psychology that uses mathematical models and techniques to study various aspects of human behavior and cognition. This field is concerned with understanding how people perceive, learn, remember, and make decisions about the world around them, using mathematical and computational tools.

       The main goal of mathematical psychology is to develop quantitative models that can explain and predict human behavior. These models are typically based on statistical, computational, and mathematical principles, and they can be used to test hypotheses about cognitive processes, decision making, and other phenomena related to human behavior.

        Mathematical psychology is a subfield of psychology that uses mathematical and statistical methods to study human behavior. It is concerned with the development of mathematical models of psychological processes, such as learning, memory, and decision-making. Mathematical psychologists use these models to test hypotheses about the nature of these processes and to make predictions about how they will operate in different situations.

        Mathematical psychology has a long history, dating back to the early 20th century. Some of the earliest work in mathematical psychology was done by psychologists such as Gustav Fechner and Charles Spearman. Fechner developed methods for measuring sensation and perception, while Spearman developed factor analysis, a statistical technique for identifying underlying dimensions of human ability.

          In the second half of the 20th century, mathematical psychology saw a period of rapid growth. This was due in part to the development of new mathematical and statistical methods, such as game theory and computer simulation. These methods allowed mathematical psychologists to study more complex psychological processes and to make more realistic predictions about human behavior.

        Today, mathematical psychology is a thriving subfield of psychology. It is used in a wide range of research areas, including cognitive psychology, social psychology, and clinical psychology. Mathematical psychologists are working to develop new models of human behavior and to apply these models to real-world problems.

Some of the key topics in mathematical psychology include:

Psychophysics: the study of the relationship between physical stimuli and the sensations and perceptions they produce.

Learning and memory: the study of how people acquire, store, and retrieve information.

Decision making: the study of how people make choices and evaluate options.

Cognitive modeling: the development of mathematical models of cognitive processes such as attention, perception, and memory.

Mathematical psychology is an interdisciplinary field that draws on ideas from mathematics, statistics, computer science, neuroscience, and psychology. It has many practical applications, including the design of better learning and training methods, the optimization of decision-making processes, and the development of more effective therapies for psychological disorders.

Data collection: Google Bard and Chatgpt 

Scopus author id

 Scopus Author ID is a unique identifier assigned by Scopus, the largest abstract and citation database of peer-reviewed literature. The Scopus Author ID is a numerical value that distinguishes one author from another and allows researchers to keep track of their publications and citations.

To obtain a Scopus Author ID, you need to create a Scopus account and add your publications to your profile. Scopus will then automatically create a unique identifier for you based on your name and publication record.

Having a Scopus Author ID can be beneficial for researchers as it enables them to track their publications' citations, h-index, and other bibliometric indicators, as well as collaborate with other researchers in their field. It also helps to establish your academic identity and increases your visibility in the research community.

Importance of ORCID during Research

       ORCID (Open Researcher and Contributor ID) is a unique identifier that helps distinguish researchers from one another and connects them with their research activities and outputs. ORCID IDs can be used in various ways during research, including:

       Publication and grant applications: Including your ORCID ID on your manuscript submissions or grant proposals can help to ensure that your work is correctly attributed to you and that your research activity is tracked and recognized.

        Professional networking: ORCID can be used as a networking tool to connect with other researchers and collaborators who share similar research interests.

     Researcher profiles: Many academic and research organizations require or encourage the use of ORCID IDs in researcher profiles to help distinguish researchers from one another and ensure that their work is correctly attributed.

      Tracking research impact: ORCID IDs can help track the impact of your research by linking your research outputs, such as publications, datasets, and presentations, to your unique identifier.

      Overall, ORCID IDs can help streamline and simplify various aspects of the research process, from publication and grant applications to networking and research impact tracking.

Data collection: Google and Chatgpt 

Lie algebra

Lie algebra is a vector space equipped with a binary operation called the Lie bracket, which measures the failure of the operation to be commutative. Specifically, the Lie bracket of two elements in the vector space is another element in the vector space, and it satisfies certain axioms related to bilinearity, skew-symmetry, and the Jacobi identity.

Lie algebras are named after the Norwegian mathematician Sophus Lie, who first introduced them in the late 19th century as a way of studying the symmetry properties of differential equations. They have since found wide-ranging applications in various areas of mathematics and physics, including group theory, representation theory, geometry, topology, and quantum mechanics.

One of the key features of Lie algebras is that they provide a way of studying Lie groups, which are groups that are also smooth manifolds. The Lie algebra of a Lie group is a vector space that is closely related to the tangent space of the group at the identity element. This connection allows Lie algebras to be used to study the structure and representation theory of Lie groups.

Lie algebras also have important applications in physics, where they provide a framework for studying symmetries and conservation laws in physical systems. For example, the Lie algebra of the Poincaré group, which is the symmetry group of special relativity, gives rise to the concept of angular momentum in quantum mechanics.

Data collection : Google and Chatgpt

Notable Athletics, Comedian and Politicians who were mathematicians

Athletics who were mathematicians 

Archimedes: He was a renowned Greek mathematician, physicist, and engineer who is known for his contributions to mathematics, such as the discovery of the principle of buoyancy and the calculation of pi. He was also a skilled athlete and is said to have invented a type of pulley system to help him lift heavy objects during his workouts.

Hypatia: She was a Greek mathematician and philosopher who is considered one of the greatest mathematicians of all time. She was also a skilled athlete and was known for her physical strength and agility. Hypatia was also a champion in horseback riding and swimming.

Leonhard Euler: He was a Swiss mathematician and physicist who is regarded as one of the greatest mathematicians of all time. Euler was also a skilled athlete and was known for his love of ice skating, skiing, and fencing.

Galileo Galilei: He was an Italian mathematician, physicist, and astronomer who is considered the father of modern science. Galileo was also a skilled athlete and was known for his strength and agility. He was an excellent horseback rider, swimmer, and fencer.

Isaac Newton: He was an English mathematician and physicist who is known for his laws of motion and his theory of gravity. Newton was also a skilled athlete and was known for his strength and agility. He was an accomplished wrestler and was also known to practice fencing and swordsmanship.

Sofia Kovalevskaya: She was a Russian mathematician who made significant contributions to the study of partial differential equations and the theory of elasticity. Kovalevskaya was also an accomplished equestrian and was known for her skill in horseback riding.

John Wallis: He was an English mathematician who is known for his contributions to algebra and geometry. Wallis was also a skilled athlete and was known for his love of wrestling and tennis.

Michael Jordan: He is an American former professional basketball player who is considered one of the greatest athletes of all time. Jordan is also known for his love of mathematics and has been quoted saying that he would have been a mathematician if he hadn't pursued basketball.

Comedian who were mathematicians 

It's rare to find comedians who also happen to be mathematicians, but here are a few examples:

Matt Parker: He is a British comedian, author, and mathematician who uses his love of mathematics to create entertaining shows that mix comedy and mathematical concepts. He has written several books on mathematics and has also given TED talks on the subject.

Tom Lehrer: He is an American musician, songwriter, and mathematician who is known for his satirical songs and humorous take on mathematics. Many of his songs are full of clever mathematical puns and references.

Steve Mould: He is a British comedian, author, and science presenter who uses his background in physics and mathematics to create entertaining shows that mix humor and science. He has written several books on science and has also appeared on television programs such as "The One Show" and "Blue Peter".

Dara Ó Briain: He is an Irish comedian and television presenter who has a degree in mathematics and theoretical physics. He often uses his mathematical knowledge to add a unique perspective to his comedy shows and has been known to make jokes about topics such as game theory and probability.

Matt McCarthy: He is an American comedian and writer who has a degree in mathematics from Yale University. Although he doesn't often incorporate math into his comedy, his mathematical background has helped him develop a unique perspective on the world that he brings to his performances.

Here are some notable politicians who also had a background in mathematics:

Ada Yonath: She is an Israeli crystallographer and politician who won the Nobel Prize in Chemistry in 2009. She later became a member of the Israeli parliament, the Knesset, from 2013 to 2015.

Hua Luogeng: He was a Chinese mathematician who made significant contributions to number theory, and later became a prominent politician in the People's Republic of China. He served as the Vice President of the Chinese Academy of Sciences and was also a member of the National People's Congress.

Nicolas Bourbaki: Although not a real person, Bourbaki was a pseudonym used by a group of French mathematicians who collaborated on writing textbooks in the mid-20th century. One of the members, André Weil, later became involved in left-wing politics and was arrested during the Algerian War for his activism.

Wu Wenjun: He was a Chinese mathematician who made contributions to differential geometry and later became a member of the National People's Congress of China. He was also a member of the Chinese Academy of Sciences and was awarded the State Preeminent Science and Technology Award.

Kōichi Kita: He is a Japanese politician who has a Ph.D. in mathematics from the University of Tokyo. He has been a member of the House of Representatives of Japan since 2012 and has served as the Vice Minister of Education, Culture, Sports, Science and Technology since 2020.

Manfred Gerlach: He was an East German politician who was a member of the State Council of East Germany from 1981 to 1990. Gerlach was also a mathematician and taught at the University of Rostock before becoming involved in politics.

Collection: Google and Chatgpt 

Actuarial Mathematics

 

Actuarial mathematics is a branch of mathematics that applies mathematical and statistical methods to assess and manage risks in the insurance and financial industries. Actuaries use these techniques to evaluate the likelihood of events such as death, illness, and accidents, and to design insurance and pension plans that provide financial security to individuals and organizations.

     Actuarial mathematics involves the use of probability theory, statistics, and financial mathematics to model and analyze risk. Actuaries use these models to estimate the probability of certain events occurring, the cost of these events, and the potential impact on financial outcomes.

        Actuarial mathematics is an important field for the insurance and financial industries, as well as for government organizations that manage pensions and other benefits. Actuaries play a key role in designing and pricing insurance products, assessing the financial health of pension plans, and managing risks associated with investments.

       Actuarial mathematics requires a strong background in mathematics, including calculus, probability theory, and statistics. Many actuaries also pursue professional certification through organizations such as the Society of Actuaries or the Casualty Actuarial Society.

Data collection: Google and Chatgpt 

List of some beautiful movies and website related to mathematics

List of beautiful movies related to mathematics 

"The Man Who Knew Infinity" (2015) - This film is based on the life of Indian mathematician Srinivasa Ramanujan, who made significant contributions to number theory and mathematical analysis despite facing numerous challenges. The film explores Ramanujan's relationship with his mentor, G.H. Hardy, and his struggles as an outsider in the world of academia.

"A Beautiful Mind" (2001) - This award-winning film is a biographical drama based on the life of American mathematician John Nash, who made groundbreaking contributions to game theory. The film depicts Nash's life, his work, and his struggle with schizophrenia, while showcasing his genius in mathematics.

"The Theory of Everything" (2014) - This biographical drama portrays the life of renowned theoretical physicist Stephen Hawking, who made significant contributions to cosmology and mathematics. The film focuses on Hawking's personal life, his scientific work, and his relationship with his wife, Jane Wilde.

"Good Will Hunting" (1997) - This critically acclaimed drama tells the story of a young janitor at the Massachusetts Institute of Technology (MIT) who is a self-taught mathematical prodigy. The film follows his journey as he works with a therapist to confront his troubled past and unlock his full potential in mathematics.

"Proof" (2005) - This film is based on a Pulitzer Prize-winning play by David Auburn and revolves around the daughter of a brilliant mathematician who struggles with her own mathematical talents while dealing with the legacy and mental health issues of her late father. The film delves into the complexities of mathematical genius and its impact on relationships.

"The Imitation Game" (2014) - This historical drama portrays the life of British mathematician and computer scientist Alan Turing, who played a pivotal role in breaking the German Enigma code during World War II. The film explores Turing's work, his contributions to the development of computer science, and the challenges he faced due to his homosexuality.

"Fermat's Room" (2007) - This Spanish thriller film revolves around a group of mathematicians who are invited to a mysterious room to solve a mathematical puzzle. As they work together to crack the code, they are faced with a series of challenges that test their skills and unravel the secrets of the room.

"The Oxford Murders" (2008) - This mystery thriller is based on a novel by Guillermo Martinez and follows a young mathematician who becomes entangled in a series of murders that are seemingly connected by mathematical symbols and theories. The film delves into the world of mathematical intrigue and intellectual puzzles.

"Pi" (1998) - This psychological thriller tells the story of a paranoid mathematician who believes that everything in the world can be understood through numbers. As he becomes increasingly obsessed with his work, he descends into a spiral of madness and paranoia.

"Donald in Mathmagic Land" (1959) - This animated short film by Disney combines live-action and animation to explore the world of mathematics in a fun and educational way. The film introduces various mathematical concepts and their applications in the real world through an engaging storyline featuring Disney character.

List of beautiful websites related to mathematics 

MathWorld (https://mathworld.wolfram.com/) - This comprehensive online encyclopedia of mathematics is maintained by Wolfram Research and provides a wealth of mathematical information, including definitions, theorems, formulas, and interactive demonstrations.

The Math Forum (http://mathforum.org/) - This website, operated by Drexel University, serves as an online community for math educators, students, and enthusiasts. It offers a variety of resources, such as math problems, lesson plans, discussions, and math-related news.

Numberphile (https://www.numberphile.com/) - This popular YouTube channel and website explores the beauty and wonders of mathematics through engaging videos. It covers a wide range of topics, from number theory to geometry, and features interviews with mathematicians and demonstrations of mathematical concepts.

The MacTutor History of Mathematics Archive (http://www-history.mcs.st-andrews.ac.uk/) - This extensive online archive, hosted by the University of St. Andrews, provides a comprehensive history of mathematics and profiles of famous mathematicians throughout history. It also includes articles, biographies, and mathematical resources.

Wolfram Alpha (https://www.wolframalpha.com/) - This powerful computational knowledge engine allows users to input mathematical queries and provides detailed solutions, visualizations, and explanations for a wide range of mathematical topics, from basic arithmetic to advanced calculus and beyond.

Cut-the-Knot (https://www.cut-the-knot.org/) - This website, created by mathematician Alexander Bogomolny, offers a collection of interactive puzzles, games, and educational materials related to various branches of mathematics, including geometry, algebra, and number theory.

MathOverflow (https://mathoverflow.net/) - This online community is a platform for professional mathematicians to discuss research-level mathematics and exchange ideas. It features questions and answers on various mathematical topics, along with discussions on research, conferences, and career advice.

The Math Page (https://www.themathpage.com/) - This website offers a comprehensive online math curriculum for learners of all levels, from basic arithmetic to advanced calculus. It includes free lessons, tutorials, practice problems, and interactive exercises, making it a valuable resource for self-paced math learning.

The American Mathematical Society (https://www.ams.org/) - This website serves as the official website of the American Mathematical Society (AMS) and provides a wealth of resources for mathematicians, educators, and students. It includes journals, publications, conferences, awards, and other information related to the field of mathematics.

The National Council of Teachers of Mathematics (https://www.nctm.org/) - This website is the official site of the National Council of Teachers of Mathematics (NCTM) and offers resources for math teachers, including lesson plans, standards, research articles, professional development opportunities, and more.

Data collection: Google and Chatgpt 

Ramanujan hypothesis

    The Ramanujan hypothesis is a conjecture in mathematics that relates to the distribution of prime numbers. It was proposed by the Indian mathematician Srinivasa Ramanujan in the early 20th century.

      The hypothesis states that the number of prime numbers less than a given number N is approximately equal to the logarithm of N divided by the difference between the logarithm of N and 1. This can be expressed mathematically as:

π(N) ≈ (log N)/(log N - 1),

    where π(N) denotes the number of prime numbers less than or equal to N.

          The Ramanujan hypothesis is closely related to the famous Riemann hypothesis, which is considered one of the most important unsolved problems in mathematics. The Riemann hypothesis provides a more precise statement about the distribution of prime numbers, and its proof would also imply the truth of the Ramanujan hypothesis.

        Despite much effort by mathematicians, the Ramanujan hypothesis remains unproven. However, it is widely believed to be true, and many results have been established that support its validity.

Data collection: Google and Chatgpt 

Controversy between Newton and Leibnitz

       The controversy between Newton and Leibnitz was centered around the invention of calculus. Both Newton and Leibnitz independently developed methods of calculus, which is a branch of mathematics that deals with rates of change and accumulation. However, there was disagreement between the two regarding who had truly invented calculus first.

      Newton claimed that he had developed the principles of calculus in the 1660s and 1670s, while he was still a student at Cambridge University. However, he did not publish his work until the 1690s. Leibnitz, on the other hand, began working on calculus in the 1670s and published his findings in 1684.

        The controversy began in the early 18th century when Newton accused Leibnitz of plagiarizing his work. Newton argued that Leibniz had copied his ideas and methods of calculus without giving him proper credit. Leibniz, however, claimed that he had developed his own independent approach to calculus and had not copied Newton's work.

     The dispute between Newton and Leibniz continued for several years and involved a number of other mathematicians and philosophers. Eventually, the Royal Society of London, of which Newton was a member, concluded that Newton had priority in the invention of calculus, but Leibnitz's methods were still considered legitimate and useful.

       Today, both Newton and Leibniz are credited with the invention of calculus, and their work has had a profound impact on mathematics and science.

Data collection - Google and Chatgpt 

Fractional share market

             A fractional share market is a type of financial market where investors can purchase a fraction of a single share of a stock or exchange-traded fund (ETF). Fractional shares allow investors to own a portion of a stock or ETF that they may not be able to afford to purchase a whole share of.

          Fractional share investing has become increasingly popular in recent years, particularly with the rise of online investment platforms that offer fractional shares. These platforms allow investors to purchase small amounts of stock or ETFs, often with no minimum investment amount.

           Fractional share investing can be particularly useful for beginners who may not have a lot of money to invest but want to get started in the stock market. It can also be useful for investors who want to diversify their portfolio without having to purchase large amounts of different stocks or ETFs.

          Some of the benefits of fractional share investing include lower transaction fees, the ability to invest in expensive stocks or ETFs that may be out of reach otherwise, and the ability to easily diversify a portfolio. However, it's important to keep in mind that fractional share investing does not come without risks, and investors should always do their own research and consider their individual financial situation before investing.

Data collection: Google and Chatgpt