Why Archimedes is the Father of Mathematics

Archimedes of Syracuse, a Greek mathematician, physicist, engineer, inventor, and astronomer, is often hailed as the Father of Mathematics. His groundbreaking contributions to mathematics and science have left an indelible mark on these fields, shaping the course of history and influencing countless generations of scholars. This blog delves into Archimedes’ life, his significant contributions, inventions, and lasting legacy, exploring why he holds the esteemed title of the Father of Mathematics.

Early Life and Education

Archimedes was born around 287 BC in the ancient city of Syracuse on the island of Sicily. His early education was influenced by his father, Phidias, who was an astronomer. Archimedes’ thirst for knowledge led him to study in Alexandria, Egypt, one of the ancient world’s great centers of learning. There, he was exposed to the works of Euclid and other prominent mathematicians, which profoundly shaped his thinking and future work.

Major Contributions to Mathematics

Archimedes made numerous contributions to mathematics that are still influential today. Here are some of his most notable achievements:

Calculation of Pi

Archimedes was the first to calculate an accurate approximation of Pi (π). Using a method involving inscribed and circumscribed polygons, he determined that Pi lies between 3 1/7 (approximately 3.1429) and 3 10/71 (approximately 3.1408). This method was revolutionary and set the foundation for future calculations of Pi.

Archimedes’ Principle

One of his most famous contributions is Archimedes’ Principle, which states that a body immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by the body. This principle is fundamental to the field of fluid mechanics and has numerous practical applications, from shipbuilding to measuring the density of objects.

Work on Levers and Pulleys

Archimedes is also renowned for his work on the mechanics of levers and pulleys. He famously stated, “Give me a place to stand, and I shall move the Earth,” illustrating the power of leverage. His studies laid the groundwork for the principles of mechanical advantage, crucial for the development of engineering and machinery.

Development of Calculus Concepts

Long before the formal development of calculus, Archimedes used methods resembling integral calculus to find areas, volumes, and surface areas of various geometrical shapes. His work on the quadrature of the parabola and the volume of a sphere segment showcased his advanced understanding of these concepts.

Contributions to Geometry and Volume Calculations

Archimedes made significant contributions to geometry, particularly in calculating the areas and volumes of shapes. He derived formulas for the surface area and volume of a sphere and a cylinder, demonstrating a profound understanding of spatial mathematics.

Inventions and Discoveries

Archimedes was not just a mathematician; he was also an ingenious inventor whose creations have had lasting impacts.

Archimedean Screw

One of his most famous inventions is the Archimedean screw, a device for raising water. This screw-shaped device could lift water efficiently and was used for irrigation and draining fields. It is still in use today in various forms.

War Machines and Defenses

Archimedes applied his mathematical prowess to design war machines to defend Syracuse from Roman invasion. These included catapults, the Claw of Archimedes (a crane-like device that could lift and capsize enemy ships), and possibly a giant mirror to focus sunlight and set ships on fire.

Innovations in Engineering

Archimedes’ innovations in engineering extended beyond military applications. He developed compound pulleys to lift heavy objects with minimal effort, showcasing his deep understanding of mechanical principles.

Impact on Future Generations

Archimedes’ influence extends far beyond his lifetime, impacting numerous mathematicians, scientists, and engineers.

Influence on Later Mathematicians and Scientists: Archimedes’ work laid the groundwork for later mathematicians such as Isaac Newton and Gottfried Wilhelm Leibniz, who developed calculus. His methods and principles continue to be foundational in mathematics and physics.

Legacy in Modern Mathematics and Science: The principles and theories formulated by Archimedes are still taught in modern mathematics and physics curricula. His work on geometry, calculus concepts, and fluid mechanics remains relevant and influential.

Archimedes’ Writings and Their Preservation: Many of Archimedes’ works were preserved through the efforts of later scholars. Manuscripts like “The Method of Mechanical Theorems” and “On Floating Bodies” were copied and studied by scholars throughout the centuries, ensuring that his contributions were not lost to history.

Archimedes’ Famous Works

On the Sphere and Cylinder

In this work, Archimedes proved that the surface area of a sphere is equal to four times the area of its greatest circle and that the volume of a sphere is two-thirds the volume of the smallest cylinder that can contain it. These findings were revolutionary and remain fundamental to the study of geometry.

The Method of Mechanical Theorems

This manuscript revealed Archimedes’ process of discovery, where he used mechanical means to arrive at mathematical truths. It provided insight into his use of infinitesimals, a precursor to integral calculus, to determine areas and volumes.

On Floating Bodies

This treatise includes the principle now known as Archimedes’ Principle, which explains the buoyancy of objects in a fluid. It laid the foundation for hydrostatics and has numerous practical applications in engineering and science.

Archimedes’ Legacy in Modern Mathematics

How His Work is Used Today: Archimedes’ principles are foundational in various fields of modern science and engineering. His methods for calculating areas and volumes are used in integral calculus, and his work on levers and pulleys informs mechanical engineering.

Examples of Archimedean Principles in Contemporary Science: The Archimedean screw is still used in water management and agricultural irrigation. Archimedes’ Principle is applied in designing ships and submarines to ensure they float correctly. His work on levers is fundamental in the design of various tools and machines.


Archimedes’ contributions to mathematics and science have earned him the title of the Father of Mathematics. His innovative methods, profound discoveries, and enduring inventions have left a legacy that continues to influence modern science and mathematics. By bridging the gap between theoretical concepts and practical applications, Archimedes set the stage for future advancements and remains a towering figure in the history of mathematics.

FAQs (Frequently Asked Questions)

What are Archimedes’ most significant contributions to mathematics?

Archimedes’ most significant contributions include the calculation of Pi, the formulation of Archimedes’ Principle, his work on levers and pulleys, early concepts of calculus, and his advancements in geometry and volume calculations.

How did Archimedes calculate the value of Pi?

Archimedes calculated the value of Pi using a method involving inscribed and circumscribed polygons, approximating Pi to lie between 3 1/7 and 3 10/71.

What is the Archimedean screw and how does it work?

The Archimedean screw is a device used to raise water efficiently. It consists of a screw inside a hollow pipe, which, when rotated, lifts water from a lower level to a higher one.

How has Archimedes influenced modern mathematics and science?

Archimedes’ work laid the groundwork for many modern mathematical and scientific principles. His methods influenced the development of calculus, his principles are foundational in mechanics and hydrostatics, and his inventions continue to be used in various applications.

What are some famous works written by Archimedes?

Some of Archimedes’ famous works include “On the Sphere and Cylinder,” “The Method of Mechanical Theorems,” and “On Floating Bodies.”



    What is 1 + 3 ?


    PNC Cognitio School, in its full capacity as a K-12 Cambridge International School also serves as an exam center for private candidates from India and around the globe. We offer a wide-range of subject choices from IGCSE, O Level and International AS/A Level to our private candidates. We cater to them through all three available series for Cambridge examinations: March, June and November making it altogether easier for students to easily manage their exam routines.

    PNC Cognitio School in its sole aim to provide an illuminated pathway for students to reach universities worldwide is an official PSAT, SAT and Advanced Placement Test Centre (#: 63838) in association with the College Board, US. 

    We currently offer all the exam series for SAT, PSAT and AP as offered by the College Board allowing students to seamlessly attempt exams at their own comfortable time and apply to universities with ease. From 2023, students will benefit from digital SAT with better exam experiences and faster results all aided by the advanced systems right here at PNC Cognitio.

    With all of the facilities available at PNC Cognitio School, we strive to be a comprehensive package to students, handing over their most powerful passport to quality education around the globe without any hassle in accessibility. 

    New Grade Familiarization Week

    Any new beginning requires mental preparedness , readiness and handling new information by the mind. Kids are no exception to this as they more dependent on parents to assist them in their decisions and actions. With the kids, it is pivotal to make them feel at home to help them ease in to the new surroundings. New Grade Familiarization week is an important stride towards this aspect. This new initiative started with the academic year 2019 -20. These five days are carefully planned and power packed with academic and co-curricular activities to help children start their new academic year on a high note.

    The onboarding process is designed in benefit of new to children build their understanding between newly found friends and teachers. All of them get to know the school culture and get familiar with their environment. Such a program with a caring vision ensures they step into their actual academic periods totally prepared and excited to begin the year long journey. All Grade students were able to start their learning pathway by bonding with teachers and getting valuable insights into their learning objectives for the new academic year. Grade 9 Students for example were able to lay hands on various tools and designs relevant to design and Implementation. It was such an endearing and pleasant sight to watch all young learners get used to the campus and enjoy the program.

    PNC School Culture and values imbibe children with immense moral insights and the program is just providing them a taste of what they are going to experience yearlong within the campus along with their mentors.

    After School Programs

    PNC’s spacious school, a community learning resource, will continue to offer a rich selection of extracurricular activities designed to enhance students’ all-around development. This array of activities is offered during the week and on the weekend. The school strives to earn an excellent State, National, and International reputation for its inter-school sports activities and tournaments.

    Regular sports activities include Swimming, Cricket, Basketball, Skating, Football and more.

    Support classes in a variety of subject areas will also be a key feature of after-school activities to ensure that any student who requires additional guidance will be able to obtain it. Upcoming activities such as Drama, Arts, Environmental Club, and Music Club will be the new features of the after-school programme. A full range of other accredited skills-based courses designed to develop various future skills will be rolled out as part of the “Skills of the Future Cognition”  development plan, which could include Leadership, ICT, Entrepreneurship, Communication, Gen X Skills, and many more.

    Applying learning and developing professional skills are key to our young people’s successful futures.

    Child's Learning Partners

    Education Professionals – Our highly qualified and motivated teachers have been carefully selected for their teaching excellence and ability to actively engage students in the learning process. We implement an ongoing programme of workshops and professional development sessions, often conducted by noted educationists in around the world, to ensure that our teachers are up to date with the latest developments in educational techniques and methods.

    The Senior Leadership Team and a team of Subject Leaders are well experienced and are complemented by professional teachers to meet the needs of our student population.

    Partnership with Parents – Parents play an important role in the learning journey of the child at school. At PNC we provide varied platforms for parents to interact with the students thus giving them the real time application of the subjects. Through a regular communication system – written and data reports, SMS, email, and a programme of consultation evenings – parents are regularly updated on the progress of their children and activities in the school. Parents are welcome to discuss their children’s individual progress with the concerned teacher or school Principal or any member of the Senior Leadership Team at a mutually convenient time.

    Parent Voice including a monthly forum with the Principal is conducted regularly. These meetings provide an opportunity for all our parents to voice any concerns, suggestions, or ideas they may have.

    Child Health & Safety

    The health and safety support network is made up of people such as extended family, friends, and community members who will work together in sync with the school to develop and maintain a plan that will ensure long-term safety, belonging, and well-being of our Children. A healthy mind and a healthy body are inseparable, binding upon each other for a productive life.

    The purpose of the School Safety and Health Program are:

    1. To promote a healthy lifestyle among students, by providing them with knowledge and skills that will enable them to take responsible decisions to protect their health and well-being.
    2. To build healthy eating habits through the Wholesome Healthy Lunch – The power of 5 food groups.
    3. To enhance the role of students in contributing actively and positively to the national health situation by following various initiatives at this level like – “Swach”.
    4. To ensure that School Health becomes and continues to be an integral part of the overall education program in all schools.
    5. Ensure health and well-being is a key learning area and healthy practices are key competencies to be instilled as part of our curriculum.
    6. The school has developed a safe, inclusive, and supportive environment that involves and communicates with children, young people and their parents/guardians.
    7. We encourage child and parent/guardians involvement and engagement that informs safe school operations and builds the capability of children and parents/guardians to understand their rights and responsibilities.

    Cambridge Pathway School

    Cambridge Primary starts learners on an exciting educational journey. Typically for 5 to 11-year-olds, it develops young learners who are confident, responsible, reflective, innovative, and engaged and includes an assessment that proves and improves learning. Students in this programme follow Stages 1 to 6 of the Cambridge Primary Curriculum, which continues to build on the foundations that are established in the Early Years Foundation Stage. Ongoing reviews ensure that each student’s progress and development are continuous and meet predetermined standards.

    We encourage students to think independently, use their initiative, and participate in a meaningful and active manner in the learning process. At the end of Grade 5 (Stage 6), students will prepare for the University of Cambridge Primary Checkpoint Examinations in English, Mathematics, and Science. The tests are marked in Cambridge to provide an international benchmark of learner performance. Learners receive a statement of achievement and a diagnostic feedback report. Feedback reports show how a learner has performed in relation to the curriculum, their learning group, the whole school, and against all learners who have taken tests in that series around the world.

    The core academic curriculum includes instruction in English, Mathematics, Science, Global Perspective (Social Studies & EVM) and Digital Learning. Kannada is taught to all students and caters for native and non-native speakers. In addition, the school offers French and Hindi. The overall educational experience is enhanced and supplemented with an enriched visual and performing arts programme that embraces both western and local culture as well as an excellent school sports provision.

    The Finnish Education Model

    Freedom to choose, express, explore and learn. These are the wings of the learning flight in PNCCS. Our pedagogy adaption to the world’s best education system is to prepare today’s learners for Gen-Z. As a resource school, it is our endeavour in providing an enriching learning environment for our Cognitions to learn.
    The Finnish Adaptation in our school is characterized by the understanding that a student who is happy in the classroom and is comfortable since he/she is free to learn at his own pace, will learn the knowledge that is needed. Finnish teachers have genuine pedagogical freedom, as well as autonomy to teach. Therefore, they are motivated in their day to day activities. Teachers spend approximately 400 + hours of training during a year. This includes a wide range of skills such as Subject Matter Expertise, Classroom Management, Equipping Students with 21st Century Skills, and many more.
    The Facilitators have at their disposal a range of ready-to-use materials in their classrooms. The learning labs and Research Points empower the teacher to promote experiential and active learning.
    Thus a plant rooted in good soil and environment bears fruits that sustains itself and the community. And so is every Cognition.
    Progressing in this pathway, two initiatives that shape our children’s mind is “Speakathon” and “Thoughtcast”. These learning platforms help the learners to reflect on various topics which impact them, the environment, and the community at large. Learners express, debate, and pen down their thoughts. Thus transforming them into confident individuals who can voice their opinions, accept or reflect on critical reviews and collaborate to find solutions.
    The pedagogy promotes mastery of learning through thinking routines. It is a synonym for the layers of soil. Each is different in texture and composition but all are important.