If mathematics is an exact science, why are there assumptions?
The term exact science was in popular use a century ago but isn't very commonly used anymore. It was used to describe those branches of knowledge which had precise mathematical formulas, and it included mathematics, physics, and chemistry. It excluded sciences where the analysis and predictions were probabilistic rather than deterministic. Exact science referred to the theoretical aspects of knowledge rather than the experimental aspects. Anyone who has ever done an experiment in physics knows that the results are anything but precise. In all theoretical knowledge there are assumptions to the theory. The importance and validity of the theory depends on its predictions and how well those predictions correlate to actual observations.We could still use the term exact science, and if we did, we would apply it to parts of many other branches of knowledge than those mentioned above. It's not a good idea, however, to hold on to the distinction between exact and inexact sciences since a probabilistic model can often be a better model than a deterministic one. The advances in probability, statistics, and computer science during the 20th century make probabilistic models ideal for the the investigation of many questions, including those in physics.
Is mathematics a science?
Science is about empericism: and observation and hypothesis. Science is known through the senses. Math is not--it is pure logic. The founding philosophy is completely different. Math uses formal proof and definitions, which is entirely different. No, math is not a science. Math is actually more a language than anything else: a completely formalized quantitative language with rigorous dynamics. Science is a method more than anything else, and it is a method not used in mathematics. Edit: to the extent that mathematics is a tool, I'd say that there are two different types of mathematicians. Those in formal mathematics are seeking ways to refine the usage of mathematics as a tool, and to get greater effeciency in applied mathematics by proving formulas, etc. These people are to an extent more like engineers, as they are engineering the tool for optimum efficacy. Applied mathematicians (eg those who do not create new theories in mathematics, but rather use mathematics to solve real problems, where the numbers refer to something real rather than mere abstractions) are more like technicians. The use a complicated and sophisticated tool and apply it to things beyond math itself. When you look at the history of complex numbers, the term "imaginary" was first applied as a derogatory word. However, further refinement of complex dynamics gave a useful new application of complex numbers, and the idea was incorporated into proper mathematics. No one "observed" imaginary numbers, they just found them useful. As for the logician, I'd regard that as a subset of mathematicians as a whole. I think that the early language of logic was much more close to verbal language, and the likeness is easier for us to manage. But ultimately, what is math? It is a formalized set of conventions, definitions and dynamics that serve as a tool for conveying meaning from one person to the next by using an abstraction. It is a tool in that it is useful, but it remains entirely incorporeal. So what other word is there for such a thing than "language?" Certainly, it doesn't fit our traditional notions of language, nor does it fit our traditional idea of a tool. But in that it consists of generalities that can be made to apply to particulars in order to convey meaning, it is very much like a language.
Is mathematics a science?
Many others will answer this question by referring to the various definitions and associations that come with the word 'science'. However, these are not even consistent between languages as Engslish, German, Swedish, Japanese, Mandarin, all have words for Science that are not 1:1 matches.So, like it is with many other questions here on Quora, one first has to look at the question itself. How would it help us to know if Math is Science? Does it improve Math, or Science? Is it good for practitioners, for learners snd society? Clearly mathematicians are faculty members at most Science faculties, so in that sense they are scientists. If Math would be seen as something that assists Science, then mathematicians would be degraded to assistants. No good. So, while the test/verify/measure/model paradigms in Science quite don't apply to Math, I prefer thinking of Maths as a part of Science for mentioned reasons.Now over to a different aspect of this, not so very often discussed. Math cannot be represented without a real world manifestation. Many think that Maths can exist all by itself, but I can't even imagine such a concept. Math requires neural states in our brains, pen and paper, cradles and blackboards, electromagnetic states in computers and programs, Ink and books. Science is about describing these things. With the use of Mathematics...So, in a rather practical way, there is an inevetable connection between Science and Maths. I'm quite sure this particular connection will be quite central in Science in the coming century.
Why is mathematics not considered a part of science?
I think mathematics is definitely a science. It has all the rigor that a regular scientific field (such as physics, biology, or chemistry, all of whom are dependent on math) has. Before science was started, there was math. The Babylonians were the first ones to come up with many mathematical formulas, and the Greeks continued their tradition. In this mathematical tradition, there was a Scientific Method character to it. The only difference between math and the natural sciences is that the evidence in math is often found in proof, and not in something tangible. However, that doesn't mean that math is not applicable. Far from it. Math is very related to the real world and we can explain many laws in nature because of math. Also, a lot of mathematicians' discoveries were very similar and applicable to natural science discoveries.
Is mathematics a science or a language?
So many misunderstandings of the word “science”. Move to the wiktionary entry on science, and you will see the following two subentries:A particular discipline or branch of learning, especially one dealing with measurable or systematic principles rather than intuition or natural ability.4. The collective discipline of study or learning acquired through the scientific method; the sum of knowledge gained from such methods and discipline.This is why we have the 3 types of science:Formal sciences - which study logic and anything that can be provenPhysical sciences - which uses empiricism and the scientific method to study physical phenomenaSocial sciences - which uses empiricism to study tendencies of holistic phenomenaMathematics falls into the first category: formal science. It is a formal science in the sense that it is a particular discipline or branch of learning, of systematic principles instead of intuition or natural ability.Now, onto the language argument. Mathematics is not a language. However, mathematicians create notation that is a language. There is a mathematical language, but the language alone is not mathematics. The rub is that it can also change from person to person, so translation is usually used, in some natural language, in order to express what is intended by the symbolic language in the text.PS. I wanted to add that not only does it change from person-to-person, sometimes it changes from paragraph to another. Again, the person making the definitions usually refers to some definition when expressing the relationship in shorthand (i.e. the symbols everything thinks is a language).Further edit:If you program in ANY WAY, this matches what programmers call scope. Sometimes we make definitions that will only be used in the next line. Sometimes we make definitions that will be used throughout a class (this is similar to definitions used throughout a section). Sometimes we make definitions that will be used throughout the program (this corresponds to a definition used throughout a paper). Sometimes we reuse previous libraries (this corresponds to referencing other papers for our notation).As you can tell, you are creating a language using this. However, it’s not a natural language, it’s more akin to a computer programming language.
Why is mathematics so important to science?
Mathematics is a useful tool to simplify science by quantification of phenomena. In fact science without mathematics can go no further than a humorous oxymoron. You just cannot do physics and chemistry without calculus (Schrodinger equation) and statistics (Boltzmann distribution), biology without statistics (neurosciences, DNA computing), electronics without complex numbers.Mathematics was actually born from science everywhere in the world from the Indus Valley to Greece. Imagine analyzing something as basic as going from point A to B - you need to do the math to figure out the time required. No wonder why our ancestors developed geometry and trigonometry just to use this knowledge to understand and exploit phenomena. Look at the architecture of the Konark temple or the Pyramid of Giza to know the mathematical intricacies involved. No wonder why most fields in mathematics - algebra, coordinate geometry, complex numbers, vector algebra, statistics - developed during the scientific revolution (1600s-1800s). No wonder why Newton added that huge 'chapter' in high school mathematics called calculus trying to understand the world around him and still the mathematical model for his physical problem is unsolvable by basic calculus. Even today most scientific principles lie underdeveloped because of the complexity of the mathematical model. This is fairly suggestive of the significance that mathematics holds in science.
What is mathematics not?
The thing that mathematics is not is the literature of mathematics.Mathematics comes from mathematikos — love of knowledge.In the tradition of Greek philosophy, mathematics was considered Natural Philosophy — a priori knowledge. A way of reading The Book of Nature rather than remembering literatures.It is used in the tradition of educating philsophers called The Liberal Arts as a means of training the memory and teaching critical thinking.The basic definition of mathematics was thought and memory until scholasticism emerges as an academic tradition after the 12th century.The scholastic tradition is the History of Mathematics. The literature of Mathematics.The idea that there is a finite canon of mathematics that can be treated as literature comes from Scholasticism.Mathematicians have never believed this and finally, in the 20th century, results by Godel, Turing and Church prove that mathematics is not finite. Or it is inconsistent.This sort of left people in Traditional Mathematics holding the bag supporting the Sciences and Primary and Secondary Education, while Physics Departments hit a plateau using a mathematical style developed by Euler in the late 1700s.Mathematics and mathematical education are simply never something that can be standardized. Standards are basically meant for engineering and commerce.Today only about 20% of mathematics is taught in the Traditional Mathematics departments at Universities. In fact, when you are looking at combinatorics, or other branches of 20th century mathematics, most of it is taught in the Computer Science department.Computer Science was developed as a branch of modern mathematics and this seems to have been forgotten by many other departments at the University.Mathematics is also taught in Engineering, Operations Research, Statistics, Theoretical Computer Science, Mathematical Linguistics, Education, Information Theory, Communication Theory, Economics, Sociology, Cognitive Psychology and the divisions of Philosophy associated with logic, semantics, semiotics and information.Learning the literature of mathematics is exactly the same as memorizing the digits of Pi.I personally am an advocate of a return to Natural Philosophy as the model for mathematics because it is based on human memory and critical thinking.In specific, I advocate the formalization of Theoretical Mathematics as a branch of Natural Philosophy that covers all uses of mathematics in engineering and the academy.
Why I am good at math but not at science?
there are a number of different reasons you would be good at one, but not very good at the other. personally, i'm the exact opposite- i'm very good at science, but not very good at math. in my opinion, anatomy and math are two very different things that don't cross paths at all. some people just have a "math brain" where math and quantitative reasoning comes easily to them, and english, for example, or science is difficult, just because they're very different. (like how some people (myself included) are better at geometry and spatial reasoning and not very good at algebra.) some things you can do: - talk to your teacher- it can't hurt you, it can only help you. ask him/her what you can do to either better prepare for tests or quizzes, or learn how to calm down during them. -study more on your own-- instead of reading the chapter once, read it twice and make sure you understand. -if you are only having trouble with multiple choice (which is what i think of when you say multiple test- if it's not the same thing, ignore this), eliminate answers you are POSITIVE the answer is not. and then with the choices you have left, pick the best answer. hope this helps!
Why is mathematics so hard?
First, because it is cumulative. Everything builds on what came before. So, if you fail to learn/understand one piece, then it is almost impossible to make sense of later parts of mathematics that depend on that piece.Second, it is taught poorly, especially in early grades. People who become elementary school teachers often (know that they) don't really understand mathematics, and think it is less important for them to fully understand mathematics. Combining this with the first point, you can see why many people will, at some point, find mathematics to be hardThird, over time, math textbooks get worse. To convince yourself of this, go find a copy of Courant’s 1937 book on calculus. In my opinion, this is the best calculus book ever written. It explains all of the key ideas and illustrates them with real applications. It teaches people how to solve hard problems. The “new math” of the 1960's replaced this approach with an emphasis on abstract theory (possibly inspired by the efforts of Bourbaki to do the same thing to math at the highest level of cutting edge research). This might have been appropriate for the miniscule fraction of people who would go on to become professional mathematicians. But it was a disaster for most students. The over-reaction was to remove most of the theoretical aspects, and replace them with … effectively nothing. This resulted in textbooks without adequate theory and without real applications. Instead, students got (and still get) drill-and-kill based on pattern recognition rather than understanding. And they got obviously artificial problems like “the melting snowman walking past the lamppost” that encouraged students to believe that calculus had nothing useful to offer.