Monthly Archives: November 2014

Thanking the Prince of Mathematics: Carl Friedrich Gauss

Standard

This post first appeared on Function Space.

Carl Gauss a prodigy mathematician born to a poor, working class parents in Brauschweig, Germany surprised his elementary school teacher by adding all the integers from 1 to 100 simply by observing that the sum of 50 pairs of numbers is 101. The story goes that he had figured that 100 numbers could be determined by the equation n(a+b)(1/2)=50(a+b) where n=100, a = the first digit in the sequence and b = the last digit in the sequence.

His mathematical talent befuddled his teachers and mentors such that he grew up to become an influential mathematician of his century.
Gauss’s wide range of discoveries, from his fundamental theorem of algebra to his ground breaking work in number theory has shaped the field to the present day.

The true genius of his work, experts think is how he ultimately took these theories and applied them to in many fields, including number theory, statistics, analysis, differential geometry, electrostatics, astronomy and optics.

He once wrote, “All the measurements in the world are not worth one theorem by which the science of eternal truth is genuinely advanced.” It was at the same time he took up the job of geodesic survey mapping irregularly shaped curved surfaces across the country. Although, he failed to produce an accurate map of Hannover, he succeeded in creating a number of important advances in mathematics of curved surfaces, development of curvilinear coordinates and established ideas on non Euclidean geometry.

To which Einstein later wrote, “If Gauss had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. The importance of Gauss for the development of modern physical theory and especially for the mathematical fundamentals of the theory of relativity is overwhelming indeed.”

Gauss’s list of discoveries extends to modular arithmetic, prime numbers, number theory, squares, quadratic reciprocity etc. But it was more astonishing that he worked on these discoveries independently without any collaborators or co workers!

This Thanksgiving lets be grateful to the man who overcame all the difficulties while pursuing mathematics and continued to discover more and more fundamentals that shaped the field to what it is today!

Happy Thanksgiving!

gauss-infographic

Click here to enlarge the above infographic.

It’s Einstein’s world that we live in.

Standard

This post first appeared on Function Space.

Thanksgiving is just around the corner, meaning it’s time to start thinking about things and people you are grateful to. It’s time to sit and celebrate the day of gratitude with Turkey on the table, Tofurkey for vegetarians!

If you are still wondering whom to thank this Thanksgiving Day, here is a food for your thought that will certainly imbibe you with gratitude towards this great man who started it all.

Albert Einstein, one of the greatest scientists in a century dominated by science. The man who made the milestones of the era – bomb, quantum physics, big bang etc.

Without realizing we encounter Albert Einstein in different fields of everyday life. For example, our cars navigate through traffic using GPS, we make purchases in supermarket through a scanner and we use digital cameras to capture memories. Einstein did not make these discoveries, nor did he write any papers stating the practical applications of his theories. But his abstract thoughts on time, light and space time led us to the innovations that seem to be normal today.

Most of us know Einstein either associated with the atom bomb or with his famous equation E=mc^2. But did you know that in 1905, he was the first person to prove the physical existence of atoms. And the mass of atoms contains enormous energy. This theory was indeed an indirect basis of the atomic revolution.

His theories had direct influence on inventions like television, digital camera etc. Thanks to his Special Theory of Relativity that we are able to broadcast sharp images and capture memories today. Electrons inside the television are accelerated and according to the theory of relativity, the mass is increased measurably. If this phenomenon of increasing mass was not taken into consideration electrons would have never exhibited divergence in millimeter range, resulting into blur images.

While all technologies that employ laser beams are based on Einstein’s theories, he was the first to recognize the principle of monochrome and the concept of bundled laser light. All the devices that work on the Global Positioning System or Satellite assisted positioning system are inspired from Einstein’s ideas.

Pieces of equipment which can relay their position with an accuracy of less than 30 meters divergence take into account the effects of relativity on time measurement by atomic clocks when these circle the earth at great speed in satellites.

Even 50 years after his death, his invention and theories have huge influence on our technologies. Where physicists have now begun dreaming of quantum computers, Einstein revolutionized it in 1935 when he discovered that particles can be in different states at the same time. This is the same observation that paved a way for an altogether new area of development called as quantum computers that certainly has revolutionized the 21st century!

He was the embodiment of pure intellect, the bumbling professor with the German accent, a comic cliched shaggy-hairstyle. Let us thank him for the unfathomably profound genius among geniuses who discovered, merely by thinking about it, that the universe was not as it seemed.

Thank you Einstein!

Einstein (1)