Researchers find optimal way to pay off student loans

After graduating or leaving college, many students face a difficult choice: Try to pay off their student loans as fast as possible to save on interest, or enroll in an income-based repayment plan, which offers affordable ...

Yeast mating—more than meets the eye

Researchers from the Max-Planck Institute for Terrestrial Microbiology have discovered a surprising asymmetry in the mating behavior of unicellular yeast that emerges solely from molecular differences in pheromone signaling. ...

How stem cells synchronize to repair the spinal cord in axolotls

The spinal cord is an important component of our central nervous system: it connects the brain with the rest of the body and plays a crucial part in coordinating our sensations with our actions. Falls, violence, disease—various ...

Predicting the evolution of a pandemic

The inclusion of biological uncertainty and the latest case data can significantly improve the prediction accuracy of standard epidemiological models of virus transmission, new research led by KAUST and the Kuwait College ...

From symmetry to asymmetry: The two sides of life

On the outside, animals often appear bilaterally symmetrical with mirror-image left and right features. However, this balance is not always reflected internally, as several organs such as the lungs and intestines are left-right ...

Eco-friendly technology to produce energy from textile waste

A team of scientists from Kaunas University of Technology and Lithuanian Energy Institute proposed a method to convert lint-microfibers found in clothes dryers into energy. They not only constructed a pilot pyrolysis plant ...

Modeling the friction between pages in a book

It all started with a shaky washing machine. Pedro Reis, head of the Flexible Structures Laboratory at EPFL's School of Engineering, rolled up a piece of fabric and placed it under the machine to stop it from moving. After ...

How cells measure themselves

Ever since scientists discovered cells under the microscope more than 350 years ago, they have noted that each type of cell has a characteristic size. From tiny bacteria to inches-long neurons, size matters for how cells ...

Liquid water on exomoons of free-floating planets

The moons of planets that have no parent star can possess an atmosphere and retain liquid water. Astrophysicists at LMU have calculated that such systems could harbor sufficient water to make life possible—and sustain it.

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Mathematics

Mathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

There is debate over whether mathematical objects such as numbers and points really exist or whether they are manmade. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records go (see: History of Mathematics). Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, in fitful bursts, until the Renaissance, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.

Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.

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