Extreme-Scale, Nano & Fundamental Engineering
/Learn at the frontier
Applied Mathematics Intern
A modelling question from another division formulated mathematically and checked for well-posedness.
Engagement
Internship
Structured, hands-on mentorship for a fixed term. This internship is on site at Kolkata, with hybrid days available by prior arrangement. It is not a remote position.
Scope of role
Contribute to live projects. Shadow senior practitioners. Build a portfolio that matters.
Please note this is an unpaid internship — the offer is real work, mentorship and experience at the frontier, not a stipend.
Research classification
Proving results and building the mathematical structures other work is expressed in. Theorems and proofs, well-posedness and convergence results, formal statements of method.
Theoretical research. Mathematical and theoretical work. Derivation and internal consistency are the standard here; experimental confirmation is not currently available at this scale.
Scale range 10^-100 m to 10^100 m
A numerical result without a convergence statement is an opinion with decimal places. This division reports the order of a scheme, the conditions under which it is stable, and the regime where its error estimate no longer holds. Where a method is used outside the range it was analysed for, that is stated rather than hoped over. Scientific integrity is a condition of every role in this department. Assumptions are stated separately from conclusions. Uncertainty is reported. Negative and inconclusive results are written up, not discarded. Speculative work is labelled speculative, including when that makes it less impressive. Fabrication, falsification, and presenting a simulation as a measurement end an engagement here.
Scale bands are a research classification, not a claim of experimental reach. Most of this span cannot be probed by any apparatus that exists: nothing below about 10^-19 m has been measured directly, and anything at 10^26 m or beyond is inferred from observation rather than engineered. Every opportunity states the kind of work it actually is.
Disciplines
01 — The role
Why this role exists at EduRankAI
Department of Extreme-Scale, Nano & Fundamental Engineering, Division D09: Mathematics & Computational Foundations. This division develops the mathematics other divisions use. It builds numerical methods and proves what they converge to, designs optimisation algorithms, and supports modelling across every scale band the department declares. It is a service division and a research division at once, and it is mandatory to the department because a method nobody has analysed is a method nobody should trust. This position: A modelling question from another division formulated mathematically and checked for well-posedness. Scale range for this work: 10^-100 m to 10^100 m. Research classification: Mathematical. Proving results and building the mathematical structures other work is expressed in. Evidential standing: Theoretical research. Mathematical and theoretical work. Derivation and internal consistency are the standard here; experimental confirmation is not currently available at this scale. A numerical result without a convergence statement is an opinion with decimal places. This division reports the order of a scheme, the conditions under which it is stable, and the regime where its error estimate no longer holds. Where a method is used outside the range it was analysed for, that is stated rather than hoped over. Scale bands are a research classification, not a claim of experimental reach. Most of this span cannot be probed by any apparatus that exists: nothing below about 10^-19 m has been measured directly, and anything at 10^26 m or beyond is inferred from observation rather than engineered. Every opportunity states the kind of work it actually is. Level 1 (Research and Engineering Intern). One well-defined problem, delivered with a reproducible artefact and a short written report.
02 — The work
What you will own
- 01 Develop the mathematical foundations other divisions build their models on.
- 02 Create numerical methods and establish what they converge to and under what conditions.
- 03 Analyse convergence, stability and conditioning, and report the regime where the analysis holds.
- 04 Develop optimisation algorithms and characterise where they fail as well as where they succeed.
- 05 Support modelling across every division, including saying when a proposed model is ill-posed.
- 06 Review other divisions' numerical work and say plainly when a result is not supported by its method.
- 07 Work on one clearly scoped problem for the duration, with a written result at the end rather than a status update.
- 08 Meet a named supervisor weekly and come to that meeting with what did not work as well as what did.
03 — The expertise
What we look for
04 — The bar
Who thrives here
- → Education: Final years of an undergraduate degree, or a postgraduate student, in a relevant discipline.
- → Experience: No professional experience required. Must be able to show at least one completed project with code or a written result somebody else can read.
- → Scope of the role: One well-defined problem, delivered with a reproducible artefact and a short written report.
- → Must have: Can state and use the definition of convergence for a numerical scheme, not just cite the order. Also: Linear algebra to the level of conditioning, decompositions and why an ill-conditioned problem is not a bug in the solver.
- → Portfolio: at least one piece of work — code, a written result, a thesis chapter, a preprint — that somebody outside your institution can read and assess. It does not need to be published.
- → Available for a full-time internship for the stated duration, working the hours set out under Terms of Engagement.
Terms of Engagement
How this internship is structured
6 days a week, about 40 hours of total engagement — 5 hours a day of project work and departmental responsibilities, plus 1 hour 40 minutes a day of holistic well-being and personal development.
Type
Full-Time
Working days
6 per week
Rest days
1 per week
Total engagement
~40 hrs/week
Project work
5h per day
Well-being
1h 40m per day
Duration
12 weeks
Project work and departmental responsibilities and holistic well-being and personal development together make up the total engagement above — the total is not all task output. Well-being time covers physical fitness, mindfulness, reading, reflective learning, leadership development and community engagement. About 480 hours of total engagement over 12 weeks — 360 hours of project work and 120 hours of well-being and personal development.
Measured by
Weekly mentor review against a published rubric, plus the completion of the recorded hours. Working materially over the commitment is treated the same as working under it.
Where this stands legally
Offered under the applicable AICTE internship framework, where one academic credit corresponds to a minimum of 45 hours of work — which is why these hours are counted and certified. The engagement sits well inside the 9-hour day and 48-hour week ceiling of the applicable state Shops and Establishments Act, and the seventh day is a full rest day.
At a minimum of 45 hours of work per academic credit, this engagement is equivalent to roughly 10.7 credits. Your institution decides what it awards; EduRankAI records the hours and the work.
The full per-level model is published at Working Hours by Level.
05 — Hiring process
What to expect after you apply
- 01
Application review
Every application is read personally within five business days. We respond either way.
- 02
Take-home or live exercise
Role-specific. Time-boxed. Real problems we are actually working on, not invented puzzles.
- 03
Conversations
Deep technical and values conversations with the team you would join. No trick questions. No panel ambushes.
- 04
Offer or honest no
If yes: digital offer letter, signed in-portal, transparent terms. If no: written feedback if you want it.
The standard
What you deliver, and how it is judged
Deliverables
- Methods with a written convergence and stability result, and an empirical verification of it.
- Reference implementations other divisions can adopt without reimplementing.
- Reviews of numerical work carried out elsewhere in the department.
- Statements of the regime of validity, attached to the method rather than to a memory.
Evaluation criteria
- Whether the convergence claim is proved or measured, and stated as which.
- Whether the method's failure modes are characterised.
- Adoption: does another division actually use it.
- Willingness to say a colleague's result is not supported by its method.
Preferred, not required
Nothing in this list is a bar to applying.
Tools you would work in
Reports to: Mathematics & Computational Foundations Lead
Works with: D01, D02, D08, D10, D11, D15
Before you start
What we will collect. What it costs. What we will not do with it.
We will collect
- Name, email, phone — Account + application updates. No marketing.
- Resume / portfolio link — Human review of your work.
- Date + place of birth — Identity verification only.
- Your written responses — Selection rubric. Read by humans.
- Government ID (later) — Anti-fraud at offer / interview stage. Not at signup.
We will never
- Sell your data
- Share with third-party recruiters
- Use for advertising
- Train models on it
- Send marketing email
Our situation
EduRankAI is a small, independent organization building long-term capabilities in educational intelligence, advanced AI systems, and research infrastructure. We take no advertiser money, no donations with strings attached, and no investor pressure on hiring decisions. Applying is free, and every application is read by a human — recruitment, technical, academic and leadership teams. It buys us the right to be honest.
Ready to apply?
We read every application personally. If you are the right person for this role — regardless of pedigree, background, or where you are based — you will hear back from us within five business days.
Apply through this page. You will be asked for your education, your experience, and links to work we can actually read — a repository, a write-up, a thesis chapter, a preprint. Send the piece of work you would defend, not the one with the best title. If a result in it turned out to be wrong, say so; we would rather read that than not know. Every application is read by a person. We assess applications on evidence of the work. We do not filter on institution, on age, on gender, on caste, on religion, on disability, or on where you are from. If any part of this process is inaccessible to you, tell us and we will change it for you.
Other roles in Extreme-Scale, Nano & Fundamental Engineering
Explore related openings
Intern Internship